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Doctoral Thesis

Bistable perception of the Necker cubeIn the context of cognition & personality

Author(s): Wernery, Jannis

Publication Date: 2013

Permanent Link: https://doi.org/10.3929/ethz-a-009900582

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ETH Library

DISS. ETH NO. 21214

Bistable Perception ofthe Necker Cube

in the Contextof Cognition & Personality

A dissertation submitted to ETH ZURICHfor the degree of Doctor of Sciences presented by

Jannis Wernery

Dipl. Phys., ETH Zurich,born 12 July 1984, from Germany,

accepted on the recommendation of

Prof. Gerd FolkersPD Dr. Harald Atmanspacher

Prof. Reinhard Nesper

2013

To the Precious Ones & all beings.

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Abstract

The Necker cube is a bistable stimulus with a very long research history,spanning more than a century. Very early, its temporal dynamics and itsstimulus properties were examined. It was found that the number of re-versals within a certain time interval were reproducible to a high accuracywithin one observer but could vary significantly between different observ-ers. Already early in the first half of the 20th century, attempts at linkingbistable perception of the Necker cube with personality were made. Eventhough much progress in the description of the reversal dynamics has beenmade since, a comprehensive understanding of inter-individual differences inbistable perception in terms personality traits and cognitive processes is stilllacking today.Two studies on neutral and voluntarily controlled perception of the Neckercube were conducted. The temporal dynamics and its dependence on stim-ulus parameters as well as its relation to personality traits, mindfulness,temporal processing, working memory, general reaction times, attention andperception of an acoustic bistable stimulus were explored.New results on initial adaptation, goodness of fit and stationarity with re-spect to cube size were found. A quantitative analysis of a perceptual biaseffect was given in terms of dwell time distributions. Individual differences involuntary control over perception of the Necker cube were found to be relatedto personality traits and mindfulness. Several personality traits not relatedto bistable perception and some related to its neutral perception were identi-fied. Furthermore, evidence for the presence of two mechanisms of temporalprocessing, namely processing speed and temporal integration, in bistableperception was discovered. Similarities and differences between perceptionof the Necker cube and a reversible word stimulus were reported. Finally,individual differences in working memory capacity seem likely not to relateto bistable perception.In conclusion, an improved description of the temporal dynamics of bistableperception and some low-level modulating factors was given. Furthermore,inter-individual differences in the dwell time distribution were shown to bereflected in several personality traits and cognitive processes, in particulartime processing. This demonstrates that variations in bistable perception be-tween individuals can indeed be better understood and classified by linkingthem to other characteristics in cognition and personality.

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Résumé

Le cube de Necker est un stimulus bistable avec une longue histoire de re-cherche s’étalant plus qu’un ciècle. Très tôt, sa dynamique temporelle et sescharactéristiques de stimulus étaient examinées. On a trouvé que le nombredes inversions en un intervalle de temps défini était reproductible avec grandeprécision au sein d’un individu mais qu’il pouvait varier considérablemententre des individus. Déjà tôt dans la première moitié du vientième siècle, ona essayé d’associer la perception bistable du cube de Necker avec les traitsde personnalité. Bien que depuis on ait fait beaucoup de progrès dans ladescription de la dynamique temporelle, une compréhension amplective desdifférences entre individus dans la perception bistable en matière de traits depersonnalité et de processus cognitifs s’en faut jusqu’à ce jour.Deux études de la perception neutre et controllée délibérément du cube deNecker etaient conduites. La dynamique temporelle, sa dépendance aux pa-ramètres du stimulus et sa relation aux traits de personnalité, à la pleineconscience, à la transformation temporelle, à la mémoire de travail, au tempsde réaction, à l’attention et à la perception d’un stimulus bistable acoustiqueétaient explorés.Nouveaux résultats sur l’adaptation initiale, sur la qualité de l’ajustementet sur la stationnarité relatif à la taille du cube etaient trouvés. Une analysequantitative d’un effet biais perceptif etait donnée en matiére de la distribu-tion des durées de phase. Differences entre individus de contrôle délibéré surla perception du cube de Necker étaient trouvées de correspondre àux traitsde personnalité et à la pleine conscience. Plusieurs traits de personnalitésne correspondant pas à la perception bistable et quelques correspondant àla perception neutre étaient identifiés. Par ailleurs, preuve à la présence dedeux mécanismes de transformation temporelle dans la perception bistable,à savoir la vitesse de traitement et l’integration temporelle, était découverte.Ressemblances et différences entre la perception du cube de Necker et d’unstimulus de mot réversible étaient reportées. Finalement, differences indivi-duelles de la mémoire de travail font l’effet de ne pas être attachées à laperception bistable.En somme, une description améliorée de la dynamique temporelle de la per-ception bistable et de quelque facteurs modulants de niveau bas était donnée.De plus, on a demonstré que les différences entre individus de durées de phasese reflètent dans les traits de personnalité et dans les processus cognitifs, enparticulier dans la transformation temporelle. Ça démontre que les variations

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entre individus dans la perception bistable en effet peuvent être conçues etclassifiées mieux si elles sont associées à des autres traits charactéristiquescognitifs et de personnalité.

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Acknowledgement

I am indebted to many who supported me during the course of my PhD, notall of whom I can list here.I would like to express my particular gratefulness to my supervisors at Col-legium Helveticum Gerd Folkers, Victor Candia, Harald Atmanspacher andReinhold Nesper who helped me increase my knowledge and skills and closelysupported my research. I would like to thank Jürgen Kornmeier and MarcWittmann of IGPP, who shared their insights and their expertise providinggreat help in designing and analysing the presented studies.I thank all my colleagues at Collegium Helveticum for their advice and com-pany.My gratefulness goes to everybody who has and does constitute, supportand shape Collegium Helveticum to be a place of broad, innovative and con-structive thinking. They have provided me with a unique environment thathas encouraged a broadening of perspective and understanding of science andculture which I appreciate and value very much.I want to thank my family, my friends and those close to me for their support,understanding and encouragement, my teachers for their guidance.

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Contents

1 Introduction 101.1 Why Look at Bistability? . . . . . . . . . . . . . . . . . . . . . 101.2 Classification of Multistability . . . . . . . . . . . . . . . . . . 11

1.2.1 Ambiguous Figures . . . . . . . . . . . . . . . . . . . . 121.2.2 Binocular Rivalry . . . . . . . . . . . . . . . . . . . . . 161.2.3 Monocular Rivalry . . . . . . . . . . . . . . . . . . . . 171.2.4 Structure-from-Motion . . . . . . . . . . . . . . . . . . 181.2.5 Apparent Motion Quartets . . . . . . . . . . . . . . . . 191.2.6 Motion-induced Blindness . . . . . . . . . . . . . . . . 191.2.7 Non-visual Multistability . . . . . . . . . . . . . . . . . 19

1.3 The Psychophysics of Visual Bistability . . . . . . . . . . . . . 201.3.1 Measuring Bistable Perception . . . . . . . . . . . . . . 211.3.2 Viewing Parameters for the Necker Cube . . . . . . . . 221.3.3 Reproducibility of Dwell Times . . . . . . . . . . . . . 24

1.4 The Physiology of Visual Bistability . . . . . . . . . . . . . . . 251.4.1 Eye Movements & Blinks . . . . . . . . . . . . . . . . . 251.4.2 Neuro-Imaging . . . . . . . . . . . . . . . . . . . . . . 261.4.3 Lesions . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

1.5 Genetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301.6 The Psychology of Visual Bistability . . . . . . . . . . . . . . 311.7 Similarities and Differences . . . . . . . . . . . . . . . . . . . . 33

2 Models of Bistable Perception 352.1 Up or Down? . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.2 Oscillators or Attractors? . . . . . . . . . . . . . . . . . . . . . 382.3 Further Approaches . . . . . . . . . . . . . . . . . . . . . . . . 40

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3 Two Studies on Perception of the Necker Cube 413.1 NC-dist: Temporal Dynamics and Low-level Features in Bistable

Perception of the Necker Cube . . . . . . . . . . . . . . . . . . 423.1.1 Research Questions of the NC-dist Study . . . . . . . . 42

3.2 NC-pers: Personality, cognitive abilities, temporal processingand the Necker cube . . . . . . . . . . . . . . . . . . . . . . . 433.2.1 Research Questions of the NC-pers Study . . . . . . . . 43

3.3 Measuring Bistable Perception . . . . . . . . . . . . . . . . . . 443.4 Analysis of Dwell Time Data . . . . . . . . . . . . . . . . . . . 46

4 Temporal Dynamics 484.1 Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2 Reproducibility . . . . . . . . . . . . . . . . . . . . . . . . . . 504.3 Dwell Times and Their Distribution . . . . . . . . . . . . . . . 514.4 Fitting Dwell Time Distributions . . . . . . . . . . . . . . . . 53

4.4.1 Kernel Density Estimation . . . . . . . . . . . . . . . . 534.4.2 Least Squares Method . . . . . . . . . . . . . . . . . . 534.4.3 Maximum Likelihood Estimation . . . . . . . . . . . . 53

4.5 Probability Density Functions . . . . . . . . . . . . . . . . . . 544.5.1 The Gamma Distribution . . . . . . . . . . . . . . . . 544.5.2 The Lognormal Distribution . . . . . . . . . . . . . . . 554.5.3 Other PDF’s . . . . . . . . . . . . . . . . . . . . . . . 56

4.6 Fit Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.6.1 Measures of Goodness of Fit . . . . . . . . . . . . . . . 574.6.2 Comparing Fit Quality . . . . . . . . . . . . . . . . . . 594.6.3 Fit residuals . . . . . . . . . . . . . . . . . . . . . . . . 64

5 Stimulus Properties 675.1 Size of the Necker Cube . . . . . . . . . . . . . . . . . . . . . 67

5.1.1 Reports on the Effect of Cube Size . . . . . . . . . . . 675.1.2 Comparing Five Cube Sizes . . . . . . . . . . . . . . . 685.1.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.1.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.2 Hysteresis Effect . . . . . . . . . . . . . . . . . . . . . . . . . 705.2.1 Hysteresis in (Psycho-)Physics . . . . . . . . . . . . . . 705.2.2 Exploring Hysteresis of the Necker Cube . . . . . . . . 715.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 72

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6 Bias Effect 766.1 Qualitative Reports . . . . . . . . . . . . . . . . . . . . . . . . 766.2 Quantifying the Perceptual Bias . . . . . . . . . . . . . . . . . 776.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 786.4 Seeing the Cube From Above . . . . . . . . . . . . . . . . . . 78

7 Voluntary Influence 827.1 Volition in Bistability and Psychology . . . . . . . . . . . . . . 827.2 Measuring Volition . . . . . . . . . . . . . . . . . . . . . . . . 857.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

8 Perception & Personality 978.1 Studies Linking Bistability and Personality . . . . . . . . . . . 978.2 Operationalisation of Personality Traits . . . . . . . . . . . . . 998.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 998.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

9 Mindfulness & Perception 1049.1 Mindfulness in Science and Perception . . . . . . . . . . . . . 1049.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1069.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1079.4 Mindfulness Relates to Perceptual Volition . . . . . . . . . . . 108

10 Temporal Processing 11210.1 Time Perception, Reaction and Attention . . . . . . . . . . . . 11210.2 Exploring Links in Time Scales . . . . . . . . . . . . . . . . . 11310.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11610.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

11 (Un-)Related Processes 12111.1 The Verbal Transformation Effect . . . . . . . . . . . . . . . . 121

11.1.1 Acoustic Multistable Perception . . . . . . . . . . . . . 12111.1.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 12211.1.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 12311.1.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 125

11.2 Working Memory . . . . . . . . . . . . . . . . . . . . . . . . . 12711.2.1 “Memory” in Bistable Perception . . . . . . . . . . . . 127

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11.2.2 Working Memory in Bistability? . . . . . . . . . . . . . 12711.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 12911.2.4 Working Memory Does Not Work Bistability . . . . . . 129

12 Bistability within 3s? 130

13 Summary & Conclusion 135

Bibliography 137

Curriculum Vitae 152

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1. Introduction

1.1 Why Look at Bistability?. . . or hear, feel or smell it, for that matter?

Bistable perception seems to have fascinated humans for a long time as nu-merous occurrences of ambiguous ornaments or pieces of art illustrate. Manychurches, for example, show ornaments like the one on the title page, whichcan found on an interior wall of the church of the Swiss monastry KlosterKappel.1 Its white areas can be seen as either the top faces of otherwiseblack cubes or as the bottom face of such cubes. If the attendant of the masskept looking at it for a while he or she would experience changes from one tothe other and back. Only lately, in the historic context of its existence, hasbistable perception become the object of extensive, rigorous scientific study.There, it provides a unique opportunity.The peculiarity of many multistable stimuli is that over time they elicit sev-eral distinct conscious impressions, or percepts, in the observer, while theactual stimulus remains completely unchanged. Anyone who is interested inthe understanding of consciousness should be fascinated by this immediately– and in fact, philosophers are, a prominent example being Ludwig Wittgen-stein. Studying multistable perception, one marvels at the fact that there aretwo or more different mental states, which the observer can vividly experienceand which are elicited by the same external stimulus. Hence, the consciousinner experience, the qualia, is clearly and distinctly modulated over timewhile externally nothing seems to change. What makes this even more in-teresting for empirically inclined researcher, is that it is quantifiable. Thetimes between perceptual changes can be measured via self-report. Thus,

1I am indebted to Richard Dähler for taking me on a cycling tour to this beautifulplace on a very hot summer day in 2012.

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multistable perception provides a system for studying consciousness in per-ception quantitatively. And it can not only be done in the visual modalitybut also in the auditory, haptic or olfactory one.Quantification brings two other aspects of multistable perception fully tolight. First, it shows the stochastic nature of perceptual reversal timing.This means that perceptual changes from one percept to the other occurrandomly and not periodically. Second, the measures describing the timesbetween perceptual changes are characterised by strong inter-individual vari-ation. In other words, for some observers the perception changes much morefrequently than for others.Goal of this thesis was to gain a better understanding of these inter-individualdifferences. The phenomenon was approached empirically with two psycho-physical studies on bistable perception of the Necker cube, which is shown inFig. 1.1a. The first one aimed at an improved understanding of how the dwelltimes, i.e. the times between perceptual reversals, can be described. This wasnecessary in order to build a solid foundation before broadening the focusof the research. The goal of the second study was to find relations to otherprocesses and traits of a person in order to integrate the inter-individual dif-ferences of bistable perception into a larger conceptual framework.The results of these two studies will be presented here. The current chapterprovides an introduction and overview over multi- and bistability. Chapter 2will review some models for visual bistability. In Chapters 3 to 11 the resultsof the two studies on bistable perception of the Necker cube will be presen-ted and discussed. Finally, some theoretical considerations on bistabilityand time perception based on common empirical findings will be stated inChapter 12.

1.2 Classification of MultistabilityA multistable stimulus is characterised by the fact that there are at leasttwo different interpretations or percepts of this stimulus. None of these isabsolutely stable, but rather will perception change spontaneously betweenthe different percepts. These perceptual changes are subjective experiencesand the timing of their occurrence cannot be exactly predicted. Usually thereare considerable inter-individual differences in the temporal dynamics of theperceptual changes. In the following, the term dwell time will be used torefer to a variable describing the time between one perceptual reversal and

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the next. I.e. dwell times indicate how long one percept is seen at a time,before perception changes to the other percept. A few other terms are usedsynonymously to dwell times in the literature, e.g. stability durations, re-versal times, switching times, perceptual durations.There are several different categories of multistable stimuli. Many multistablevisual stimuli are in fact bistable, i.e. there are only two possible percepts, atleast approximately. In the following, an overview over the most importantclasses of visual bistable stimuli will be given. Also, a few examples of bi-and multistable stimuli in other sensual modalities will be presented.It should be noted that there are different nomenclatures for the classific-ation of multistable stimuli. Thus, terms might vary from publication topublication and alternative expressions are given in the following whenevercommon.

1.2.1 Ambiguous FiguresMany different ambiguous figures gained public attention in the last twocenturies. Some of those have been studied extensively in scientific research.Ambiguous figures are one subclass of multistable visual stimuli character-ised by their ability to elicit two or more mutually exclusive percepts in anobserver while the figure itself stays constant. Bistable ambiguous figuresare a special case of ambiguous figures, having only two rivaling percepts. Incontrast to binocular rivalry, both eyes view the same stimulus. This type ofbistable stimulus is also called perceptual rivalry sometimes.Note, that multi- and bistability is contingent on two factors. The first isknowledge of reversibility. Rock and Mitchener (1992) showed for severalcommon bistable figures that reversals are largely absent if the observer isunaware of one of the possible interpretations of the stimulus. The secondone, which concerns in particular bistable perception, is the neglect of pos-sible but infrequent or improbable perceptual alternatives. A perspectivereversing figure, like the Necker cube or the Mach book, for example, cannot only be seen in its two three-dimensional perspectives, but can also beperceived as an abstract two-dimensional drawing. Most studies do not takethese considerations into account in order to explore certain aspects of thestimuli in isolation, namely the reversals behaviour between the most dom-inant interpretations of the figure. This approach will be followed here, too.Some examples of different ambiguous figures will be presented in the follow-ing.

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Perspective Reversing Figures

Perspective reversing figures are characterised by the ambiguity of a two-dimensional drawing with respect to its three-dimensional interpretation.These stimuli are usually symmetric and low in semantic content. Also,both interpretations are rather similar compared to stimuli with strong dif-ferences between the percepts, like in the old woman/young woman figure.A famous and probably the most extensively researched example of a per-spective reversing figure is the Necker cube (Fig. 1.1a). The stimulus goesback to observations of Necker (1832) on drawings of minerals found in theSwiss alps.2 The cube can be either seen from above with the lower rightface in the front or from below with the upper left face in the front. Thisstimulus was used in the two studies on bistable perception described in thisthesis.The Schröder staircase illustrated in Fig. 1.1b was mentioned by Schröder(1858) and can be seen either as a staircase going up from right to left oras an inversed staircase. Later this staircase found its way into the works ofM. C. Escher.The physicist Ernst Mach described a reversible figure in the 19th centuryby asking his readers to imagine a folded business card placed on a tablewith the central edge pointing towards the observer (Mach, 1885/1902). Acorresponding drawing, known as the Mach book can be perceived as eitherfacing the observer or as pointing away from them (Fig. 1.1c).All three of these figures have been used in many studies on bistable percep-tion.

Figure-Ground Reversing Stimuli

Figure-ground perception is a perceptual grouping, discerning between thefigure and the background. This is also an important process in Gestaltpsychology.A very well-known figure-ground stimulus is the vase/faces figure. Therehave been many different drawings of that kind in the last few centuries. Thefigure was brought to great popularity, though, by the Danish psychologistEdgar Rubin. It has since been used in many studies on bistability. A typicaldrawing is shown in Fig. 1.1d.

2Necker actually did not draw a cube in his seminal paper but a parallelepiped. Onlylater was the form changed to a cube. So the original stimulus could be called the “Neckerrhomboid”.

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(a) Necker cube

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(b) Schröder staircase (c) Mach book

(d) Vase/faces (e) Canadian flag

(f) Batman & the Joker

Figure 1.1: Different ambiguous figures of the categories perspective reversal and figure-ground reversal: (a) the Necker cube (own drawing), (b) the Schröder staircase (repro-duced from Strüber and Stadler (1999)), (c) Mach book (own drawing), (d) vase/faces(drawing by Bryan Derksen), (e) Canadian flag, (f) Batman & the Joker (paper cut by“eyez2theskiez” on flickr, 2007).

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(a) Duck/rabbit (b) Wife/mother in law

Figure 1.2: Different ambiguous figures of the content reversal category: (a) Duck andrabbit (published in “Fliegende Blätter”, October 23, 1892, München), (b) wife/mother inlaw (advertisement by the Anchor Buggy company, 1890).

Interestingly, also parts of the Canadian flag feature some figure-groundambiguity. The upper boundaries of the maple leave can be seen as theprofiles of two people arguing, clashing at their foreheads, the lower part ofthe maple leave outlining their shoulders (Fig. 1.1e).A hero of popular culture and his enemy are pictured in the Batman & theJoker paper cut presented in Fig. 1.1f.Also, the artist M. C. Escher made use of figure-ground perception in afascinating way in several of his drawings.

Content Reversal Stimuli

In the classification employed here, content reversal stimuli shall denote fig-ures, for which the reversals are due to its content and not due to perspectiveor figure-ground.A famous representative of this class is the duck/rabbit figure first pub-lished in the German humor magazine, Fliegende Blätter3 (Fig. 1.2a). Itfeatures either a duck with the beak facing to the upper left or a rabbit withits mouth on the right hand side of the image. Later, the American psycho-

3Fliegende Blätter, p. 17, October 23, 1892, München

15

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Figure 1.3: Typical binocular rivalry stimulus (house/face) reproduced from Brascampet al. (2005). The left image is presented to the left eye and the right one to the right eye.

logist Joseph Jastrow published an adapted version (Jastrow, 1899). AlsoLudwig Wittgenstein incorporated an adapted version in his PhilosophischeUntersuchungen (Wittgenstein, 1953/2006).Another well known stimulus is the old woman/young woman figure, alsoknown as wife/mother in law. It can be seen as either an old woman facingleft, with a huge nose and no neck or as a young woman with a ribbon aroundher neck, her gaze pointed away from the observer. A popular version, usedas an advertisement by the Anchor Buggy Company in 1890, is shown inFig. 1.2b. Boring (1930) introduced this stimulus into scientific research.

1.2.2 Binocular RivalryA second, very important category of bistable perception is binocular rivalry.In this paradigm, different images are presented at the same retinal locationsof each eye, leading not to a merged percept of both images but rather to analternation between them. A typical stimulus is displayed in Fig. 1.3. Forlarge stimuli also so-called piece-meal rivalry can occur, namely fluctuatingpatchworks consisting of intermingled portions of both eyes’ views Blake andTong (2008).The phenomenon of binocular rivalry was already reported in the 16th cen-tury by the polymath Giambattista della Porta (Wade, 1996), who tried toread two books simultaneously, one with each eye, in order to increase hisproductivity, but realised that it was impossible.Today one can find a huge amount of research papers on the subjects. Forreviews, the following current articles are recommended: Blake and Tong(2008), Maier et al. (2012) and Kang and Blake (2011).

16

(a) Two overlaid gratings

organisation such as Marroquin patterns (Wilson, Krupa, & Wilkin-son, 2000), monocular rivalry, and binocular rivalry.

There are at least three general similarities between monocularrivalry and binocular rivalry that suggest commonality. The basicphenomenology is similar in that both involve periods of alternat-ing dominance. Both forms of rivalry become more vigorous asstimuli are made more different in colour (e.g., Wade, 1975), orin orientation and spatial frequency (e.g., Atkinson, Fiorentini,Campbell, & Maffei, 1973; Campbell, Gilinsky, Howell, Riggs, &Atkinson, 1973; O’Shea, 1998). The two forms of rivalry can influ-ence each other, tending to synchronise their alternations in adja-cent regions of the visual field (Andrews & Purves, 1997; Pearson &Clifford, 2005).

Although monocular and binocular rivalry are similar in thesethree respects, this is by no means an exhaustive list of possiblecomparisons. Here we test whether monocular rivalry shares threeother hallmarks of binocular rivalry. First, binocular rivalry can oc-cur between any two images, providing they are sufficiently differ-ent. For example, Porta (1593, cited in Wade, 1996) observedrivalry between two different pages of text. Wheatstone (1838) ob-served rivalry between two different alphabetic letters. Galton(1907) observed rivalry between pictures of different faces. Yetmonocular rivalry has always been shown between simple repeti-tive stimuli such as gratings, leading some to suppose that suchstimuli are necessary for monocular rivalry (e.g., Furchner & Gins-burg, 1978; Georgeson, 1984; Georgeson & Phillips, 1980; Maieret al., 2005). In Experiments 1 and 2, we show that monocular riv-alry occurs between complex pictures of faces and houses. Wedemonstrate this in Fig. 1.

Second, binocular rivalry has a characteristic distribution ofdominance times, a gamma distribution, and the duration of oneepisode of dominance cannot be predicted by any of the preceding

ones (e.g., Fox & Herrmann, 1967; Levelt, 1967). Yet the distribu-tion and predictability of episodes of monocular rivalry dominanceare unknown. In Experiment 3, we show that the temporal periodsof monocular rivalry are similar to those of binocular rivalry: gam-ma distributed and stochastic.

Third, binocular rivalry suppression is accompanied by a char-acteristic loss of visual sensitivity. When a stimulus is suppressedduring binocular rivalry and becomes invisible, stimuli presentedto the same retinal region are also invisible, provided the newstimuli are not so abrupt or so bright as to break suppression(e.g., Fox & McIntyre, 1967; Nguyen, Freeman, & Alais, 2003; Nor-man, Norman, & Bilotta, 2000; Wales & Fox, 1970). This is usuallydemonstrated by showing a loss of sensitivity during periods ofsuppression relative to periods of dominance, however it is un-known whether monocular rivalry also shows such suppression ef-fects. In Experiment 4, we show that monocular rivalry doesindeed produce threshold elevations during suppression, althoughthe effect is weaker than in binocular rivalry.

The experiments in this paper have been published individuallyin abstract form (O’Shea, Alais, & Parker, 2005, 2006; O’Shea and LaRooy, 2004). Here we draw these experiments together and givetheir details to provide evidence for similarities between monocu-lar rivalry and binocular rivalry.

2. Experiment 1

Maier et al. (2005) reviewed studies of monocular rivalry, andconcluded that monocular rivalry occurs only between simple,faint, repetitive images, such as low-contrast gratings. They ob-served, however, that alternations in clarity could occur betweencomplex images, such as the surface of a pond and a reflectionon it of a tree, although they did not measure rivalry with suchstimuli. Boutet and Chaudhuri (2001) optically superimposed twofaces that differed in orientation by 90!. They reported that thetwo faces alternated in clarity in a rivalry-like way, but they didnot measure rivalry conventionally. They forced observer’s choicesabout whether one or two faces was seen after brief stimulus pre-sentations of 1–3 s. Monocular rivalry, however, usually takes sev-eral seconds, or even tens of seconds, before oscillations becomeevident (e.g., Breese, 1899). We decided to measure monocular riv-alry with complex images in a conventional way, by showingobservers optically superimposed images for 1-min trials, and ask-ing them to track their perceptual alternations using key presses.We used images of a face and a house. Moreover, we explicitlycompared monocular rivalry with binocular rivalry for identicalstimuli over a range of stimulus sizes. We chose to manipulate sizebecause, at least with gratings, it has powerful effects on binocularrivalry (e.g., Blake, Fox, & Westendorf, 1974; Breese, 1899, 1909;O’Shea, Sims, & Govan, 1997).

3. Method

3.1. Observers

One female and three males volunteered for this experimentafter giving informed consent: HF (age 23), DLR (age 33), and RS(age 24) had some experience as observers; ROS (age 50) was ahighly trained observer. All had normal or corrected-to-normal vi-sion. All observers were right handed. HF and RS were naive as tothe purpose of the experiment.

3.2. Stimuli and apparatus

Stimuli were digitized photographs of ROS’s face and part of hishouse on plain backgrounds, similar to that shown in Fig. 1 except

Fig. 1. Illustration of one of the monocular-rivalry stimuli from Experiment 2: a redface and a green house. To experience monocular rivalry stare approximately at thecentre of the image, say at the bridge of the face’s glasses. Be patient! Monocularrivalry takes a while to develop. But after a time, 10–30 s or so, you will noticefluctuations in the relative clarity of the two images. You may even see one of thetwo images become exclusively visible briefly, along with brief composites in whichdifferent parts of the images appear in different parts of the visual field. (Forinterpretation of the references to colour in this figure legend, the reader is referredto the web version of this article.)

672 R.P. O’Shea et al. / Vision Research 49 (2009) 671–681

(b) House/face

Figure 1.4: Two monocular rivalry stimuli: (a) Monocular rivalry stimulus created byAlexander Maier consisting of two superimposed sine wave gratings. (b) Monocular rivalrystimulus reproduced from O’Shea et al. (2009). The authors gave the following viewinginstructions: “To experience monocular rivalry stare approximately at the centre of theimage, say at the bridge of the face’s glasses. Be patient! Monocular rivalry takes a whileto develop. But after a time, 10-30 or so, you will notice fluctuations in the relative clarityof the two images. You may even see one of the two images become exclusively visiblebriefly, along with brief composites in which different parts of the image appear in differentparts of the visual field.”

Leopold and Logothetis (1999) reviewed evidence that binocular rivalry isclosely related to other forms of multistable perception as it is not character-ised by specialised interocular inhibitory processes but rather by competitionbetween central stimulus representations. This finding is supported by strongsimilarities in the dwell time distributions of binocular rivalry and ambiguousfigures (Brascamp et al., 2005). But there are also considerable differencesto the perception of ambiguous figures, like the amount of voluntary controlthat can be exercised (Meng and Tong, 2004) or the role of eye movementsin instigating perceptual reversals (van Dam and van Ee, 2006).Similarities and differences between these two types of stimuli will be dis-cussed in more detail in Sec. 1.7.

1.2.3 Monocular RivalryIn monocular rivalry, two visual stimuli are superimposed and viewed withboth eyes. An example of such a stimulus is given in Fig. 1.4. O’Shea et al.(2009) compared monocular rivalry to binocular rivalry and found severalcommonalities. In particular, the authors reported gamma distributed dwell

17

(a) Structure-from-Motion

64 H. HOCK, J. KELSO, AND G. SCHONER

relationship is important because the two phenomena,though potentially separable, are functionally interdepen-dent influences on the stability of perceptual patterns. Thatis, although it is logically possible for hysteresis to be ob-served under conditions in which there is very high temporal.stability (no spontaneous change) and vice versa, we showin this article that hysteresis modifies the likelihood of spon-taneous perceptual change, and we further show that theoccurrence of spontaneous changes in organization modifiesthe magnitude of the hysteresis.

The initial objective of this study is therefore to establishthe interdependence of hysteresis and temporal stability andto do so in the context of a paradigm that minimizes someof the experimental limitations and interpretive problemsassociated with earlier studies of perceptual hysteresis. Onerequirement is the systematic variation of stimulus param-eters. Fisher (1967) reported hysteresis for a series of man-woman reversible figures, but it is difficult to assess theeffect of gradually changing the value of a parameter for thisexample because different aspects of the figures changehaphazardly from one figure to the next. Another, moredifficult problem concerns the distinction between percep-tual hysteresis and hysteresis in the subject's response; sub-jects continually responding to gradual changes in a param-eter may persevere in their response even after their percepthas changed. To limit this problem, Fender and Julesz(1967) and Williams et al. (1986) changed the values oftheir manipulated parameters very slowly. This solution,however, is too restrictive. It does not allow one to test theeffect of rate of parametric change on perceptual hysteresis(as we do in Experiment 6) because rate of change alsoinfluences susceptibility to hysteresis in responding. Stillanother problem is decision uncertainty. Are hysteresis ef-fects truly perceptual, or do subjects persist in an earlierdecision while the varying parameter passes through valuesfor which subjects are uncertain about what they are seeing?It is possible that the hysteresis effects obtained by Fenderand Julesz (1967) and Williams et al. (1986) involve deci-sional as well as perceptual components.

Our second objective is to demonstrate that experimentalparadigms assessing perceptual stability can provide evi-dence for a nonspecific perceptual influence of stimulusinformation. The specifying function of the stimulus hasbeen articulated through ecological (Gibson, 1966, 1979)and computational (Marr, 1982) perspectives. We provideevidence that visual information can influence perceptionby providing a nonspecifying context that shapes the oper-ation of intrinsic visual mechanisms without defining theirfinal product. Nonspecifying stimulus information mightfavor one percept in relation to another, but the informationin the stimulus is not sufficient to account for what isperceived. We show that when hysteresis is observed underconditions of high temporal stability, patterns are perceivedthat are not specified by the stimulus.

To provide evidence for a nonspecific influence of a ma-nipulated parameter, it is necessary to know that subjects'responses are not based on the detection of the parameteralone. For example, in the Williams et al. (1986) study ofhysteresis, the manipulated parameter was the proportion of

dots whose direction of motion was selected from a re-stricted range of possible directions; when subjects reportedthat they perceived coherent motion, it was in the directionof the mean of this restricted range of directions. Subjects'reports of coherent global motion in this experiment mightindeed have been due to a nonspecific influence of themanipulated parameter on intrinsic organizational pro-cesses; Williams et al. proposed intrinsic mechanisms in-volving nonlinear excitatory and inhibitory interactionsamong units that detect motion. If, however, their subjectswere reporting nothing more than the detection of the stron-gest directional component in the display (Williams et al.'sparametric manipulation varies the prominence of this com-ponent), the influence of the manipulated parameter wouldhave been specific rather than nonspecific. To demonstratethe nonspecific influence of the manipulated stimulus pa-rameter in our experiments, we use a paradigm for whichparameter values are not perceptually confusable with themotion patterns observed as values of the parameter arechanged.

We study hysteresis, bistability, and spontaneous changesin perceptual organization through the use of a classicalparadigm in which points of light are presented in corners ofan imaginary rectangle, and apparent motion is seen invertical or horizontal directions (Hoeth, 1968; Kruse, Sta-dler, & Wehner, 1986; Ramachandran & Anstis, 1985; vonSchiller, 1933). Two point lights are presented at a time, onepair from two of the diagonally opposite corners of therectangle and then after a brief delay a second pair from theother two diagonally opposite corners of the rectangle (fol-lowing Anstis & Ramachandran, 1987, we refer to thesestimuli as quartets, or motion quartets). Although the si-multaneous perception of horizontal and vertical motion is alogical possibility for these stimuli, only one or the othermotion direction is perceived. That is, parallel motions areseen either in opposite vertical or opposite horizontal direc-tions (see Figure 1). The exclusivity of vertical and hori-

ALTHOUGH IT IS LOGICALLY POSSIBLE,VERTICAL AND HORIZONTAL MOTION ARE

NEVER PERCEIVED AT THE SAME TIME

• D

EITHER VERTICAL MOTIONIS PERCEIVED

OR

HORIZONTAL MOTIONIS PERCEIVED

Figure I. Illustrative motion patterns for the motion quartetdisplays.

(b)

64 H. HOCK, J. KELSO, AND G. SCHONER

relationship is important because the two phenomena,though potentially separable, are functionally interdepen-dent influences on the stability of perceptual patterns. Thatis, although it is logically possible for hysteresis to be ob-served under conditions in which there is very high temporal.stability (no spontaneous change) and vice versa, we showin this article that hysteresis modifies the likelihood of spon-taneous perceptual change, and we further show that theoccurrence of spontaneous changes in organization modifiesthe magnitude of the hysteresis.

The initial objective of this study is therefore to establishthe interdependence of hysteresis and temporal stability andto do so in the context of a paradigm that minimizes someof the experimental limitations and interpretive problemsassociated with earlier studies of perceptual hysteresis. Onerequirement is the systematic variation of stimulus param-eters. Fisher (1967) reported hysteresis for a series of man-woman reversible figures, but it is difficult to assess theeffect of gradually changing the value of a parameter for thisexample because different aspects of the figures changehaphazardly from one figure to the next. Another, moredifficult problem concerns the distinction between percep-tual hysteresis and hysteresis in the subject's response; sub-jects continually responding to gradual changes in a param-eter may persevere in their response even after their percepthas changed. To limit this problem, Fender and Julesz(1967) and Williams et al. (1986) changed the values oftheir manipulated parameters very slowly. This solution,however, is too restrictive. It does not allow one to test theeffect of rate of parametric change on perceptual hysteresis(as we do in Experiment 6) because rate of change alsoinfluences susceptibility to hysteresis in responding. Stillanother problem is decision uncertainty. Are hysteresis ef-fects truly perceptual, or do subjects persist in an earlierdecision while the varying parameter passes through valuesfor which subjects are uncertain about what they are seeing?It is possible that the hysteresis effects obtained by Fenderand Julesz (1967) and Williams et al. (1986) involve deci-sional as well as perceptual components.

Our second objective is to demonstrate that experimentalparadigms assessing perceptual stability can provide evi-dence for a nonspecific perceptual influence of stimulusinformation. The specifying function of the stimulus hasbeen articulated through ecological (Gibson, 1966, 1979)and computational (Marr, 1982) perspectives. We provideevidence that visual information can influence perceptionby providing a nonspecifying context that shapes the oper-ation of intrinsic visual mechanisms without defining theirfinal product. Nonspecifying stimulus information mightfavor one percept in relation to another, but the informationin the stimulus is not sufficient to account for what isperceived. We show that when hysteresis is observed underconditions of high temporal stability, patterns are perceivedthat are not specified by the stimulus.

To provide evidence for a nonspecific influence of a ma-nipulated parameter, it is necessary to know that subjects'responses are not based on the detection of the parameteralone. For example, in the Williams et al. (1986) study ofhysteresis, the manipulated parameter was the proportion of

dots whose direction of motion was selected from a re-stricted range of possible directions; when subjects reportedthat they perceived coherent motion, it was in the directionof the mean of this restricted range of directions. Subjects'reports of coherent global motion in this experiment mightindeed have been due to a nonspecific influence of themanipulated parameter on intrinsic organizational pro-cesses; Williams et al. proposed intrinsic mechanisms in-volving nonlinear excitatory and inhibitory interactionsamong units that detect motion. If, however, their subjectswere reporting nothing more than the detection of the stron-gest directional component in the display (Williams et al.'sparametric manipulation varies the prominence of this com-ponent), the influence of the manipulated parameter wouldhave been specific rather than nonspecific. To demonstratethe nonspecific influence of the manipulated stimulus pa-rameter in our experiments, we use a paradigm for whichparameter values are not perceptually confusable with themotion patterns observed as values of the parameter arechanged.

We study hysteresis, bistability, and spontaneous changesin perceptual organization through the use of a classicalparadigm in which points of light are presented in corners ofan imaginary rectangle, and apparent motion is seen invertical or horizontal directions (Hoeth, 1968; Kruse, Sta-dler, & Wehner, 1986; Ramachandran & Anstis, 1985; vonSchiller, 1933). Two point lights are presented at a time, onepair from two of the diagonally opposite corners of therectangle and then after a brief delay a second pair from theother two diagonally opposite corners of the rectangle (fol-lowing Anstis & Ramachandran, 1987, we refer to thesestimuli as quartets, or motion quartets). Although the si-multaneous perception of horizontal and vertical motion is alogical possibility for these stimuli, only one or the othermotion direction is perceived. That is, parallel motions areseen either in opposite vertical or opposite horizontal direc-tions (see Figure 1). The exclusivity of vertical and hori-

ALTHOUGH IT IS LOGICALLY POSSIBLE,VERTICAL AND HORIZONTAL MOTION ARE

NEVER PERCEIVED AT THE SAME TIME

• D

EITHER VERTICAL MOTIONIS PERCEIVED

OR

HORIZONTAL MOTIONIS PERCEIVED

Figure I. Illustrative motion patterns for the motion quartetdisplays.

(c)

Figure 1.5: (a) Random dot pattern of a structure-from-motion rotating sphere, generatedwith PTB-3 in Matlab. Due to the position dependent velocity profile the dot patterncan be perceived as a sphere rotating either clockwise or counter-clockwise. (b) & (c)Horizontal and vertical apparent motion in an apparent motion quartet (reproduced fromHock et al. (1993)).

times – a finding which puts monocular rivalry conceptually close to ambigu-ous figure perception (cf. Chapter 4 and especially Sec. 4.6 for dwell timedistribution of the Necker cube). Monocular rivalry is also sometimes calledpattern rivalry.

1.2.4 Structure-from-MotionIn structure-from-motion a perception of depth is induced by retinal motion(Andersen and Bradley, 1998; Brouwer and van Ee, 2006). I.e. a moving two-dimensional stimulus evokes a strong impression of depth even in absence ofother depth cues. This phenomenon is also often referred to as the kineticdepth effect (Wallach and O’Connell, 1953). Commonly used stimuli are therotating cylinder and the rotating sphere. Here, a set of dots follows a con-stant velocity profile on an imaginary surface, giving the illusion of depth.4For the rotating sphere, for example, a number of dots move within a circularregion – half of them from left to right, the other half in the opposite direc-tion. Thus, the rotation direction is ambiguous and the perceived directionwill spontaneously alternate between clockwise and counter-clockwise. Anexample of a random dot pattern of such a stimulus is shown in Fig. 1.5a.

4The velocity profile on the display surface is, of course, not constant but follows a sineor cosine function.

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1.2.5 Apparent Motion QuartetsIn an apparent motion quartet, four light points are arranged in a square.First, two lights that are diagonally opposite light up for a short amount oftime. Then, after a brief delay, the other two diagonally opposite light pointslight up briefly. The cycle is repeated after another short delay. This leadsto perception of either a horizontal movement of the lights or a vertical one(Fig. 1.5b and 1.5c). Perception will spontaneously switch between these twopercepts (Hock et al., 1993; Kruse et al., 1986).

1.2.6 Motion-induced BlindnessMotion-induced blindness is another form of multistable perception, in whicha small, salient visual stimulus in front of moving background (the mask)seems to temporally disappear (Bonneh et al., 2001). An animation of theeffect can be found in Bonneh and Donner (2011). According to the samereview, the temporal dynamics of the reversals between target visible andtarget invisible are similar to that of ambiguous figure perception.

1.2.7 Non-visual MultistabilityNot only in the visual domain are there stimuli that allow for more thanone interpretation. There are also a number of acoustic multistable stimuli,as well as a haptic and olfactory one. Schwartz et al. (2012) give a reviewover multistability in different modalities. A comparison of bistability acrossmodalities is interesting as it might reveal modality-independent processingof bistable stimuli.

Acoustic

In the auditory domain there are several different types of bi- and multistablestimuli.Auditory streaming is characterised by an alternation of high and lowfrequency tones. A repeated ABA pattern of high (A) and low frequencytones (B) will be perceived as either one stream (ABA-ABA) or two streams(A-A-A and -B—B-) (Pressnitzer and Hupé, 2006).Using a repeated sequence of high and low frequency tones (A-B-A-B-. . . )with out-of-phase binaural presentation, Deutsch (1974) found that mostobservers perceived a single tone oscillating between the ears in synchrony

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with the pattern rhythm. For most observers the high tone was alwaysheard in one ear while it was possible under prolonged listening, that thispreference switched sponteously (Deutsch, 1975). This result indicates abinaural rivalry process similar to binocular rivalry in the visual modality.Furthermore, there is the verbal transformation effect, a change in theperceived word when the recording of a suitable word is played in a loop.It was first described by Warren and Gregory (1958) for words like say andstress. Radilova et al. (1990) reported some quantitative findings for differentwords and drew a comparison to bistable visual perception. In Sec. 11.1 adetailed account of the temporal dynamics of the verbal transformation effectand its relation to perception of the Necker cube will be given.

Haptic

Carter et al. (2008) described the tactile complement to the visual apparentmotion quartet (see above). In this setup, participants were stimulated on asmall square area of their finger tips. When stimuli periodically alternatedbetween the opposing endpoints of the two diagonals of the square, parti-cipants reported switches between perceived left-right and up-down motion.

Olfactory

An olfactory analogue to binocular rivalry was reported by Zhou and Chen(2009). In this study, participants were presented with two different smellsfor each nostril and they reported perceiving one smell at a time, switchingspontaneously between them.

1.3 The Psychophysics of Visual BistabilityAfter this overview over multistability in different modalities, the focus willnow be directed on visual bistability, in particular on the Necker cube. Itconstitutes the most important stimulus for this thesis as all the experimentspresented later employed this ambiguous figure.Thus, in the following, a more detailed description of the psychophysics ofbistable perception of the Necker cube will be given, including the measure-ment of dwell times and an outline of key parameters.

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1.3.1 Measuring Bistable PerceptionBistable visual perception is usually explored with the help of self-report bythe observer. Over the course of the last century, this technique has been re-fined from giving verbal report of the occurrence of reversals (Washburn et al.,1931) or counting out loud the number of reversals (Jones, 1955) to press-ing of a button recorded with high temporal precision (e.g. Borsellino et al.(1972), Brascamp et al. (2005), Kornmeier et al. (2009); also cf. Chapter 3).While the first approach allows for analysis of the number of reversals pertime interval or for mean dwell times, the latter yields at least approxim-ate knowledge of perceptual dwell times, i.e. the times between successivereversals. This is necessary in order to describe the statistical distributionof dwell times and thus fully capture the temporal dynamics of perceptualreversals.The approaches described above are all accompanied by a significant tem-poral inaccuracy. This is due to the finite reaction time between perceivedreversal for the observer and the consecutive button press. It cannot be as-sumed that the reaction time will be the same for every button press, as itwill have a certain variation, even for the same observer.5 But as there areno direct physiological predictors of perceptual reversals yet, in particular forambiguous figures, dwell time measurements still have to rely on self-report.There are several approaches, though, that aim at finding neural correlatesof perceptual reversals (cf. Sec. 1.4).A second issue with self-report is the lack of control over participants re-sponses. It cannot be guaranteed that responses given by the observers reallycorresponds to their percept. In order to estimate the extend of incorrect re-sponses, some studies on bistable stimuli included so-called “catch periods”in the measurements (e.g. Brascamp et al. (2005)). That are intervals dur-ing the measurement in which unambiguous versions of the bistable stimuluswere shown in order to check whether participants would indicate the cor-rect percept. Such an approach is better suited for stimuli like binocularrivalry where the unambiguous versions of the stimuli can be included in away so that participants are not able to clearly discern a catch period fromthe regular measurement. An alternative approach to this problem is tohave participants practice with feedback before the actual measurement us-ing randomly alternated unambiguous stimuli (Kornmeier et al., 2009). For

5Own data shows that this variation is not small. In fact, the reaction time data takenin the NC-pers study, 65 participants, had standard deviations of roughly 100 %.

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a stimulus like the Necker cube, its unambiguous versions are very differentform the ambiguous one, so that the training effect might not directly relateto the actual experiment.Some work has been done towards the recognition of perceptual reversalswith the use of physiological measures. For several types of bistable stim-uli, Einhäuser et al. (2008) found that pupil dilation preceded perceptualreversals. Similarly, for discontinuous presentation of the Necker cube, brainactivity in the right inferior parietal cortex has been identified as a precursorof perceptual reversals (Britz et al., 2009). In both instances, these changescan only be detected in averages over many trials. Hence, they are not suitedas markers for a single perceptual reversal.

1.3.2 Viewing Parameters for the Necker CubeThe research on bistable perception in the second half of the last centurywas strongly influenced by the classification of explanations in terms of“top-down” and “bottom-up” (cf. Long and Toppino (2004) for a review).The top-down approach assumes active, volitional processes near perceptualawareness as responsible for figure reversals, while in the bottom-up approachpassive, automatic and locally adaptable mechanisms during early visual pro-cessing create the reversals (Kornmeier et al., 2009). Psychophysical findingson stimulus parameters were cited mainly in favour of the latter model. Thus,in the following, some stimulus parameters that play a role in the perceptionof the Necker cube will be discussed. Evidence for top-down influences aswell as the need for an integration of both perspectives of the debate will begiven in Sec. 2.1.

Size

The relation of the size of the Necker cube to its perception, in particular thetemporal dynamics in terms of the dwell times and its statistical distribution,was studied by several research groups (Bergum and Flamm, 1975; Borsellinoet al., 1982; Dugger and Courson, 1968; Toppino, 2003; Washburn et al.,1931). The results of all groups indicate that dwell times are longer thelarger the cube is. This is an important finding regarding the comparabilityof different studies on the Necker cube. A more detailed overview over thestudies cited above and own results will be given in Sec. 5.1.

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(Dis-)Continuity of Presentation

Orbach et al. (1963) examined the intermittent presentation of the Neckercube and its effect on the number of reported reversals. Different dura-tions of presentations and “off-times”, where the stimulus was removed, wereused. The results show that the number of reversals initially increases withincreasing “off-time”, starting from continuous presentation. At about onethird of a second, the maximum is reached, after which a further increase ofoff-time decreases the number of reversals. These findings have been inter-preted in favour of models incorporating adaptation (cf. Sec. 2.1) and havebeen successfully modeled by the Necker-Zeno model of bistable perception(Atmanspacher et al., 2008, 2004). The results of Orbach and co-workershave furthermore been reproduced and extended by Kornmeier et al. (2007).

Completeness of Stimulus

Cornwell (1976) could show that an incomplete Necker cube reverses lessfrequently that a complete one. The authors explained this decrease in termsof less stimulation and hence slower adaptation. A similar result was foundby Babich and Standing (1981).

Colour

The colour surrounding the visual stimulus seems to have an influence onbistable perception. For some bistable stimuli, there is a so-called bias effect,i.e. one percept is favoured, with the corresponding dwell times being signific-antly longer than those of the other percept. Kornmeier et al. (2011b) foundthat this bias was weakened for the Necker cube if the cube was surroundedby blue colour.

Illumination

Even though Cipywnyk (1959) report an increase of the number of reversalswith increasing illumination of the Necker cube for a small sample of femalestudents, both Heath et al. (1963) and Riani et al. (1984) failed to reproducethis finding in better controlled designs. Thus, it seems that luminosity ofthe lines of the Necker cube and the background illumination do not influencethe number of reversals.

The dependence of perceptual reversals of the Necker cube on the above

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parameters, apart from illumination, is indicative of bottom-up componentsof bistable perception, as they mainly involve early processes of visual per-ception. The bottom-up vs. top-down classification of bistable perception aswell as the model of adaptation will be presented in detail in Sec. 2.1. There,also the other class of evidence, namely that for the top-down influence, willbe outlined.

1.3.3 Reproducibility of Dwell TimesAn important aspect of the temporal dynamics of bistable perception is thereproducibility of dwell times. Whether mean dwell times, or the numberof reversals, could be reproduced within one person was asked already veryearly in the research history of bistable perception, in order to find out howmuch of “trait”-character this measure had. If the number of reversals withina given amount of time were indeed more or less stable within a person, thestudy of potential relations to other rather stable characteristics, like person-ality traits, would be sensible.Guilford and Hunt (1931) seem to have conducted the first rigorous test of thehypothesis that reversal rates are in fact reproducible within in one personto a high accuracy. Five individuals reported perceptual reversals for threeminutes, at three times of the day for six days. The authors found that bothwithin one day and between days, the number of reversals were not signific-antly different. The most stable reproduction with the least amount of testingwas found for taking the average over three days. Also Frederiksen and Guil-ford (1934), whose study has been cited often with regard to the questionof reproducibility, reported high correlations between number of reversals ofthe Necker cube for subsequent days. Guilford and Hunt (1931) furthermorefound that the variations of the mean number of reversals within one indi-vidual over time were much smaller than the variation of mean number ofreversals within a group of observers. This property led to the classificationof observers into “fast” and “slow” reversers (as in Borsellino et al. (1972)).There seem not to be more recent studies than those of Guilford and co-workers examining the reproducibility of the number of reversals for theNecker cube. Hence, a pilot study described in Sec. 4.2 was conducted thatconfirmed the above findings, also showing no significant differences in thedwell time distributions on consecutive days. It must be taken into accountthat only a small number of participants were tested in that pilot study, sothat further corroboration of these results with a larger sample would be

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desirable.In conclusion, the number of reversals as well as the mean dwell times inperception of the Necker cube are characterised by (1) a considerable intra-individual temporal stability and (2) a significant inter-personal variation.Hence, it is probably that other intra-personally temporally stable character-istics with a certain inter-individual variation, like personality traits, wouldcorrelate with these measures of bistable perception. This line of thoughtwill be followed up on later in Chapters 7 through 11.

1.4 The Physiology of Visual BistabilityIn this section, the most important physiological aspects of bistable percep-tion, in particular of the Necker cube, will be described. In part, these areimportant for the study of bistability itself – e.g. eye movements – or, onthe other hand, concern the question of physiological, in particular neuro-physiological, correlates of bistable perception. The search for the latter hasthe potential to deepen our understanding of the processes involved and theirrelations.

1.4.1 Eye Movements & BlinksThe role of eye movements and eye blinks in perceptual switches for bistablestimuli has been debated for a long time. Already Necker himself pointedout that he could influence the perception of his drawing by adjusting hiseyes to certain aspects of the figure (Necker, 1832) – a finding that the readercan easily test him- or herself by experimenting with Fig. 1.1a. There areseveral studies that show that one or the other percept is favoured by fixatingdifferent locations of the figure (cf. review by Long and Toppino (2004)).With modern eye tracking technology, today more detailed analyses are pos-sible. Einhäuser et al. (2004) studied the effect of eye position on perceptualreversals of the Necker cube in a free viewing condition, i.e. with no instruc-tions to fixate. The authors found “a tight link between switches in perceptionand eye position.” At the perceptual reversal the eye positions were at ex-treme position and after that the eye gaze would shift to the newly establishedpercept. Building on these results, van Dam and van Ee (2006) found thatfor ambiguous figures there is no or only a weak positive correlation betweensaccades and perceptual reversals – while there is strong one for binocularrivalry. The same pattern was found for a condition where participants tried

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to voluntarily control perception. Furthermore, while the fixation positiondid not determine the percept, the authors found that observers preferredto look at different positions when instructed to hold different percepts ofthe stimulus. Also, van Dam and van Ee (2005) examined the role of eyemovements and blinks for slant rivalry, an ambiguous figure with temporaldynamics comparable to the Necker cube. The authors found that there wasno positive correlation between reversals and either saccades or blinks occur-ring before these reversals.In conclusion, it can be stated that for perception of the Necker cube, blink-ing and saccades do not determine perceptual reversals. van Dam and vanEe (2006) also showed, that this was different for binocular rivalry. For thatstimulus type, there is in fact a correlation between saccades and reversalsat about the moment of reversal.

1.4.2 Neuro-ImagingApart from the psychophysical and outer physiological descriptions, it is de-sirable to gain a neuro-physiological understanding of perceptual bistability.With the advanced development of neural imaging techniques it is possible tostudy the brain regions and neural structures involved in bistable perception,and in particular those involved in perceptual reversals.

EEG

Electroencephalography (EEG) has been successfully applied in order tostudy perceptual reversals of ambiguous figures. A good review has beengiven by Kornmeier and Bach (2012). Compared to functional magnetic res-onance imaging (fMRI), EEG provides the advantage of a very high temporalresolution in the range of a few miliseconds. This is of course, a very usefulfeature in order to study a temporal process like perceptual reversals. As thevoltages measured with EEG across the skull are usually very small, manytrials have to be averaged in order to achieve an acceptable signal-to-noiseratio. For this, a common temporal reference in all these trials is necessary.There are two main approaches in using EEG to explore perceptual reversals:(1) using manual response as the afore-mentioned time reference or (2) usingstimulus onset as time reference. Both approaches have some difficulties. Inthe first, the temporal information is strongly blurred due to the large vari-ation in timing of manual response (i.e. button press). Kornmeier and Bach(2004) demonstrated this effect by averaging EEG recordings of unambiguous

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illustrations of the Necker cube to both manual response and stimulus onsetand comparing the two. In the second approach, discontinuous presentationof the stimulus is used so that a precise stimulus onset is created, whichposes the question whether discontinuous presentation is representative ofcontinuous presentation.Using the first approach with the Necker cube, Strüber et al. (2001) found aP300-like event-related potential (ERP) component, i.e. a positive compon-ent about 300ms before button press. It has maximum intensity in the rightparietal region and it has been interpreted as indicating conscious recogni-tion of a perceptual reversal. Isoglu-Alkaç et al. (2000) found a decrease inalpha-band power in the time range of that positivity compared to the timeimmediately before it.Improving a design by O’Donnell et al. (1988), Kornmeier and co-workersfollowed the second approach, i.e. temporal averaging with respect to stim-ulus onset in discontinuous presentation (Ehm et al., 2011; Kornmeier andBach, 2006; Kornmeier et al., 2011a; Kornmeier and Bach, 2004). Therewere three main findings: (1) a positivity at 130ms after stimulus onset inthe occipital region, (2) decrease in alpha-band activity in the left occipitalto frontopolar regions lasting from roughly 130ms to 210ms and (3) a delayof all subsequent components for endogenously induced reversals comparedto exogenously induced ones (Kornmeier and Bach, 2012). The authors in-terpreted the positivity as a marker of a decision conflict occurring with theambiguity of the stimulus. The subsequent alpha decrease might accom-pany the process of dissolving the ambiguity. After 250ms this process iscompleted, the manual report of the reversal follows much later, at around600ms. No influences of voluntary control (“top-down”) or of modulationof the inter-stimulus interval in discontinuous presentation (“bottom-up”) onthe EEG signatures before 250ms were found, though, which poses a chal-lenge for the interpretation of this interval as the crucial time window for thereversal process (Kornmeier and Bach, 2012).

fMRI

Many studies have explored the neural structures involved in bistable percep-tion using functional magnetic resonance imaging (fMRI). A great numberof them have explored binocular rivalry, also in animal models.Studying ambiguous figures with an apparent motion quartet stimulus, Sterzerand Kleinschmidt (2007) found an earlier and increased activation in the

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right inferior frontal cortex for endogenously compared to exogenously in-duced perceptual reversals. Similar results have been found by Shen et al.(2009) for a Necker lattice stimulus.6 Also comparing endogenous and exo-genous reversals, the authors identified destabilising signals from the rightdorsal frontal cortex and furthermore stabilising signals from the right an-terior portion of superior temporal sulcus. The latter was associated withperceptual memory, i.e. the accumulated influences of previous perceptions.A review of the neurophysiological processes involved in bistable perceptionwas composed by Sterzer et al. (2009). The authors pointed out evidence forinteractions of both low- and high-level brain regions and for early and lateprocessing.

TMS

In contrast to methods like EEG and fMRI, transcranial magnetic stimula-tion (TMS) is better suited to detect causal involvement of brain regions, asit can produce temporally limited “virtual lesions”.With a spinning wheel illusion stimulus, a bistable apparent motion stim-ulus, Ge et al. (2007) applied TMS to the right superior parietal lobule.By comparing this condition to one without TMS stimulation, the authorsfound that this region plays a critical role in perceptual reversal of this am-biguous figure. Kanai et al. (2011) used TMS in order to study the neuralbases of visual bistability for both binocular rivalry and for an ambiguousstructure-from-motion rotating sphere. For both stimuli, the authors foundthat stimulation of the anterior right superior parietal lobule decreased dwelltimes while stimulation on the posterior part of the same structure increasedthem. This shows the fractionation of parietal cortex function with respectto bistable perception. Also for a structure-from-motion sphere stimulus,de Graaf et al. (2011) demonstrated that the dorsolateral prefrontal cortexis causally relevant for voluntary control over perceptual switches, while it isnot for passive observation of the same stimulus. Thus, these TMS studiescomplement the findings using fMRI presented above, in particular with re-spect to the role of the frontal cortex.Showing a novel bistable stimulus based on apparent motion, Zaretskayaet al. (2013) used both fMRI and TMS on the same group of participants.This stimulus alternates between a dynamic global illusory contour Gestalt

6This is an array of Necker cubes, which has the effect of enhancing neurophysiologicalstimulus responses (Kornmeier et al., 2004; Shen et al., 2009).

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and moving ungrouped local elements. The authors found that two sites inthe parietal cortex, namely the superior parietal lobe and the anterior intra-parietal sulcus, specifically correlated with the illusory global Gestalt but notwith the local elements. Furthermore, TMS over the anterior intraparietalsulcus shortened the dwell times for the global Gestalt percept but not thelocal elements.All in all, these TMS studies greatly enhance the knowledge of the neuralbasis of bistable perception. And even though no studies on the Necker cubeusing TMS were given here, the results on TMS for structure-from-motionstimuli are likely to be at least partly transferable due to the similar natureof both stimulus types.

1.4.3 LesionsComplementing the results gained from studies employing neuro-imagingtechniques or TMS, lesion studies can provide valuable insights into whichbrain regions are causally involved in perceptual reversals.Already Cohen (1959a) examined war veterans with missile wounds on theirperception of the Necker cube. He found that unilateral frontal lesions, par-ticularly in the right hemisphere, decreased the number of reversals whilebilateral frontal lesions increased it. Posterior lesions on the other hand, ledto a smaller reduction in number of reversals. These findings are likely tobe somewhat less reliable than later studies, as exact lesion location withcomputer tomography had not been available at that time.Ricci and Blundo (1990) tested the ability of 40 lesions patients with uni-lateral frontal or posterior brain damage on their ability to recognise severalvisual bistable stimuli, including a vase/faces and an old woman/young wo-man figure. The frontal lesion patients needed significantly more prompts bythe experimenters than healthy controls, until they perceived both percepts.Furthermore, they had greater difficulty in shifting from one perspective tothe other than posterior patients or healthy controls. This line of research wasfurther pursued by Meenan and Miller (1994). Presenting a host of bistablefigures to patients who had undergone focal frontal or temporal lobectomy,the authors found that all patients could distinguish at least one percept ofeach figure. Only the patients with right frontal lesions had a significantimpairment in recognising the second percept. This influence of lateralisa-tion was confirmed by von Steinbüchel (1998) in a study with patients withunilateral frontal and posterior lesions as well as left-sided subcortical le-

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sions and a control group. Using both visual bistable stimuli, the Neckercube and vase/faces, and auditory streaming, von Steinbüchel discovered in-creased dwell times only for patients with lesions in the right frontal cortex.

The lesion studies presented here are in good agreement with the fMRI andTMS studies cited above and further validate the importance of the rightfrontal cortex for perceptual reversals. Research employing TMS and fMRIhas provided additional insights on exact locations and demonstrated otherinvolved brain regions, while the temporal aspects of the reversal process havebeen elucidated with the help of EEG. Hence, the different approaches com-plement each other in deepening our understanding of the neurophysiologyof bistable perception.

1.5 GeneticsRecently, also genetics have been related to bistable perception. Shannonet al. (2011) explored perception of the Necker cube and binocular rivalryin both monocygotic and dicygotic twins. They found strong correlations inboth stimulus types between monocygotic but not dicygotic twins (r ≈ 0.55).Also, they showed that between monocygotic twins the number of reversalsfor binocular rivalry correlated with the number of reversals for the Neckercube (r = 0.37). There was no such correlation between dicygote twins.These results led the authors to the conclusion that there is a heritable basisfor bistable perception and that similar genes are involved in determiningthe temporal dynamics for different forms of multistable perception.Kondo et al. (2012) compared the number of reversals among genotype groupsfor two genes and different visual and acoustic multistable stimuli. Poly-morphisms of catechol-0-methyltransferase (COMT) Val158Met and serotonin2A receptor (HTR2A) -1438G/A were considered. The authors found differ-ences in the number of reversals for acoustic bistability (auditory streamingand verbal transformation) in the COMT genotype groups, while the HTR2Agenotype groups differed in perception of the Necker cube and a vase/facesstimulus. It was concluded that the serotonin system is related to percep-tion of ambiguous figures, in particular closely linked to the so-called “shape”factor that the authors identified with a factor analysis. The authors sug-gested that developmental differences due to the variances in the serotoninsystem might cause the differences in reversal behaviour.The results of Shannon et al. (2011) suggest that about 30% of the inter-

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individual variation in bistable perception of the Necker cube (r2 = 0.552 =0.30) could in principle be explained genetically. Thus, a very exact analysisof the temporal dynamics of the bistable stimulus would be needed in orderto detect these differences. Furthermore, in order to gain a deeper under-standing of the genetic influence, a broader range of polymorphisms wouldbe desirable – a conclusion that was also drawn by Kondo et al. (2012).

1.6 The Psychology of Visual BistabilityThe perception of bistable stimuli in general and the Necker cube in partic-ular has not only been studied on the levels of psychophysics and physiologybut also on the level of psychology and psychopathology. These influenceson bistable perception are mainly rather high-level aspects, or so-called top-down aspects.A very well known top-down aspect that was mentioned already very earlyin the research history of bistability, namely by Necker himself in his originalpublication (Necker, 1832) is voluntary control. Many studies have proventhe influence of voluntary control on bistable perception (e.g. Kornmeier et al.(2009); Strüber and Stadler (1999)), which is stronger for ambiguous figurescompared to binocular rivalry (van Ee et al., 2005). These experiments showthat reversals can be slowed down and sped up to some extend. But they alsodemonstrated that it is not possible to prevent reversals altogether. A moredetailed review over research on voluntary control will be given in Chapter 7where an experiment on this subject will be presented.Several reports linked perception of the Necker cube with personality traits.A strong correlation was found between creativity and the number of exper-ienced reversals (e.g. Bergum and Bergum (1979b)). There are several otherfindings relating personality and reversal behaviour which will be reviewedin Chapter 8 together with a presentation of own results on bistability andpersonality.Furthermore, the concept of mindfulness, originating from Eastern reli-gious practice, in particular meditation, was shown to be related to bistableperception. Sustained training in mindfulness correlate with the ability toprolong dwell times in different forms of bistable and multistable perception(Carter et al. (2005); Sauer et al. (2012), cf. also Chapter 9).Sheppard and Pettigrew (2006) reported a relation of positive mood state

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to bistable perception of a plaid motion rivalry stimulus7 (Hupé and Ru-bin, 2003). The proportion of time spent with the percept of a single mov-ing plaid correlated positively with mood state. It would be interesting totest whether this finding can be reproduced with perceptual biases for otherbistable stimuli and a larger sample, as Sheppard and Pettigrew (2006) hadonly ten participants.For different content reversal stimuli, Allen and Chambers (2011) comparedambiguous figure perception between adolescents with autism spectrumdisorder and learning disability. By having them copy the stimuli underdifferent conditions, the authors found that the participants with autismspectrum disorder processed the images conceptually differently, not beinginfluenced by contextual information.Bilingualism seems to be another characteristic related to bistable percep-tion. Bialystok and Shapero (2005) found that bilingual children (ca. 6 yearsof age) discovered the alternatives of the content reversal stimuli faster thanmonolingual children.Patients of schizophrenia and bipolar disorder were tested in percep-tual reversals of the Necker cube by Hunt and Guilford (1933). The authorsfound that the group of schizophrenic patients was almost identical to acontrol group in terms of numbers of reversals whereas the bipolar patientsreported much less reversals than the controls. The authors suggested thatbistable perception might be developed into a diagnostic tool. Krug et al.(2008) also reported a lower amount of reversals for bipolar patients com-pared to healthy observers, but this time a structure-from-motion rotatingcylinder was used as stimulus. The authors conclude, though, that bistableperception is not suitable as a diagnostic tool due to the larger inter-personalvariation of dwell times. For binocular rivalry, similar findings were statedby Miller et al. (2003). The authors found that patients with bipolar dis-order experienced less reversals than controls, while schizophrenic patientsand those with major depression did not differ from a control group in thatrespect.

7In this stimulus two gratings are overlaid and moved with respect to each other. Theyare seen through a circular aperture and can be perceived as either sliding over each otherindependently or as a single plaid moving in one direction.

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1.7 Similarities and DifferencesHaving presented a variety of bistable stimuli in Sec.1.2 and subsequentlysome of their psychophysical, physiological and psychological properties witha focus on the Necker cube, the question remains of how these stimuli dif-fer between each other. The question is indeed of practical relevance as itsanswer would allow to conceptually merge the results of studies done withdifferent stimuli. This would be very useful as some stimuli types are moreuseful with certain problems than others. For example, binocular rivalry ismuch better suited for research with animals than ambiguous figures.To give a comprehensive comparison of all these different bi- and multistablestimuli would not be feasible, though. There is a multitude of parameters in-fluencing a stimulus’ perception, with different parameters for each stimulustype. It is not realistic to compare all of those. But of course, some generaldifferences and similarities can be highlighted.One important aspect, which accentuates differences between bistable stim-uli, is voluntary control over reversals. Binocular rivalry is characterisedby a lower susceptibility to voluntary influence by the observer than am-biguous figures (van Ee et al., 2005). Within the class of ambiguous figures,content reversal figures can be controlled better than perspective reversalstimuli – both for speeding up reversals and for slowing them down. Withinperspective reversal stimuli, a higher meaningfulness is conducive to controlover reversals (Strüber and Stadler, 1999).Also, the amount of “discreteness” of bistability, i.e. how abrupt the re-versals between percepts are, varies between stimuli. In binocular rivalry,perceptual dominance can arise locally and over time spread over the wholestimulus (Kang and Blake, 2011), sometimes as traveling waves (Wilson et al.,2001). Thus, a reversal in binocular rivalry is not a discrete, “all-or-none”,process. By taking this into account with the use of a joystick to indicatethe current percept, i.e. a continuous indicator, the detection of correlationswith physiological measures was made possible (Naber et al., 2011). Further-more, structure-from-motion stimuli are typically characterised by clearerand faster transitions from one percept to the other than for example theNecker cube.The temporal dynamics of bistable perception of ambiguous figures andbinocular rivalry, on the other hand, seem to be very similar. Brascampet al. (2005) compared the fit residuals of dwell time and inverse dwell times

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for two ambiguous figures and two binocular rivalry stimuli, finding a highdegree of similarity between all of them.

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2. Models of Bistable Perception

In this chapter several models for bistable perception will be reviewed. Earlyapproaches were mainly qualitative, while currently there are several quantit-ative models reproducing the temporal dynamics of bistable perception thatare based on neurally plausible mechanisms.

2.1 Up or Down?

Research on bistable perception in the second half of the 20th century wasstrongly influenced by the debate about whether it was a bottom-up ora top-down phenomenon. The top-down view-point assumes active, cog-nitive processes near perceptual awareness as being responsible for figurereversals, while in the bottom-up theory passive, automatic and locally ad-aptable mechanisms during early visual processing are seen as responsiblefor the reversals (Kornmeier et al., 2009). Long and Toppino (2004) remarkthat most of the research articles in that time endorsed either of the twotheoretical perspectives. Evidence in support of both theories are listed inTabs. 2.1 and 2.2, respectively. References for most of these classes of resultscan be found in Long and Toppino (2004).The results supporting bottom-up explanations of bistable perception weremainly interpreted in line with adaptation models. In a modern conceptu-alisation, this adaptation denominates the selective tuning of neural channelsto certain characteristics of the retinal stimulus. Within this model, percep-tual reversals depend on low-level, automatic processes which (1) criticallydepend on the features of the stimulus, (2) are localised to those retinal re-gions that undergo excitation, adaptation and recovery and (3) are mainlyindependent of higher cognitive processes (Long and Toppino, 2004). Theresults summarised in Tab. 2.1 are explained well within this framework.Until recently, adaptation models did not detail how the stochastic nature of

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Evidence for bottom-up theoriesInitial adaptation Initial increase of the number of reversals, i.e. decrease

of dwell times. As demonstrated in Sec. 4.1, this ef-fect seems to be mainly due to an initial confusion inthe experimental situation and the need to familiar-ise with the reversal phenomenon, as a short trainingsession seems to remove the effect to a large extend.

Local adaptation Toppino and Long (1987) found that if, after initialadaptation, a stimulus is moved to a different locationin the visual field, reversal rates are again on the samebaseline level as prior to adaptation.

Multiple-figurepresentation

Simultaneous observation of two or more bistablestimuli is characterised by independent reversals aswell as independent adaptation (Toppino and Long,1987).

Reverse-bias(priming)

Prolonged exposition to an unambiguous version of abistable stimulus leads to a preference of the respect-ive other perspective of that stimulus in subsequentobservation of it (Long et al., 1992). This seems tobe an adaptation effect as it disappears when the am-biguous stimulus is presented to another retinal regionafter the priming.

(Dis-)Continuity ofpresentation

Presenting bistable stimuli discontinuously influencesthe number of reversals substantially, even leadingto complete absence of reversals for sufficiently longinter-stimulus intervals (Leopold et al., 2002).

Viewing paramet-ers

Different viewing and stimulus parameters, like size,stimulus completeness etc., have an influence on thenumber of reversals (cf. also Sec. 1.3.2).

Table 2.1: Some classes of evidence supporting bottom-up explanations of bistable per-ception. Further details and references can be found in Long and Toppino (2004).

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Evidence for top-down theoriesVoluntary control Voluntary effort has been shown to influence dwell

times in many studies. Dwell times can be specificallyincreased and decreased to a certain extent. It is notpossible, though, to prevent reversals altogether. Amore detailed description of these effects is given inChapter 7.

Knowledge of re-versibility

Without the knowledge of reversibility, reversals areabsent in the majority of participants (Rock andMitchener, 1992).

Priming (set effect) Showing an unambiguous figure or priming with se-mantically related words leads to a bias of perceptiontowards the primed percept.

Cognitive load Diverting attention to a distractor task has beenshown to slow down the reversal process for ambigu-ous figures and binocular rivalry (Alais et al., 2010;Reisberg and O’Shaughnessy, 1984).

Table 2.2: Classes of evidence for top-down effects in bistable perception. For furtherreferences cf. Long and Toppino (2004).

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dwell times could be incorporated and quantitatively reproduced.The results summarised in Tab. 2.2, on the other hand, show influences ofhigher order and cognitive processes. These processes are more of an activenature and closer to conscious perception.As there is ample evidence for both bottom-up and top-down effects inbistable perception, it has become clear that both types of effects have tobe implemented in a useful model of bistable perception (Long et al., 1992;Toppino and Long, 1987). Thus, Long and Toppino (2004) proposed a qual-itative hybrid model consisting of four levels: feature-extraction, processing,representation and a nonsensory cortical level, which interact in several ways.Kornmeier and Bach (2012) suggested another qualitative model based ontwo attractors in a state space which are modulated in their depth by destabil-isation and disambiguation processes. In this approach both bottom-op andtop-down aspects can influence these processes.

2.2 Oscillators or Attractors?The approaches presented above are mainly qualitative. In the last decade,increasingly more quantitative models have been developed that are basedon actual neuronal structures. Most of them fall into either of two classes.The oscillator -type models feature a noisy oscillator circuit, with adapta-tion being the driving force behind reversals. In the attractor -models, onthe other hand, noise is the driver of perceptual reversals, with adaptationonly modulating this process. That means, that without noise, there wouldbe no reversals in a noise-driven model, while oscillator models would beperfectly periodical without noise (Shpiro et al., 2009). On the other hand,noise-driven models without adaptation predict exponential distributions ofdwell times, not gamma or lognormal distributions (Braun and Mattia, 2010).Thus, it seems that models being based exclusively on one or the other pro-cess are not realistic.Shpiro et al. (2007) compared four oscillator-type models for binocular rivalrywhich were based on cross-inhibition. The authors found regimes of differ-ent dynamical charactersitics in the space spanned by the model parameters,which can accompany effects of varying stimulus strength, i.e. variations inthe input for the models.An attractor model with weak adaptation was presented by Moreno-Boteet al. (2007), which is implemented both in firing rate mean-field and in

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spiking cell-based neural networks. Thus, the model goes beyond abstractenergy-based constructions. The authors propose fluctuations in N-methyl-D-aspartate receptors as a possible source of noise, allowing for variations ofthe right timescale (O(1 s)).Shpiro et al. (2009) created a framework that allowed them to smoothly gofrom adaptation-driven (oscillator) to noise-driven (attractor) models. Theauthors studied their model with respect to the range of observed dwell timesand the range of the corresponding coefficient of variation. In order to re-produce these empirical value ranges, the models must feature a balancebetween adaptation and noise, operating near the boundaries of being noise-driven or adaptation-driven. In terms of simulated dwell time distributions,the authors found that the noise-driven variants are fitted by the gammadistribution and the adaptation-driven variants by the Weibull distribution.The lognormal distribution did not yield good fits. This is at odds with sev-eral reports on dwell time distributions (Brascamp et al., 2005; Krug et al.,2008; Zhou et al., 2004) as well as with own findings presented in Chapter 4.As in these own analyses the Weibull distribution is clearly shown to be abad fit, the results of Shpiro and co-workers indicate that noise-driven modelsshould be preferred for modeling perception of ambiguous figures. Anotherdifference between the two types of models shows in correlations between suc-cessive dwell times. The adaptation models produce stronger correlations,r ≈ 0.25 − 0.3, than the noise-driven models, r ≈ 0.1. Contrary to the dis-cussion in Shpiro et al. (2009), finite correlations between successive dwelltimes for perception of the Necker cube were reported (Gao et al., 2006; vanEe, 2005). Gao et al. (2006) only give a typical example of an autocorrelationfunction but no data for the whole sample. But according to data of van Ee(2005), correlations are around 0.17, i.e. roughly in the middle of the resultspredicted by noise- vs. adaptation-driven models. Thus, further experimentaldata would be desirable to make an adequate comparison between the mod-els. Finally, Shpiro et al. (2009) noted that the range of the coefficient ofvariation of the dwell times is better satisfied by the noise-driven model. Inconclusion, noise-driven attractor models with weak adaptation seem to bebetter suited to model bistable perception than adaptation-driven models.A further advance in this direction was reported by Gigante et al. (2009)(see also Braun and Mattia (2010) for a review). The authors presented anoise-driven model featuring nested attractors. The model is able to explainthe scalar property of dwell times for different observers or conditions. Thismeans that the variability of dwell times increases with increasing mean dwell

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time so that the normalised shape of the dwell time distribution of fast revers-ers is very similar to those of slow reversers. Furthermore, in order to explainthe decrease in reversals observed for intermittent presentation of ambiguousfigures for inter-stimulus intervals larger than about 350ms (Kornmeier andBach, 2012), noisy oscillator models have to resort to postulating an addi-tional adaptation process at longer time scales. This can alternatively beachieved by a hierarchy of attractors operating at different time scales.

2.3 Further ApproachesWhile the oscillator and attractor models reviewed above are based on real-istic neural structures, there are also a few more abstract models for percep-tion of bistable stimuli that will be mentioned very briefly here.Models based on Bayesian decision processes were presented by van Ee et al.(2003) for slant rivalry, an ambiguous figure, and Sundareswara and Schrater(2008) for the Necker cube.Gershman et al. (2009) suggested a model of perceptual inference, mainly forbinocular rivalry, based on Markov Chain Monte Carlo methods.The mathematical formalism of a quantum-mechanical effect is used in theNecker-Zeno model of bistable perception (Atmanspacher et al., 2008, 2004).In analogy to the quantum Zeno effect, a two-level system with a periodicupdating, or “measurement” process, was proposed. Decoherence was in-troduced with a time evolution operator, leading to a “decay” of the wavefunction and eventually a perceptual reversal. Under the inclusion of anearly adaptation phase in perception of a bistable stimulus, calculations ofthe transition probabilities predict gamma distributed dwell times.

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3. Two Studies on Perception ofthe Necker Cube

In the following, the results of two empirical studies on the perception of theNecker cube will reported. As the experiments cover a large variety of aspectsof bistable perception and its context, they will be arranged and presented inconceptually arranged chapters. Each of these will contain the background,methods, results and discussion relevant for the respective topic. The generalmethods relevant to most chapters will be presented in this chapters.

In this section the general design, hypotheses, methods and analysis of thetwo studies, that were conducted for this thesis, will be described. The stud-ies are called NC-dist and NC-pers, respectively, indicating the focus onthe distribution and low-level features of the Necker cube of the first studyand focus on personality and predominantly high-level aspects of the secondone. A detailed description of both studies and the individual experimentsconducted will be given in the following chapter.Both studies were almost exclusively conducted in a highly automated, com-puterised design using Matlab and Psychtoolbox-3. The Psychtoolbox-3,PTB-3, (Brainard (1997), Pelli (1997), Kleiner et al. (2007)) is an open-source toolbox for Matlab that allows for high-precision control of visual andacoustic stimuli using a host of C-routines.Using a highly automated design provides the advantages of reducing con-founding influences of varying oral instructions and errors in the protocol anddata collection. Furthermore, a swift and smooth conduction of the studyis facilitated. Custom routines in Matlab and PTB-3 were written for theimplementation of the experiments.Data analysis, too, was performed in the Matlab environment with custom

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routines making use of functions of the StatisticsToolbox for statistical ana-lysis and distribution fitting.Both studies were approved by the ethics committee of the ETH Zürich.Participants were compensated monetarily for their participation in the stud-ies, receiving about 20CHF per hour. Different participants attended eitherstudy. They were recruited via an online platform of the University of Zürichand were mainly students of either ETH Zürich or University of Zürich.

3.1 NC-dist: Temporal Dynamics and Low-levelFeatures in Bistable Perception of the NeckerCube

The first study was mainly focused on low-level aspects of bistable perceptionof the Necker Cube, while also exploring some high-level features. The Neckercube was used as stimulus as it is characterised by low semantic content anda high geometric symmetry. Thus, for this figure less confounding influenceswere expected compared to a stimulus like the old woman/young womandrawing.

3.1.1 Research Questions of the NC-dist StudyThe following questions were supposed to be answered in this study:

• What is the most reliable description of the dwell time distribution?

• Is there a clearly distinct initial phase of bistable perception of theNecker cube when an observer experiences perceptual reversals for thefirst time?

• How does perception of the Necker cube depend on stimulus size forsmall visual angles?

• Which common features are shared between the verbal transforma-tion effect and bistable perception of the Necker cube?

To address these questions, the NC-dist study with 5 sub-experiments and 2questionnaires was conducted in a randomised design with 23 healthy, Ger-man speaking, right-handed participants. For each participant, dwell times

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were measured for 6 different cube sizes in order to explore size dependence.A paradigm analogue to the Necker cube experiment was employed for theacoustic domain: the verbal transformation effect. Here two different wordscan be identified in a stream of alternating syllables. A more detailed de-scription of the research questions of this study as well as the results will befound in the following chapters.

3.2 NC-pers: Personality, cognitive abilities, tem-poral processing and the Necker cube

Having gained some insights into several low-level aspects of bistable percep-tion of the Necker cube, the second study was aimed at linking the foundperceptual patterns more broadly to cognition, personality and temporal pro-cessing.

3.2.1 Research Questions of the NC-pers StudyIn particular, the following questions were supposed to be addressed:

• How can perception of ambiguous figures be linked to personality ingeneral and the concept of mindfulness in particular?

• Are individual differences in voluntary control over perceptual re-versals related to differences in personality and cognition?

• Which measures of cognition and temporal processing are relatedto the perception of the Necker cube?

• Is there a hystersis effect for transformations of the Necker cube?

The second study, NC-pers, addressed these questions with 8 sub-experi-ments and 8 questionnaires in a randomised design with each experiment orquestionnaire being conducted with or filled out by either 32 or 65 healthy,German speaking, right-handed participants. The difference in number ofparticipants is due to a split in the NC-pers study: after taking data from32 participants with all experiments described in the paragraphs below, apreliminary analysis was conducted. In order to gain more statistical power,some of the experiments were continued with more participants. Thus, forsome experiments 32 data sets are available, for some 65. The number of

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data sets actually used was lower than that due to outliers and missing data.The following experiments were used.In a voluntary control paradigm for the Necker cube, after a neutral, “passive”condition, participants were asked in different conditions to try to hold eitherof the two percepts or speed up the reversal process. To assess temporal pro-cessing, a simple GoNogo reaction time task, an acoustic measurement oftemporal order threshold (Ulbrich et al., 2009) and a temporal integrationtask (Szelag et al., 1996) were conducted. Two other cognitive measures,namely working memory capacity, conceptualised with a reading span taskand a backward digit span task (Oberauer et al., 2000), and attention probedwith the d2 attention task (Brickenkamp, 2002) were examined. A paradigmby Hock et al. (1993) was adapted for the Necker cube in order to testwhether in the transformation process from one unambiguous perspective ofthe Necker cube to the other perceptual reversals are “lagging behind” thetransformation. The presence of such a lag would be called hysteresis effect.Concerning personality, two short questionnaires were used to assess sensa-tion seeking behaviour and ambiguity tolerance, namely the Brief SensationSeeking Scale, BSSS, (Hoyle et al., 2002) and the Ungewissheitstoleranz-skala, UGT, Dalbert (1999). Furthermore, a German version of the NEO-Five-Factor Inventory (NEO-FFI/BIG-5) was used for a coarse personalitycharacterisation (Körner et al., 2008). Mindfulness was assessed using theFMI (Walach et al., 2006) and CHIME questionnaires (Bergomi et al., 2012),both of which are not based on specialised vocabulary describing meditationor religious aspects of mindfulness. The STAI trait and state inventory (Lauxet al., 1981) was used to assess anxiety, while action-control was exploredwith the HAKEMP questionnaire (Kuhl, 1994) and self-leadership with theRSLQ-D (Andreßen and Konradt, 2007).Also for this study, more details on the individual experiments will be givenin the following chapters.

3.3 Measuring Bistable PerceptionThis section describes the general procedure for the experiments on bistableperception of the Necker cube as employed in the current work. In all ex-periments, the Necker cube was presented as a black on white line drawingon a computer screen using PTB-3. An illustration of the cube is given inFig. 3.1. In the NC-dist study the Necker cube was shown in 6 different size

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Figure 3.1: The Necker cube. The cube can be seen either from above with the lower rightface being in front. This perspective will be referred to as percept A (above). Or it canbe seen from below with the top left face being in front. This perspective will be labelledpercept B (below).

covering visual angles 1 to 6 ◦, whereas the cube size in NC-pers covered avisual angle of 5 ◦.1 Viewing distance was 2.0 and 1.3m in the two studies,respectively.In both studies, after having initially been introduced to the reversal phe-nomenon, participants were shown a Necker cube to experience at least onereversal (in the NC-dist study four reversals were awaited). Subsequently, thedrawing was removed again and there was either a waiting period (NC-dist)or further instructions (NC-pers). Only then would the actual measurementperiod of 3 minutes begin. During this period, participants indicated via twodifferent keyboard buttons whenever they experienced a perceptual reversal.The time of each button press was recorded with high precision using PTB-3for Matlab.In the NC-dist study, different cube sizes were presented in a randomisedfashion for 3 minutes each, interrupted by breaks of half a minute. In NC-pers, after the first session of neutral observation of reversal behaviour, 3conditions with instructions to attempt voluntary control over perceptionwere conducted in randomised order. These were “hold A”, were participantswere instructed to hold perspective A as long as possible and to try and avoidperspective B (i.e. in case of a reversal to B switch back to A quickly), “hold

1The sizes given here indicate the maximal diagonal extension of the cube, i.e. top-leftto bottom-right.

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B” (the inverse of hold A) and “speed up”, where participants were instructedto switch between percepts as quickly as possible.In both studies participants rested their head in a chin rest in order to minim-ize movements of the head and in order to keep the viewing distance constant.Furthermore, they were also instructed to minimize eye and head movementswhile fixating a little cross that was shown in the middle of the Necker cubethroughout presentation. In the first study and in the neutral condition ofthe second one, they were asked to observe reversals in a passive fashion,without trying to exercise any voluntary control over reversals.

3.4 Analysis of Dwell Time DataThe raw dwell time data recorded for all Necker cube experiments consistedof the machine time of each button press and a code for which button waspressed. Before further analysis, relative dwell times were calculated by sub-tracting subsequent dwell times from each other. The first dwell time of eachdata set was deleted, as the context of the first button press differs from allthe others, not being preceded by another reversal.Additionally, dwell time data had to be corrected for consecutive presses ofthe same button. In those instances it was unclear what the participant ac-tually perceived. Four possibilities exist. First, the participant could havepressed the button in order to reconfirm his current percept. After the exper-iment, some participants spontaneously reported having used this behaviourwhen their percept became ambiguous for a short instance but then returnedto the same percept as before, i.e. no reversal occurred. To correct the datain this case, it would be indicated to add up the two involved dwell timesin order to get the times between perceptual reversals. Secondly, the parti-cipant could have failed to indicate a reversal in between the two consecutivebutton presses. I.e. a sequence “A–A” would have actually been “A–B–A”.Here, the first of the two dwell times should be removed as it would splitinto two separate dwell times, the size of which is not known. Thirdly, it ispossible that the participant mixed up the two buttons, pressing the wrongone. Such a mix-up, if not corrected by another quick button press of theparticipant, would result in three consecutive occurrences of the same but-ton. Then the button code middle one should be altered. Fourthly, theparticipant might have accidentally pressed a button. There is no way tocorrect for that, as one does not know whether the first or the second dwell

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time would be the accidental button press. In general, it is not possible todistinguish between these four cases just from the data. Hence, a combinedcorrection of dwell time data was applied, aiming at covering all mentionedpossibilities. For that, if a sequence of two or more button presses occurred,the whole sequence was deleted. This approach covers all four possibilitiespresented here. It reduced the number of dwell times drastically for someparticipants so that their data could not be used for further analysis.In the NC-pers study, all in all for 7 of the 65 participants, dwell time datawas insufficient, resulting in 58 data sets to be used for the complete study.In the NC-dist study, one data set for bistable perception had to be excludedbecause of insufficient amount of data after correction, so that 22 data setscould be used.After these corrections, measures describing the reversal process were de-termined. Mean and median dwell times were calculated directly from thecorrected dwell time data. Additionally, both the gamma and the lognormaldistribution were fitted to the data. It turned out that the lognormal dis-tribution has the best fit quality. The details will be described in Sec. 4.6.The fit parameters of these distributions were estimated with the maximumlikelihood method. Reasons for the choice of method and distributions aswell as more details about them are given in Chapter 4. In addition to thetwo parameters of each distribution, the mode, i.e. the position of the peakof the distribution, and the variance of the distributions were calculated andused for further analysis.

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4. Temporal Dynamics

This chapter will detail the temporal dynamics of bistable perception of theNecker cube, with a strong focus on the distribution of dwell times.

4.1 StationarityBefore exploring the details of the dwell time distribution and finding ad-equate fit functions for it, the issue of stationarity of the dwell time distri-bution should be addressed.Several articles on bistable perception of the Necker cube mention an initialincrease of the number of reversals over roughly the first minute. Brascampet al. (2005) reported that a drift in dwell time data was restricted to thefirst 30 s of observation without showing data for this finding. Cohen (1959b)recorded the number of reversals in every 15 s. The authors found this meas-ure to increase and then to level off after one minute. Babich and Standing(1981) presented similar results with leveling after 75 s. Studying the actualdata given, though, the number of reversals in fact does not stay constant butvaries still. A complete constance of reversals would, of course, contradictthe stochastic nature of bistable perception. Sadler and Mefferd (1970), onthe other hand did not find such an increase in reversals within one minute.Furthermore, with a pile of cubes stimulus, Price (1967) found an initialdecrease of dwell times only for the preferred percept and a constant dwelltime level for the non-preferred percept. This stimulus is different from theNecker cube and might vary in its temporal dynamics.It should be note that the studies by Cohen, Babich, Sadler and their respect-ive co-workers had participants indicate reversals either verbally or with a

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tmean tmedian30 s 0.82 0.3760 s 0.91 0.79

Table 4.1: p-values of the Wilcoxon tests between the first and second 30 and 60 s, re-spectively, for both mean and median dwell times.

typewriter.1 The resultant data quality and precision is hence certainly lowerthan using a computer keyboard button or even a dedicated reaction timebutton, as is common today.The different results in the above studies might be due to differences in in-struction and in pre-training before the actual measurement. This is crucial,as participants have to clearly understand the instructions, memorise theresponse mode and gain a certain familiarity with the reversal process. Oth-erwise, an initial confusion or uncertainty with the task and procedure mightconfound the perceptual dynamics underlying the observation of an ambigu-ous figure. The importance of instructions was demonstrated by Rock andMitchener (1992) who showed that many participants do not reverse at all,if the alternative percept has not been pointed out to them.In order to exclude such confounding issues for the initial phase of the ex-periment, in both studies participants were first familiarised with the phe-nomenon of spontaneous perceptual reversals and the experimental task, asdescribed in Sec. 3.3. Both possible three dimensional percepts were ex-plained to the participants and the experience of at least one reversal wasrequired before beginning the experiment.In the NC-dist study, four reversals were awaited and furthermore, a waitingperiod of one minute was introduced before the measurement. In order totest whether there is an adaptation phase in the initial phase of perception ofthe Necker cube, mean and median dwell times of the very first measurementwere compared between the first and second half minute and one minute in-terval, respectively. I.e. mean and median dwell times were calculated for theintervals from 0 to 30 s and from 30 and 60 s as well as for those from 0 to60 s and 60 to 120 s. Both measures were tested for differences between thefirst and the second interval using Wilcoxon signed rank tests. In order toguarantee the use of the correct intervals, only data from participants with

1The participant would indicate every reversal by pressing a certain key, while theinvestigator would press a different key every 15 s.

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at least two and a half minutes of dwell time data was used. This resultedin the exclusion of 3 data sets, out of 23. The Wilcoxon tests showed thatthere were no significant differences between the first and the second intervalfor both measures and interval lenghts (cf. Tab. 4.1).Measures describing the dwell time distribution were not considered, as thereare too few dwell times in the respective intervals for a reliable estimation ofthe dwell time distribution. In order to explore stationarity of the dwell timedistribution, a way to increase the amount of available data points within ashort interval of time would have to be found. One possibility that could beconsidered for this would be normalising dwell times and merging data fordifferent participants (e.g. Pressnitzer and Hupé (2006)). The assumptionsmade in this approach would have to be tested thoroughly, though.One can conclude that after a short training and waiting phase, as implemen-ted here, there is no evidence for a significant systematic decrease in dwelltimes within the first 30 or 60 s. This finding is in agreement with a studyby Nakatani and van Leeuwen (2006) who did not find an initial decreasein dwell times while still reproducing the usual temporal dynamics in termsof the dwell time distribution. One prerequisite to observing stable meandwell times is, of course, that participants are aware of the reversal phe-nomenon and have experienced it clearly. Instructions do play an importantrole for this as Rock and Mitchener (1992) already showed. The authorsdemonstrated that ignorance of the reversal process would prevent reversalsfor as much as 70% of participants in the first 30 s. Thus, the existence ornon-existence of an initial decrease in dwell times in different articles in theliterature on bistable perception of the Necker cube might be related to theway instructions are given.For the current purposes, it is sufficient to observe that after familiarisationwith the reversal phenomenon mean dwell times do not change significantlyover the initial phase of observation so that all dwell time data can be usedfor further analysis.

4.2 ReproducibilityAs detailed in Sec. 1.3.3, Guilford and Hunt (1931) and Frederiksen andGuilford (1934) showed that the mean number of reversals per time intervalwhen the Necker cube is fairly stable within one person. In a small pilotstudy, four participants viewed the drawing of a Necker cube on consecutive

50

days at roughly the same time. Viewing angle varied slightly between parti-cipants, but was kept constant for the same person. No chin rest was used.The other experimental details and the data analysis were as for the NC-distand NC-pers studies, described in Chapter 3. Participants viewed the Neckercube neutrally for three minutes, i.e. without exercising voluntary control.Also, they had a short practice session in order to familiarise with the task.Mean dwell times for day 2 were highly significantly correlated to those ofday 1 (r = 0.99, p = 0.008, Pearson correlation coefficient). Furthermore,the dwell time distributions within participants were compared between dayswith the Wilcoxon rank sum test (also referred to as the Mann-Whitney test).For none of the participants was there a significant difference between days(p = 0.63, 0.67, 0.97 and 0.47, respectively).These results confirm the findings of Guilford and co-workers on reproducib-ility between days, as the reproducibility of mean dwell times also implies theone of the number of reversals. Additionally, they show that also the dwelltime distribution is fairly reproducible. This is an important confirmationof the relative stability of perception of bistable stimuli. It motivates thesearch for related intra-individually stable measures, which will be detailedlater (Chapters 7 through 11).In the following, a more detailed examination of the distribution of dwelltimes shall be pursued.

4.3 Dwell Times and Their DistributionBistable perception is characterised by the stochastic nature of perceptualswitches. That means that the timing of a perceptual switch cannot be ex-actly predicted. One can only estimate the probability of a perceptual switchto occur after a particular time. Assuming that the ongoing reversal processis stationary (as discussed in the previous section), the probability densityfunction (PDF) of dwell times can be estimated from a sufficiently large setof dwell time data. For every dwell time t the probability density functionp(t) gives an estimate of how likely the occurrence of this particular dwelltime will be. The estimation of the PDF can either be done using a paramet-rised function that closely fits the observed dwell time data, like the gammaor the lognormal distributions, or a non-parametric function can be determ-ined, using for example kernel density estimation (KDE).Instead of using the whole dwell time distribution p(t) as a means of quan-

51

tifying the reversal process for one given observer, it is also possible to onlyconsider certain characteristic measures of the dwell time distribution, likethe mean, the median or the modal dwell time. The mean dwell time, inthe following indicated with t̄, can be estimated either by calculating thearithmetic mean of the recorded dwell times or by fitting a parametric PDFand calculating its mean. Analogously, the median, t̃, can be estimated intwo ways: either calculating it directly from a parametric PDF or by findingthat value in the data that separates the lower from the higher half of thesample.2 The mode, which will be labelled t0 in the following, is that value ofa random variable which is most likely to occur, i.e. it is the point where thePDF has its maximum. It can thus be directly calculated from a parametricPDF. It can also be determined from a non-parametric PDF by finding itsmaximum. On the other hand, the mode cannot be estimated directly frommeasured values of a continuous random variable, in this case dwell times,without further assumptions.3As mean, median and mode are, in each case, measures describing only onecharacteristic of the full PDF, a good estimation of the PDF provides a moredetailed description of the temporal dynamics of bistable perception. On theother hand, measures describing central tendency of the dwell time distri-bution, in particular mean and median, seem to be more robust and hencethese measures are more likely to be the better choice for small data sets.Nevertheless, it is important to try to gain as thorough an understanding oftemporal dynamics as possible. This indicates the use of the full PDF andnot only one of its measures, e.g. the mean. In particular, this approachallows for the study of relations between the overall shape of the PDF andmeasures describing other aspects of cognition or personality, for example.Thus, first an overview over possible fitting procedures will be given, followedby a description of several parametric PDF’s that seem to yield good fits fordwell time data. Finally, the issues of fit quality and the stationarity of thedistribution of dwell times will be approached with the help of dwell timedata from the NC-pers study.

2If the number of data points is even, such a data point does not necessarily exist. Inthat case, the median is usually estimated as arithmetic mean of the smallest value in thehigher half of the sample and the largest value in the lower half.

3To estimate the mode from a large enough set of measured values of a continuousrandom variable, one can discretise the data by introducing a binning. The mode will bethe mid-point of the bin with the highest number of data points in it.

52

4.4 Fitting Dwell Time DistributionsThere are two popular candidates for fitting dwell time data of the Neckercube: the gamma and the lognormal distribution (Borsellino et al. (1972);De Marco et al. (1977); Zhou et al. (2004)). Two parametric methods wereconsidered to fit these two distributions to dwell time data, namely the “leastsquares” and “maximum likelihood” methods. Furthermore, a non-parametricprocedure, “kernel density estimation” (KDE) was used to estimate the prob-ability density function (PDF) of dwell times.

4.4.1 Kernel Density EstimationThe PDF of dwell times can be approximated non-parametrically by a weigthedsum of kernels for each data point. Here, Gaussian, i.e. normal, kernels wereused with the Matlab routine ksdensity. The mode of the dwell time distri-bution is then found as the position of the maximum of the PDF. Note thatthe width of the kernels is not uniquely fixed but was adjusted according tothe variance of the data.

4.4.2 Least Squares MethodIn the least squares method those values of the distribution parameters arefound that minimise the sum of the squared differences between fit functionand empirical cumulative distribution function (CDF). Sorting dwell times inascending order, the empirical CDF is found as a step function that increasesby 1

neach time the next larger dwell time is reached on the time axis, where

n is the number of dwell times. The quality of least squares fits, as for KDE,depends on the number of sampling points. Compared to KDE it has theadvantage, though, that it yields values for the two parameters of the gammadistribution, so that both PDF and CDF, as well as other measures of thedistribution, like mode, variance etc., can be calculated.

4.4.3 Maximum Likelihood EstimationThe maximum likelihood method finds that set of parameter values of theconsidered model that is most likely to have produced the current set of data.This is done by maximising the log-likelihood, the logarithm of the joint dens-ity function for all observations, with respect to the parameters of the model,in this case the gamma and of the lognormal distributions. Thus, as with

53

least squares, the maximum likelihood method yields the parameters of theconsidered distribution from which CDF, PDF and measures of the distribu-tion can be calculated. An advantage of this method is that no assumptions,like finding a bandwidth or determining sample points, are needed. Usingthe Fisher information matrix, estimates of the standard deviations of theparameters of the fitted distribution can be determined.Because of these two advantages over the other two methods, here, the max-imum likelihood estimation will be preferred over KDE and least squaresfits.

4.5 Probability Density Functions

4.5.1 The Gamma DistributionSeveral authors (De Marco et al. (1977); Borsellino et al. (1972); Brascampet al. (2005)) found that dwell time distributions can be modeled using thegamma distribution. The following parametrisation of the gamma distribu-tion is used throughout this treatise:

fγ(t) =ba+1

Γ(a+ 1)tae−bt (4.1)

where a, b ∈ R, with a > −1, b > 0 and Γ(x) is the gamma function. Thegamma distribution is a right-skewed, unimodal distribution. Its mode, i.e.the t-value of its maximum, can easily be calculated analytically. DefiningC := ba+1

Γ(a+1), the first two derivatives of fγ(t) are:

f ′γ(t) = Cta−1e−bt(a− bt)f ′′γ (t) = Cta−2e−bt(a(a− 1)− 2abt+ b2t2)

(4.2)

In order to determine the maximum of fγ one sets f ′γ(t0,γ) = 0 yielding

t0,γ =a

b(4.3)

as the only non-vanishing solution. The second derivative of fγ at t0,γ is

f ′′γ (t0,γ) = C(a

b)a−2e−2(−a) < 0 (4.4)

for a, b > 0. Hence the gamma distribution has a local maximum at t0,γ = ab

for a > 0.

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For −1 < a ≤ 0, fγ(t) is monotonically decreasing for t ≥ 0, but thiscase is not really relevant for dwell time distributions as the dwell times arebounded from below by a finite reaction time of participants. Hence for theexperimental data one would always expect a peak at a t-value larger than0, even though a small amount of data points might lead to a fit result of−1 < a ≤ 0.

4.5.2 The Lognormal DistributionAnother candidate for modeling dwell time data of the Necker cube is thelognormal distribution (Zhou et al. (2004), Krug et al. (2008)). The followingparametrisation shall be used here:

flogn(t) =1

t√

2πσ2e−

(ln(t)−µ)2

2σ2 (4.5)

where µ, σ ∈ R.As the gamma distribution, the lognormal distribution is right-skewed andunimodal. The mode can be determined by calculating the first two derivat-ives

f ′logn(t) = −e−(ln(t)−µ)2

2σ2 · 1

t2√

2πσ2(1 + ln(t)−µ

σ2 )

f ′′logn(t) = e−(ln(t)−µ)2

2σ2 · 1

t2√

2πσ2(3 ln(t)−µ

σ2 + (ln(t)−µ)2

σ4 + 2− 1tσ2 )

(4.6)

and setting f ′logn(t0) = 0 which yields:

t0,logn = eµ−σ2

(4.7)

One finds that

f ′′logn(t0,long) = − e−σ2

2

σ2e3(µ−σ2)√

2πσ2(4.8)

which is negative for µ, σ ∈ R. Hence, t0,logn = eµ−σ2 is always an absolute

maximum of the lognormal distribution for any real µ and σ.A noteworthy property of the lognormal distribution is its invariance underinversion. This means that if a random variable X is lognormally distributedwith parameters µ and σ, then 1/X is also lognormally distributed withparameters −µ and σ.

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4.5.3 Other PDF’sApart from the gamma distribution and the lognormal distribution, for fittingdwell time data both the Weibull distribution

fWeibull(t) = ba−btb−1e−( ta

)b a, b > 0 (4.9)

and the Rayleigh distribution

fRayleigh(t) =t

σ2e−

t2

2σ2 σ > 0 (4.10)

can be considered.The Weibull distribution is unimodal and right-skewed for b > 1. In fact,it is a generalisation of the Rayleigh distribution and for b = 2 the Weibulldistribution equals the Rayleigh distribution with a2 = 2σ2.Zhou et al. (2004) tested the fit quality of the Weibull distribution for dwelltime data of the Necker cube but found that it is inferior to the gamma andlognormal distributions. The Rayleigh distribution has not been evaluatedyet for a fit of dwell time data.

4.6 Fit QualityThe fit quality of the gamma, lognormal, Weibull and Rayleigh distributionsfor dwell time data of the Necker cube were evaluated. Dwell time data of58 participants (29.0± 9.5 years, 27 male) from the neutral condition of theNC-pers study was used for the analysis. Data of 7 participants of the avail-able 65 was not used because of too many multiple subsequent presses of thesame button occurred. After familiarisation with the reversal process eachparticipant viewed the Necker cube for 3 minutes and indicated reversals viabutton presses. Participants were instructed to passively view the Neckercube, i.e. not to try to influence the reversal process. Further details on ex-perimental procedure and first analysis are given in Secs. 3.2, 3.3 and 3.4.Each data set was fitted with each of the distributions described above. Ad-ditionally, inverse dwell times were fitted with the gamma distribution inorder to reproduce a report by Brascamp et al. (2005). The authors fitteddwell times with gamma and beta prime distributions as well as inverse dwelltimes with gamma distributions and found that the goodness of fit was bestfor the inverse dwell time gamma fit, which they called “gamma rate” fit.

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As this rate fit produces good results also for the current data, here, the rateswere also fitted with the lognormal distribution. This will be referred to aslognormal rate fit or as the lognormal rate distribution.All distributions were fitted over the same interval of the t-axis, namely fromzero to the longest dwell time that occurred. Exemptions are the gammarate and the lognormal rate fits for which the fit interval from zero to thelargest inverse dwell time was used.In the present analysis, goodness of fit, i.e. the fit quality, was then evaluatedusing (1) the sum of squared errors (SSE) and (2) Monte Carlo Kolmogorov-Smirnov tests between empirical and fitted cumulative distribution func-tions (CDF’s).

4.6.1 Measures of Goodness of Fit

Sum of Squared Errors

The SSE is determined by calculating the CDF for the experimental dwelltime data and for the fitted function. For numerical computation of theempirical CDF a discrete sampling has to be chosen. Here the maximal dwelltime, tmax, over all participants was determined and divided into 5000 stepsfor sampling. The CDF of the fitted PDF is found by integrating the PDFfrom zero to each sampling point. In general, the CDF of a continuous PDF isgiven as the probability that the random variable T takes any value smalleror equal to a certain value t, i.e.: FCDF,T (t) = P (T ≤ t). For a positive,real-valued random variable as in the present case, the CDF is calculated byintegrating the PDF up to the given value t: FCDF,T (t) =

∫ t0f(t′)dt′, where

f(t) is the fitted PDF.The SSE is the sum of the squared difference between the empirical andthe fitted CDF at each sampling point. I.e. SSE =

∑i(FCDF,emp(ti) −

FCDF,fit(ii))2. As a measure of goodness of fit SSE/(n − 2) was calculated,

where n is the number of sampling points used for the CDF’s. The lower thisvalue, the better the fit.

Monte Carlo Kolmogorov-Smirnov Test

As a further measure of goodness of fit, Kolmogorov-Smirnov (K-S) tests wereperformed between the empirical and the fitted CDF. The K-S test checks theNull-hypothesis of equality of two continuous, one-dimensional probabilitydistributions. The one-sample K-S-test which was used here compares an

57

experimental sample with a reference distribution. The K-S test statistic isdefined as:

Dn = supt|Fn(t)− F (t)| (4.11)

where Fn(t) is the empirical CDF for a sample of n observations, i.e. n dwelltimes. F (t) is the CDF of the fitted probability density function. I.e. geo-metrically, the test statistic Dn is the maximal vertical distance between theempirical and the fitted CDF.Dn is then compared to critical values of the Kolmogorov distribution. Thus,it can be decided whether the Null-hypothesis should be rejected or not. Also,p-values corresponding to each Dn are tabled.If the reference distribution contains parameters that are estimated from thesample, then the critical values determined from the Kolmogorov distribu-tion are too conservative, though (Woodruff et al. (1984), Massey (1951)).I.e. the actual critical values would be lower. This is because by estimat-ing the parameters of the PDF from the given data will change the relationbetween Fn(t) and F (t) and hence the distribution of the test statistic Dn

(Keutelian, 1991).The K-S test can still be conducted, but the proper critical values of thetest statistic Dn have to be determined. This can be done by estimating thedistribution of Dn using Monte Carlo methods (Keutelian, 1991; Lilliefors,1967; Woodruff et al., 1984). Keutelian used this approach for a Gaussiandistribution for which the parameters had been estimated from the data thatwas tested. He introduced the notation DNp to label the test statistic inthe case of estimated parameters. Using Monte Carlo simulations he demon-strated that the distribution of DNp was indeed shifted to the left comparedto that of DN . In other words, the modified K-S test yielded lower criticalvalues.The Monte Carlo approach had to be used here as well because all considereddistributions were fitted to the empirical data and were not given a priori.Note, that this approach was not used in the cited publications (Brascampet al., 2005; Zhou et al., 2004), i.e. the critical values of the K-S test usedin these articles were not modified to accommodate the fact that paramet-ers were estimated from the tested data. Thus, a difference in p-values andrejection rates to the results presented below is reasonable.In the present analysis, first, for each data set the parameters of the distribu-tions were determined with the maximum likelihood method. Then the Nulldistribution of the test statistic was estimated with Monte Carlo methods,

58

i.e. the distribution of Dn when the Null hypothesis is true. For that, foreach parameter value pair (or single value, in case of the Rayleigh distri-bution) a large number of data sets, 1000 in this case, were sampled fromthe corresponding distribution function. This was done with correspondingsampling algorithms available in Matlab. All sampled data sets were of thesame size as the original one. For each sampled data set the test statisticDn = supt |Fn(t) − F (t)| was calculated. From these 1000 values of Dn, acumulative distribution function was calculated as described in Sec. 4.4.2.Thus, an estimate of the CDF of Dn was obtained for each fitted function.The critical value for the modified K-S test then is the 1−α abscissa of thisCDF, where α is the desired confidence level. Here α was set to 0.05 andthe corresponding value was used to determine whether the Null hypothesiswould be rejected or not. The p-value of the modified K-S test is 1 minus theordinate of the value of the test statistic Dn calculated from original sampleand fitted distribution.For each set of dwell time data and each distribution described above, thisp-value, labelled pKS, was calculated as a measure of goodness of fit. A highpKS-value indicates that the Null hypothesis most likely does not have to berejected, i.e. that both distribution are equal. A low pKS, particular below0.05, means that the hypothesis of empirical and fitted distribution beingequal should be rejected. Thus, the larger the pKS, the lower the probabilityof rejecting the Null hypothesis of equality of distributions and hence thebetter the fit.

4.6.2 Comparing Fit QualityFor each data set and each fitted distribution both SSE/(n−2) and pKS werecalculated. The results were plotted as boxplots and are shown in Fig. 4.1.Both measures basically show similar results, thus reinforcing each other.The lognormal rate and the gamma rate distributions yield the best fits interms of the SSE, as both their medians as well as the 25%-to-75%-boxesand the whole sample are lower compared to all the other distributions. Thelognormal rate distribution is somewhat better than the gamma rate; medi-ans of SSE being 1.93 and 2.23, respectively. The lognormal distribution isin third place and followed by gamma, Weibull and finally Rayleigh distri-bution.In terms of pKS-values, the picture is slightly different. Gamma rate andlognormal distribution exchange places. That is, the lognormal rate distri-

59

0

0.2

0.4

0.6

0.8

1

lognormal logn. rate gamma gamma rate Weibull Rayleigh

pKS

<−−

bad

fit

g

ood

fit −−>

0

1

2

3

4

5x 10−3

lognormal logn. rate gamma gamma rate Weibull Rayleigh

SSE/

(n−2

)

<−−

good

fit

b

ad fi

t −−>

0

0.2

0.4

0.6

0.8

1

lognormal logn. rate gamma gamma rate Weibull Rayleigh

pKS

<−−

bad

fit

g

ood

fit −−>

0

1

2

3

4

5x 10−3

lognormal logn. rate gamma gamma rate Weibull Rayleigh

SSE/

(n−2

)

<−−

good

fit

b

ad fi

t −−>

Figure 4.1: Boxplots of SSE and pKS for 58 observers of the Necker cube as measures ofgoodness of fit for all considered distributions. For the sum of squared error (SSE, toppanel), a small number mean a good fit. For pKS a value close to 1 indicates a good fit.

60

bution again produces the best fit, judged by taking into account the medianand the 25%-to-75%-boxes. Second best is the lognormal fit. Only after thatcome the gamma rate and gamma distributions and finally the Weibull andRayleigh distributions. Looking at the number of rejected data sets, the sameorder is discovered. The amount of data sets for which the modified K-S testrejects the Null hypothesis at the 0.05-level is smallest for the lognormal ratefits (6, 10% of all data sets), followed by lognormal fits (10; 17%), gammarate fits (12; 21%), gamma fits (20; 34%), Weibull (28; 48%) and Rayleighfits (40; 69%).As a control, the same analysis was repeated on dwell time data of the NC-dist study. One data set was excluded from the analysis due to a very highincidence of multiple button presses which suggests that the instructions werenot correctly understood. Also, correction of these response patterns as de-scribed in Sec. 3.4 would decrease the amount of available data points toomuch. Hence, dwell time data of 22 participants (25.9± 7.9 years, 12 male)of the cube covering a visual angle of 5 ◦ was used. Thus, the experimentalconditions are almost identical to the NC-pers study. The only variation wasthe viewing distance which was shorter for the NC-pers study. This shouldin principle not influence the results as the retinal image for participants wasthe same in both studies because of the same viewing angle.The results of the goodness of fit analysis are similar to those of the NC-pers data and shown in Fig. 4.2. In terms of the SSE, the lognormal ratedistribution provides the best fit. Only slightly worse is the gamma rate fit,followed by lognormal, gamma Weibull and Rayleigh distribution. In termsof pKS-values, the lognormal distribution clearly yields the best fit, followedby the lognormal, gamma rate, gamma, Weibull and Rayleigh distributions.Rejection rates of the modified K-S test are: lognormal rate: 9%, lognormal:23%, gamma rate: 27%, gamma: 32%, Weibull: 41% and Rayleigh: 68%.Again, this is similar to the results of the NC-pers study.Between both studies, one can conclude that the lognormal rate distributionprovides the best fit for dwell time data, both in terms of SSE and pKS.Lognormal fits and gamma rate fits take the second and third place, respect-ively. The gamma distribution, which is widely used in order to fit dwelltime data only comes in fourth place, followed by Weibull and Rayleigh dis-tributions.One should note, though, that the lognormal distribution is invariant underinversion (cf. Sec. 4.5.2) and hence the lognormal rate fit and the lognormalfit are equivalent – a property that does not hold for the gamma and gamma

61

rate distributions. Inspection of the results of the maximum likelihood showsthat the fitted parameter values of the lognormal and the lognormal rate fitsare in fact identical. Thus, no new information is generated by fitting theinverse dwell times with the lognormal distribution compared to the originaldwell times. But as SSE and pKS show, neither dwell times nor rates areperfectly lognormally distributed. The empirical dwell time distribution dif-fers from the lognormal distribution in a certain way. This difference is ingeneral not invariant under inversion. That is why both SSE and pKS aredifferent between the lognormal and the lognormal rate fit and why a differ-ent fit quality is found for times and rates. This is in fact confirmed by ananalysis of fit residuals in Sec. 4.6.3, that shows a somewhat different shapeof the residual curves of the lognormal and lognormal rate fits.As the two lognormal fits are equivalent and as the lognormal distributionconstitutes the second best fit – at least in terms of pKS values – it is ap-propriate to use the lognormal distribution in order to describe the dwelltime distribution for bistable perception of the Necker cube. This providesthe advantage that the description is in terms of times and not inverse times.While the former have a clear correspondence to the perception of the Neckercube, namely as an estimation of the time between perceived reversals of per-spective, the inverse times do not have such a correspondence, i.e. they arenot directly relatable to the observation of the ambiguous figure. This isalso an advantage of the lognormal fits over the gamma rate fits. Here, thisadvantage as well as the clearly higher pKS-values of the lognormal fits com-pared to the gamma rate fits are judged more important than the better SSEvalue of the gamma rate fits. Hence, the lognormal distribution will be usedthroughout this work in order to describe the perception of the Necker cubeas it provides the best combination of fit quality and descriptiveness.A few more remarks concerning the pKS-values are appropriate. The numberof rejected fits for Weibull and Rayleigh distributions indicate that these twofunctions are clearly not appropriate fitting functions. Also for the gammadistribution, a significant portion of the fits, namely one third, have to berejected. One should further note that no rejection of the Null hypothesisof equality, i.e. pKS > 0.05, does not imply that the fit is necessarily a goodone. It only means that in terms of the test statistic, the tested fit fallswithin the region that covers 95 % of the sampled data. To speak of a goodfit, pKS values significantly larger than 0.05 would be desirable. Even for thegamma rate and the lognormal distributions, a bit less than 20% of data setsare not fitted adequately. This may of course be due to the low number of

62

data points, i.e. dwell times, in each data set (mean number of dwell timesper participant were about 45). Also, in a bistable perception experiment asdescribed here, it is very likely that there is always a lower bound for dwelltimes introduced by the finite reaction time of participants. This hypothesis,of course, only holds if one assumes that the steps “perceptual reversal”, “but-ton press”, “next perceptual reversal” and “next button press” are all at leastpartially sequential. Mean reaction time as measured with a Go/Nogo taskwas roughly 180ms for this group of participants (for details cf. Chapter 10).Thus, under this hypothesis, a discrepancy between empirical CDF and fittedCDF is likely to exist for small times, as the empirical CDF must be always0 for times smaller than about 200ms, whereas the fitted CDF has a finitevalue in this range.How do these results compare with findings of other researchers? The lognor-mal distribution was reported to provide better fits than the gamma distri-bution by several groups (Brascamp et al., 2005; Krug et al., 2008; Zhouet al., 2004). Brascamp et al. (2005) found the gamma rate distribution tobe superior compared to the lognormal distribution, which is at odds withthe current results. Furthermore, the rejection rate of the K-S test reportedby the same authors is lower. Probably the main reason for this discrepancyis that the modified K-S test was used here in order to account for the com-parison of an empirical cumulative distribution function with one fitted tothe former. Also, Brascamp et al. (2005) did exclude the smallest and largest2 % of their dwell time data from the analysis, which was not done here. Itis reasonable to assume that these variations in analysis method explain thediscrepancies found.In conclusion, it was found that the most appropriate fit for dwell time dataof bistable perception of the Necker cube is achieved by the lognormal dis-tribution for the dwell times. In the NC-pers and the NC-dist study, forroughly 17 and 23% of data sets, respectively, this fit was rejected by themodified Kolmogorov-Smirnov test using Monte Carlo simulations to estim-ate the critical values. Even though the lognormal rate fit performed betterin terms of fit quality, as it is equivalent to the lognormal fit and less usefulin terms of descriptiveness, the lognormal fit to dwell times is preferred. Thegamma distribution, which is widely accepted as a good fit for dwell timedata in bistable perception, has a rejection rate of about one third at the0.05-level, thus clearly not being an ideal fit.With the necessary care, the lognormal distribution can be taken as an ap-propriate description of the temporal dynamics of bistable perception of the

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Necker cube. Hence, the parameters and measures of the lognormal fits willbe used in the following chapters to explore bistable perception of the Neckercube and its potential relations to other domains, like cognition, temporalprocessing and personality.Before those analyses, fit residuals will be discussed in the following section.

4.6.3 Fit residualsAnother way to study the quality of the fits is to examine the fit residuals.Fit residuals are the differences between empirical and fitted dwell time dis-tribution. Residuals were studied here in analogy to the analysis presented inBrascamp et al. (2005). For that, the differences between empirical and fittedCDF were calculated for lognormal, lognormal rate, gamma and gamma ratefits. These differences were binned with respect to a detrended ordinate: thetime value in each time-residual data pair was substituted by the correspond-ing probability value of the empirical CDF, so that residual plots of differentparticipants could be averaged in spite of differences in the variance of thedistributions. The same was done for the rate-residual data pairs in caseof the lognormal rate and the gamma rate fits. After this detrending step,every participant has an unevenly and differently spaced ordinate. Hence,residuals of all participants were collected in 20 equidistant bins covering theordinate interval [0, 1]. Each bin then contains a varying number of residuals.For each such bin, and each fit method, mean residuals were calculated andplotted vs. bin ordinate.The results are plotted in Fig. 4.3. The lognormal rate distribution showsthe lowest residuals, with a more or less flat curve. The residuals of thelognormal fit are similar, but a bit larger for medium probabilities and smal-ler for low and high probabilities. This demonstrates again the differencein fit quality between lognormal and lognormal rate fits mentioned in theprevious section. The gamma rate distribution shows a peak just below 60%probability, which is also present for the gamma fits, but much broader andalso higher.Thus, this analysis confirms that the best fit quality is achieved by fittingthe inverse dwell times with a lognormal distribution, while the lognormalfits to the dwell times do not perform much worse. It is noteworthy that allresidual curves are positive, which means that the fitted CDF lies below theempirical. I.e. all fits systematically underestimate the actual distribution.This finding could be one starting point to further improve fit quality.

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Figure 4.2: Boxplots of SSE and pKS for 22 observers of the Necker cube in the NC-diststudy. The cube size was 5 ◦ of visual angle. Note that part of the SSE boxplot for theRayleigh distribution is out of the range of the plot – this was not corrected to allow forbetter readability of the other distributions.

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Figure 4.3: Fit residuals as calculated from the difference between empirical and fittedcumulative distribution function for lognormal rate, lognormal, gamma rate and gammafits. Ordinates were transformed from time and rate, respectively, to probabilities, whichis referred to as detrending and allows the comparison between participants with differenttemporal dynamics in bistable perception. Standard deviations were not plotted in orderto retain readability of the plot.

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5. Stimulus Properties

After the exploration of dwell time dynamics in the last chapter, in this one,low level stimulus properties will be considered. First, the question of theinfluence of cube size on perception of the Necker cube will be addressed.Subsequently, a potential hysteresis effect will be explored.

5.1 Size of the Necker Cube

5.1.1 Reports on the Effect of Cube SizeThere are several studies on the Necker cube that explored the influence ofstimulus size on the number of reversals. Already Washburn et al. (1931)tested three cube sizes of visual angles 0.7, 7 and 64 ◦ with a small sampleof female participants who indicated reversals verbally. The authors foundthat the large cube would have less reversals than the smallest one. Duggerand Courson (1968) considered three visual angles, namly 3, 8 and 13 ◦, andfound a significant decrease in number of reversals from 8 to 13 ◦, again usingverbal reports. Testing sizes of 2.6, 12.8 and 25.1 ◦, Bergum and Flamm(1975) also discovered a significant decrease of the number of reversals withincreasing cube size. In this study, dwell times were recorded using buttonpresses, thus providing a higher accuracy than the two studies mentionedbefore. Borsellino et al. (1982) covered a broad range of sizes (0.9, 1.7, 8.6,17, 33.4, 61.9 ◦) and reported a plateau with respect to mean dwell timesbetween 5 and 20− 30 ◦.These results all indicate that dwell times increase with increasing visualangle. The goal of the experiment presented in the next section was toexplore the lower range of cube sizes in order to gain a finer description ofsize dependence.

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t̄ t̃ t0,logn µ σ varlognp 0.06 0.11 0.31 14.28 0.09 0.01χ2 9.16 7.56 4.76 6.87 8.07 12.80

Table 5.1: p-values and χ2 of Friedman tests for mean and median dwell times, mode,parameters and variance of the lognormal fit for cubes of sizes of 1, 2, 3, 5 and 6 ◦.

5.1.2 Comparing Five Cube SizesIn Section 4.1 it was shown that after a short training phase there is nodistinct initial phase in the perception of the Necker cube. Hence, for testingthe effect of size on bistable perception all data of the NC-dist study couldbe used – after correction for double presses. Thus, dwell time data for cubesizes of 1, 2, 3, 5 and 6 ◦ of 22 participants (25.9 ± 7.9 years, 12 male) wastested for differences. As in Chapter 4, data of one participant was excludeddue to a high amount of multiple subsequent button presses. The data forthe cube size of 4 ◦ was not used in order to prevent position effects, as themeasurements of this cube size were performed at the beginning and the endof the measurement series of each participant.Friedman tests were performed on mean and median dwell times as well ason the parameters of the lognormal fit and its mode and variance. This wasdone in order to check for significant differences between the perception ofcubes covering visual angles of 1, 2, 3, 5 and 6 ◦.

5.1.3 ResultsResults of the Friedman tests are shown in Tab. 5.1. None of the testedmeasures show a significant effect for size, with the exception the variance ofthe lognormal fit. The mean dwell time is very close to significance.Fig. 5.1 displays the mean values and the standard deviation of mean dwelltimes, median dwell times, the mode and the variance of the lognormal fitsplotted against cube size.

5.1.4 DiscussionThe Friedman tests indicated only a significant effect of cube size for thevariance of the lognormal fit. Inspection of the data showed that this is dueto the data set of one participant for the cube covering 3 ◦ with a very highvariance (cf. also Fig. 5.1, bottom right). The significant result indicated by

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Figure 5.1: Size dependence of mean (left) and median dwell times (right) as well as themode (bottom left) and variance (bottom right) of the lognormal fit for different visualangles. For each measure, mean values are shown with standard deviations.

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the Friedman test for the variance is thus not a systematic result and can beneglected being the consequence of an outlier.Considering the other measures, namely mean, median and modal dwelltimes, there is an overall trend towards an increase in dwell times with in-creasing cube size. This finding is in agreement with the studies cited abovethat have explored size dependence for the Necker cube. Notably, the presentstudy provides a higher resolution for small cube sizes compared to the citedarticles. It also shows that in order to properly resolve changes in dwelltimes with respect to cube size in this precision, a higher statistical poweris needed, i.e. a larger number of participants, as the standard deviation islarger that the effect size.The dependence of reversal behaviour on cube size in this lower range is ofspecial interest for research as many studies on the Necker cube use cubesizes covering visual angles of less than 10 ◦.Concerning the size dependence of dwell times in general, Long and Toppino(2004) suggested a tentative explanation, assuming an increased likelihood ofeye-movements for large stimuli compared to small ones. This would lead to adecrease first in stimulation of particular retinal regions and then a decreasein neural adaptation for the corresponding cortical structures. In the ex-planatory framework of mutually inhibiting, satiating neural processes, sucha decrease of adaptation then entails a slower satiation of the correspondingneural processes, which implies less perceptual reversals.

5.2 Hysteresis Effect

5.2.1 Hysteresis in (Psycho-)PhysicsIn order to further characterise bistable perception, perceptual hysteresis wasexplored in the NC-pers study. The term hysteresis (from “ὑστερέω”, ancientGreek for “to lag behind”) was first introduced into science by J. A. Ewing inorder to describe the change of magnetisation in relation to a cyclically chan-ging magnetising force: “Thus, when there are two qualities M and N suchthat cyclic variations of N cause cyclic variations of M, then if the changes ofM lag behind those of N, we may say that there is a hysteresis in the relationof M to N” (Ewing, 1885).Perceptual hysteresis is a similar effect in perception. One speaks of per-ceptual hysteresis if, when morphing (i.e. gradually changing) an image into

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another one and back again, the point in the morphing series at which theperception of an observer changes from the first image to the second is dif-ferent from the changing point in the other direction. Perceptual hysteresishas been described for a bistable, apparent motion stimulus by Hock et al.(1993). They formulated the definition of hysteresis as follows: “Hyster-esis is indicated when the transition from Pattern A to Pattern B, whichis observed when the parameter is gradually increased, occurs at a higherparameter value than the transition from B to A, which is observed whenthe parameter is gradually decreased.” This is basically a dicretised versionof Ewing’s definition above, i.e. one adapted to a discrete variable instead ofa continuous one such as magnetisation.The design of Hock and co-workers was adopted for bistable perception ofthe Necker cube in order to test for potential “lagging” effects.

5.2.2 Exploring Hysteresis of the Necker CubePerceptual hysteresis for the Necker cube was determined analoguely to theexperiments of Hock et al. (1993) who studied hysteresis for apparent mo-tion. Transition images between the two unambiguous variants of the Neckercube were created in 10 steps. This was achieved by gradually changing theopacity of the six relevant inner lines of the cube. Let 0 denote the unam-biguous variant A, 10 the variant B, analoguely for points in between.In each trial 11 transition images were displayed, each for 200ms. End-points of the transitions varied between image 0 and 10. The first image wasdisplayed for more than one step, if the end point of the trial was not the re-spective other unambiguous image. Thus, series like 0-0-0-1-2-3-4-5-6-7 werecreated, each series lasting for 2 s in total. The A-to-B series had 10 differentdegrees of transformations ranging from almost no transformation with 10%of percept B at the end of the series (image series: 0-0-0-0-0-0-0-0-0-0-1) tofull transformation with 100% of percept B at the end (0-1-2-3-4-5-6-7-8-9-10). The B-to-A series ranged from full transformation to A with 0% ofpercept B at the end of the series (10-9-8-7-6-5-4-3-2-1-0) to almost no trans-formation with 90% of percept B at the end (10-10-10-10-10-10-10-10-10-10-9). The display time of all series was kept the same so that no confoundinginfluence would be expected from varying display time. I.e. that switcheswould be more probable in one series because it was longer.10 trials for each of the 10 possible end points of the series were displayed,for morphing series from A to B and from B to A. This resulted in 200 trials

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in total, presented in random order. Participants were asked to indicate bybutton press after each trial whether they experienced a reversal in that trial.Trials were separated by a 1.5 s interval during which the participant’s re-sponse was collected.As the starting point of each series is unambiguous, the perceptual variantat the end point of a series is determined by whether the participant exper-ienced a reversal during its course. The possibility of multiple reversals islargely excluded by the short duration of the series. Thus, for each of the 10possible end points the probability to experience reversal was estimated asthe total number of reversals for each end point divided by 10, the total num-ber trials per end point. For the A-to-B curve, the reversal ratio correspondsto the ratio of trial for which the final percept is B. Similarly, for the B-to-Acurve the reversal ratio indicates the ratio of trials for which percept A is thefinal percept. From these ratios, the means and the standard deviations werecalculated over all participants for each end point and both transformationdirections.Mean percept ratios were finally plotted as a function of stimulus trans-formation to percept B for both the A-to-B transformation and the B-to-Atransformation. The axis for the ratio of percept A was inverted so thatboth axes, if read from bottom to top, display the amount of trials for whichpercept B was seen as final percept.

5.2.3 ResultsThe two curves for the transformations A-to-B and B-to-A are shown inFig. 5.2. The most striking effect seen in the graph is the fact that bothtransformation curves saturate at values lower than 1. In other words, tak-ing the A-to-B curve as an example, in about 40% of all cases percept B wasnot seen, even though the final percept was a completely unambiguous illus-tration of percept B. The analogue holds true for the B-to-A transformation.

5.2.4 DiscussionThe results found on the gradual transformation of the perspective of theNecker cube show a substantial methodological difficulty in testing for hys-teresis with the Necker cube. Namely, in both transition curves, A-to-B andB-to-A, the percept towards which the transformation moves is not exclus-ively perceived for a complete transformation. In other words, even if the

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Figure 5.2: The ratios of perception of B in the A-to-B transformation and perception ofA in the B-to-A transformation are plotted against the percentage of transformation fromA to B. The blue curve (A-to-B) reads from left to right, the green one (B-to-A) fromright to left.

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last percept is unambiguously a representation of percept B, participants didnot see B in about 40% of the cases. This produces the problem that the endpoint of the transformation in one direction is not identical with the startingpoint of the transformation in the other. Thus, the explanatory power of thisexperiment is very limited in terms of hysteresis, as its description presup-poses a closed loop in parameter space spanned by the two variables involved.Here this is the degree of transformation to percept B and the ratio of trialswith B as last percept. In the original context of magnetisation the variableswere the field strength of the applied magnetic field and the magnetisationof the tested material.To illustrate the difference to the original report of hysteresis, a plot fromEwing (1885) is reproduced in Fig. 5.3. It can be clearly seen that the mag-netisation B on the vertical axis lags behind with respect to the appliedmagnetic force H, with a finite magnetisation at zero external force.In contrary to the physical example, perception of Necker cube as studiedhere provides the difficulty of a mixture of two effects. A potential hysteresiseffect is blended with the spontaneous reversal behaviour characteristic ofbistable perception. In case of the apparent motion stimulus used by Hock

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et al. (1993) this confounding seems to have been avoided. Maybe longertransformation sequences are necessary to reproduce these results for theNecker cube. The results presented here show that a stronger adaptationis necessary in order to design an experiment testing for hysteresis with theNecker cube.

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6. Bias Effect

Even though, the Necker cube is a very symmetric figure, there is a preferencefor one of the two percepts. This finding has been noted anecdotally byseveral researchers. A detailed quantitative description of this bias effect willbe given in this chapter. It is indeed a very interesting effect as it providesanother piece of evidence for high-level influences in bistable perception, afinding which will be discussed below.

6.1 Qualitative ReportsThere are several articles that mention a preference in the perception of theNecker cube, namely that it is preferably seen in the perspective from above(percept A). Troje and McAdam (2010) call this the “viewing-from-above”bias. In their work they find that the rotational bias in an ambiguously ro-tating shilouette of a dancer is due to an elevated viewpoint.Kornmeier et al. (2009) mention that “it is well known that the cube-front-side bottom is the preferred initial percept of most observers”. They referto two studies authored by John R. Price that demonstrate that mean dwelltimes over observers are longer for one percept than the other. In one case(Price, 1967) the stimulus is a “pile of cubes” reproduced from Warren (1919),and in the other it is a rotating wire cube (Price, 1969), which is ambigu-ous with respect to the perceived direction of rotation. Both studies do notquantify the strength of this bias. Furthermore, and more importantly, theyuse stimuli different from the Necker cube, so no direct conclusion can bedrawn to the Necker cube.Nakatani and van Leeuwen (2006) show fitting results of both the gammaand the lognormal distribution for both percepts separately. However, theydo not discuss the difference in dwell times or test whether the differences ingamma and lognormal parameters between the two percepts are significant.

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A study by Sundareswara and Schrater (2008) shows that the time spent ineach of the two perspectives of the Necker cube can be modulated by con-textual images depicting unambiguous cubes.Thus, it seems that there is a so-called “bias effect" for bistable perception,i.e. an asymmetry between the dwell time distributions for the individualpercepts. This bias can be context dependent. Up to now there is no studyquantifying this effect in terms of dwell times and their distributions forbistable perception of the Necker cube.Whether there is indeed a quantifiable, systematic bias effect for the Neckercube is an interesting question, as a priori the geometrical symmetry of thestimulus itself would suggest that there should be none. It is a further tesserain the conceptualisation of bistable perception in terms of “bottom-up” and“top-down” processes and phenomena (cf. Long and Toppino (2004)). A sys-tematic bias effect would be a further contribution to the phenomena clas-sified as “top-down” influences, because a symmetric visual stimulus wouldnot be expected to evoke an asymmetric response if it was an exclusivelylow-level phenomenon.

6.2 Quantifying the Perceptual BiasIn order to study the bias effect for the Necker cube, dwell time data of theneutral condition of the NC-pers study was examined for differences betweenthe two percepts A and B. Dwell time data of 58 participants (29.0 ± 9.5years, 27 male) was used for the analysis (7 data sets could not be used dueto insufficient data). After having familiarised themselves with the reversalprocess, participants viewed the Necker cube passively for 3 minutes and in-dicated perceptual reversals using two separate buttons depending on theircurrent percept. The Necker cube extended over 5 ◦ of visual angle. Forfurther experimental details refer to the description of the neutral conditionin Sec. 3.3.For data analysis, dwell times were separated by percept. Mean and me-dian dwell times were calculated for both percepts separately. Additionally,dwell time data of both percepts were fitted with the lognormal distribution,yielding estimates of the two parameters µ and σ as well as the mode t0,lognand the variance varlogn of the distribution. These measures were tested forsignificant differences between the conditions using the Wilcoxon signed ranktest. Multiple testing was corrected for by using the false discovery rate pro-

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t̄ ∗∗∗ t̃ ∗∗∗ t0,logn∗∗ µ ∗∗∗ σ ∗∗ varlogn

∗∗∗

0.85 s 0.64 s 0.20 0.18 0.05 8.2222.8% 19.8% 8.4% 16.2% 9.6% 134.6%

Table 6.1: Absolute (top) and relative (bottom) differences between measures for perceptA and percept B (left to right: mean and median dwell times, mode of the lognormalrate distribution, its parameters and variance). Positive values signify larger values forpercept A. Stars indicate the size of uncorrected p-values: ∗: p ≤ 0.05, ∗∗: p ≤ 0.01 and∗∗∗: p ≤ 0.001.

cedure (Benjamini and Hochberg, 1995). Mean values of all measures werecalculated for both percepts. Values for percept B were subtracted fromthose of percept A to determine mean absolute differences between percepts.By dividing by the smaller of the two values, relative differences betweenpercepts were calculated.

6.3 ResultsAbsolute and relative differences of the tested measures are given in Tab. 6.1.The positive values indicate that a measure is greater for percept A. In fact,all six tested measures are significantly larger for percept A compared topercept B. After correction for multiple testing with the false discovery ratemethod, the five correlations are all still significant at the 0.01-level.The effect sizes of the differences listed in Tab. 6.1 show that for percept Adwell times are significantly larger than for percept B (∼ 20% for mean andmedian dwell times, ∼ 8% for the mode). The variance of the lognormal fitis particularly sensitive to the differences, showing a very large effect size.

6.4 Seeing the Cube From AboveThe results presented here quantitatively demonstrate a perceptual bias ef-fect in terms of the distribution of dwell times for bistable perception of theNecker cube. It is shown that the perspective from above (A) is perceptuallyfavoured over the one seen from below (B). I.e. dwell times are longer forpercept A than for percept B. Furthermore, it was shown that the shape ofthe distribution of dwell times is different between percepts: both parametersµ and σ, as well as the variance of the distribution are significantly larger forpercept A. The effect of these differences in the distribution shape can also

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Figure 6.1: Dwell time distributions plotted from the means of the parameters of thelognormal fits over all participants. The blue curve displays the distribution correspondingto percept A, the green curve corresponds to percept B.

be seen in Fig. 6.1. Here, lognormal distributions were plotted separately forboth percepts using the mean values of µ and σ over all participants. Theblue curve corresponding to percept A is shifted to the right, compared tothe green one. This indicates longer dwell times and a higher variance. Theeffect of larger dwell times is captured most strongly in the mean dwell timesand the variance. Both measures are sensitive to the occurrence of very largedwell times, while the median and particularly the mode are less affected bythis. This is also reflected in the lower peak of the blue curve, representingpercept A. While the most probable dwell time, the mode, is not shifted somuch, the whole curve is flattened out towards the right. This indicates thatfor percept A large dwell times are more probable.These results show that the geometrically symmetric visual stimulus of theNecker cube indeed produces an asymmetric response pattern. Thus, the pro-cessing of this visual stimulus can not be exclusively “bottom-up”. I.e. theremust be at least some higher order processes involved, attributing slightlydifferent semantic content to both percepts. That bistable perception hasnot only low-level processes is not a new result. There are several aspects ofbistable perception evidencing high-level processes, such as voluntary control

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over perception (see e.g. van Ee et al. (2005) and Chapter 7), the influence ofattention (Strüber and Stadler, 1999) or the knowledge of reversibility (Rockand Mitchener (1992); tested for the Mach book stimulus, which similar tothe Necker cube). For a review about top-down and bottom-up aspects seeLong and Toppino (2004). But that there is a systematic bias effect forthe Necker cube is indeed a new contribution to this category of findings onbistable perception. The current results are hence in good agreement withthe existing knowledge on the reversal process.Finally, the question remains how this bias can be explained. It might behypothesised that cube-like objects, i.e. cubes or cuboids, are mainly per-ceived from a viewpoint higher than the object itself. For example boxes,books or dice are mostly seen from above. Only when they are lifted to beput on a high shelf for example, do we see them from below. Of course, onthe other hand, there are buildings which are often of rectangular shape andwe usually do not take a bird’s eye view of these structures. But we also donot see them dangling above our heads either, as Necker cube in percept Bdoes. So, it could be speculated that small cube-like structures do providefrequent priming to the “from above” percept of the Necker cube and rarepriming to the “from below” percept while large cuboids do not prime eitherpercept.Priming in bistable perception of the Necker cube has been described byLong et al. (1992). The authors show that a short display of a few seconds ofan unambiguous drawing of the Necker cube favours subsequent perceptionof the corresponding percept in the ambiguous version of the cube, i.e. thecorresponding dwell times are longer. Thus, a short display of the unam-biguous version acts as a prime. A longer display on the other hand leads toa decrease of the time spent in the corresponding percept for the ambiguousstimulus. This is attributed to neural fatigue or selective adaptation of theneural networks underlying figural reversal as a consequence of which the un-adapted percept then dominates perception (Long and Toppino, 2004). Thisadaptation is also called “reverse-bias” sometimes. This might be perceivedas being in disagreement with the “priming effect” suggested here to explainthe asymmetry between the two percepts. In fact, it does not. One hasto note that seeing cube-like objects in everyday situations more frequentlyfrom above than from below would actually not be one long priming leadingto a fatigue effect as described by Long et al. (1992). Rather, the manyinstances of comparably short perceptions of the above perspective may actas many short primes leading attention to percept A and thus prolonging the

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corresponding dwell times.This tentative explanation might be tested by trying to use cube-like objectsas primes for the Necker cube in a controlled experiment. In a two-groupdesign, in one group participants would be primed many times with a bird’seye perspective on a cuboid for short periods of times and at different retinallocations to avoid fatigue effects. The second group would receive similarprimes but from a worm’s-eye view, i.e. seeing the object from below. Dwelltime distributions of a subsequent Necker cube experiment could the be com-pared. If the dwell times for percept A would be longer for the first groupthan for the second, the presented hypothesis would be supported.

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7. Voluntary Influence

After having reported some properties of bistable perception of the Neckercube with a passive mindset in Chapers 4 to 6, in this chapter findings onvoluntary control over bistable perception and its relations to personality willbe described.

7.1 Volition in Bistability and PsychologyIn several studies it has been shown that bistable perception of the Neckercube can be influenced voluntarily. In fact, some participants of the stud-ies presented here spontaneously remarked that they were able to influencethe speed of alternations. In a two-group design, Pelton and Solley (1968)reported that there were significantly more reversals of the Necker cube ifthe participants were instructed to switch as often as possible compared tothe instruction to switch as little as possible. Voluntary control was reportedby Liebert and Burk (1985) to be correlated across different stimulus types,namely the Schröder staircase and a reversible screen stimulus, “suggestingthe presence of stable individual differences in ability to control perceptionvoluntarily”. In a more recent work, van Ee et al. (2005) compared volun-tary control between different bistable stimuli, three ambiguous figures andone binocular rivalry stimulus. The authors used “neutral”, “hold percept 1”,“hold percept 2” and “speed up” conditions, reporting significant differencesbetween these conditions. Furthermore, they found a clear ability to volun-tarily control perception and similar patterns of temporal dynamics acrossstimuli, with binocular rivalry being harder to control than rivalry betweenambiguous figures. Similarly, Strüber and Stadler (1999) demonstrated thatrivalry between ambiguous figures can be controlled better for content rivalrystimuli, like the duck/rabbit figure, than for perspective or figure-groundrivalry, e.g. Necker cube or vase/faces. The most extensive study in terms of

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conditions was performed by Kornmeier et al. (2009). The authors used threedifferent hold conditions, the previous ones plus an unspecific one, as wellas a speed up condition and examined the combined influence of voluntarycontrol and discontinuous presentation on bistable perception. The authorsfound that the effects of both influences were fully additive. These reportson voluntary control of bistable perception also showed that while reversalscould be slowed down or sped up by participants, it was not possible for themto prevent reversals altogether.1Two straight-forward strategies to influence perceptual reversals are oftenmentioned by observers of the Necker cube. The first is to use blinks to pro-duce a perceptual reversal. The second is the employment of gaze positionto hold a given percept or switch to the other one. In terms of a bottom-upvs. top-down categorisation, both of these strategies constitute bottom-upaspects of bistable perception, as they employ early, rather low-level featuresof vision. But voluntary control over reversal rates is particular interestingas a top-down feature – i.e. when mental effort is used to influence perceptionand not low-level phenomena like blinking.Let voluntary control be understood as top-down feature in the following,excluding potential effects of gaze position or blinking. Voluntary controlis then a quantifiable effect of conscious control of perception. As detailedin Sec. 1.1, bistable perception is a very important and interesting model inthe quest to understand consciousness because two conscious mental statesare associated with a constant external stimulus. The essential point is thatthe process of changing between these two mental states can at least approx-imately be quantified. One promising approach to understanding how twomental states exist during unchanging stimulation is to try and explore mod-ulation of the reversal process between those two states. That was exactlythe goal of the experiments described in this chapter.For that it was important to exclude bottom-up influences on reversals asmuch as possible. Head and eye movements can be reduced by using a chinrest and a fixation cross in the middle of the Necker cube. Thus, the head ofthe participant is stabilised and the person can rest their gaze on the cross.More important for the judgement of bottom-up influences are several studiesthat report that neither saccades (i.e. fast movements of the gaze) nor blinks

1A noteworthy outlier in this respect is the study of Carter et al. (2005), which demon-strated the extreme prolongation of dwell times by Tibetan Buddhist monks in binocularrivalry. These findings will be discussed in detail in Chapter 9.

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are essential for reversals of ambiguous figures but can play a big role in bin-ocular rivalry (van Ee et al., 2005). van Dam and van Ee (2005) examined therole of eye movements and blinks for slant rivalry, an ambiguous figure withtemporal dynamics comparable to the Necker cube. The authors found thatthere was no positive correlation between reversals and both saccades andblinks occurring before these reversals. van Dam and van Ee (2006) reportedthat for the Necker cube, saccades and gaze position did not determine per-ceptual reversals in a voluntary control paradigm.2 Toppino (2003) studiedthe combined effect of gaze position and voluntary control for the Neckercube simultaneously and found that the effects were additive. Furthermore,the influence of gaze position could be eliminated by using a small cube. Anarticle by Kornmeier et al. (2009) points in a similar direction, reporting thatparticipants exhibited high precision in fixation, so that gaze position couldbe eliminated as a confounding factor.Thus, predominantly top-down aspects of voluntary control are likely to becaptured in an experimental design that uses the following three features: 1)a chin rest to prevent head movements, 2) a fixation cross to reduce saccadesand 3) the instruction to exclusively rely on mental effort for voluntary con-trol to minimise the usage of blinking as trigger of reversals.Being able to access this high-level aspect of bistable perception, it is ofparticular interest to explore whether, and if so how, it is related to otherhigh-level processes and aspects of mind and person. In other words: is theability to influence bistable perception linked to personality characteristicsor cognitive processing? Cognitive aspects will be discussed in Chapter 10(temporal processing) and Section 11.2 (working memory capacity). The re-lations of personality traits to voluntary control on the other will be coveredin this chapter (with an entire chapter, namely Chapter 9, being dedicatedto the concept of mindfulness).The literature on relations between voluntary control over perception of theNecker cube, or ambiguous figures in general, and personality is very sparse.A rather early finding in the research history of the Necker is a report by Jones(1955) on a negative correlation between authoritarianism and number of re-versals in a speed up condition. This result should probably be re-evaluatedas only two 15 s-trials, i.e. a very short measurement period, were used. On

2Note that the same study revealed a marked positive correlation between saccadesand perceptual flips for binocular rivalry. The conclusions drawn here on the top-downcharacter of voluntary control are hence only valid for rivalry between ambiguous figuresbut not for binocular rivalry.

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the other hand, it supports the hypothesis that personality is likely to berelated to voluntary control over bistable perception. Similarly, Haronianand Sugerman (1966) found that the number of reversals in a hold condi-tion for the Necker cube correlated with two measures of field-independence.Field-independence is a concept of cognitive style that indicates how much aperson relies on their own inner knowledge and analysis compared to externalinformation. In a study by Aydin et al. (2013) age-related differences in theability to influence bistable perception of a vase/faces stimulus were reported.The authors suggested abnormal attentional mechanisms as an explanation,categorising the finding more as a cognitive effect than one of personality. Asanother finding, Sauer et al. (2012) showed that experienced meditators, whoshowed high scores in mindfulness, where significantly better at prolongingdwell times of the Necker cube than a control group. This result and itsrelation to own findings will be discussed in more detail in Chapter 9.To further explore voluntary control over bistable perception more rigor-ously was one of the objectives of the NC-pers study. In this Chapter, adetailed analysis of the experiment on voluntary will be given. Relationsto personality were explored with questionnaires on self-leadership, action-control and the Big Five personality traits. Self-leadership and action-controlwere chosen as two psychological concepts that describe voluntary humanbehaviour. Strategies aiming at the improvement of motivation and self-direction in order to perform well were operationalised with the concept ofself-leadership (Andreßen and Konradt, 2007). The concept of volition, ormore specifically action-control, was added as a measure closer to actual ac-tion performance (Kuhl, 1994). Finally, the BIG-5 inventory (Körner et al.,2008) was used to gain a broad classification of personality. The Big Fivepersonality traits are openness, conscientiousness, extraversion, agreeable-ness and neuroticism. A classification in terms of these categories couldserve as a basis for further exploration, relating facets of each of these di-mensions to bistable perception.The exact methods of the study of voluntary control over perception of theNecker cube will be given in the following section.

7.2 Measuring Volition65 healthy participants (age 28.8 ± 9.1 years, 31 male) completed this exper-iment. It consisted of four 3-minute trials of viewing the Necker cube. The

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maximal diagonal extension of the Necker cube covered 5 ◦ of visual angle.For more details of stimulus and procedure cf. Sec. 3.3.After basic instructions detailing the reversal phenomenon and a short prac-tice, participants spent the first 3-minute trial observing the Necker cubewhile indicating every perceptual reversal with one of two buttons on thecomputer keyboard depending on which perspective they saw. They wereinstructed not to exert voluntary control over the reversals, but to observethem passively. Furthermore, they were asked to avoid movements of thehead and keep their gaze fixated on a little cross in the middle of the Neckercube.After this neutral condition, three conditions with instructions to voluntarilyinfluence the reversals followed in randomised order with breaks of half aminute between trials. Each condition was precluded by the instructions forvoluntary control. In the “holdA” condition, participants were instructed tohold percept A of the Necker cube – the one as seen from above – and try toavoid percept B. I.e. participants were supposed to maximise the time spentseeing perspective A and minimise seeing perspective B. The “holdB” condi-tion is the reverse of the “holdA” condition, i.e. maximising the time spentwith perspective B. In the third condition, “speed up”, participants were in-structed to change between the two percepts as quickly as possible. In allconditions, participants were asked to use two buttons to indicate whenevera switch from one percept to the other occurred.Times of button presses were recorded and prepared for further analysis asdescribed in Sec. 3.4.Of the 65 data sets, 7 were excluded, due to insufficient data after correc-tion for multiple subsequent presses of the same button. Mean age of the 58participants of the remaining data sets was 29.0± 9.5 years, with 27 of thembeing male.In the following, let t̃neut be the median over all dwell times of the neutralcondition and t̃neut,pA and t̃neut,pB be the corresponding medians over dwelltimes for percepts A and B, respectively. In analogy, t̃hA and t̃hApA and t̃hApBshall denote medians for the holdA condition over all dwell times, for perceptA and B, respectively. Similarly, the subscripts “hB” and “sp” indicate thecorresponding measures for the holdB and the speed up conditions. Severaltentative measures describing voluntary control over bistable perception ofthe Necker cube were calculated from these dwell times.

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To describe the ability to hold percept A the following measures were defined:

∆hA = t̃hA − t̃neut (7.1)∆hApA = t̃hApA − t̃neut,pA (7.2)∆hApB = t̃hApB − t̃neut,pB (7.3)

In analogy for the hold B. . .

∆hB = t̃hB − t̃neut (7.4)∆hBpA = t̃hBpA − t̃neut,pA (7.5)∆hBpB = t̃hBpB − t̃neut,pB (7.6)

. . . and the speed up conditions:

∆sp = t̃neut − t̃sp (7.7)∆sppA = t̃neut,pa − t̃sppA (7.8)∆sppB = t̃neut,pB − t̃sppB (7.9)

These measures were calculated for each participant. Median values wereused in all cases as for some participants there was only a small number ofdata points per condition due to slow reversal behaviour. The mean andstandard deviation were determined over all 58 participants. For any of theabove measures, a finite value for any of these measures would indicate adeviation from the neutral condition. To test for significance of such de-viations, non-parametric one-sided Wilcoxon tests were performed betweenmedian dwell times for the neutral and the voluntary control conditions.These tests were calculated separately for dwell times for percept A and B aswell as for dwell times of both percepts. A non-parametric test method wasused, as mean or median dwell times usually are not normally distributedover participants. A one-sided test was used because for each case the hypo-theses were directed. All ∆’s were expected to be positive, except for ∆hApB

and ∆hBpA. p-values of the Wilcoxon tests were corrected with the false dis-covery rate method (FDR, Benjamini and Hochberg (1995); Benjamini andYekutieli (2001))Additionally, Spearman correlation coefficients between median dwell time inthe neutral condition, i.e. passive perception of the Necker cube, and volun-tary control, namely ∆hApA, ∆hBpB and ∆sp, were calculated. This was donein order to better understand the relation between neutral and voluntarily

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controlled perception. Median dwell times were favoured over mean dwelltimes in order to afford better comparability as the measures for voluntarycontrol were all calculated from median values. Furthermore, the correla-tions were also calculated for relative measures of voluntary control. Thesewere labelled ∆hApA,rel, ∆hBpB,rel and ∆sp,rel and calculated from the ∆’sdescribed above by dividing them by the appropriate baseline value of theneutral condition, for example:

∆hApA,rel =t̃hApA − t̃neut,pA

t̃neut,pA=

∆hApA

t̃neut,pA, (7.10)

and analogously for the other conditions. Furthermore, the three absolutemeasures of voluntary control were checked for correlations with each otherin order to see how persistent the ability to control perception is over thethree conditions. p-values of both these families of correlation tests werecorrected using FDR.In addition to the perception experiment, participants completed the Germanversion of the Revised Self-Leadership Questionnaire (RSLQ-D, Andreßenand Konradt (2007)) and a German version of the NEO-Five-Factor Invent-ory (BIG-5, Körner et al. (2008)). A subgroup of 28 participants (mean age30.6 ± 10.9 years, 12 male) also filled out the HAKEMP-90 action-controlquestionnaire (Kuhl, 1994). The scores for the nine subscales of the RSLQ-D, the five subscales of the BIG-5 and the three subscales of the HAKEMP-90were tested for correlations with three measures of voluntary control over per-ception of the Necker cube, namely ∆hApA, ∆hBpB and ∆sp. This was done inorder to explore relations between psychological concepts of self-leadership,personality and volition with perceptual ones. For correlation tests betweenneutral bistable perception and self-leadership, personality in general andvolition, respectively, cf. Chapter 8.Each family of correlation tests (all ∆’s with RSLQ-D, BIG-5 and HAKEMP-90, respectively) was corrected for multiple testing with the FDR method.

7.3 ResultsMean values and standard deviations of all measures introduced in Eqs. 7.1 to7.9 are plotted in Fig. 7.1 to show the effect of voluntary control. Additionally,p-values for the Wilcoxon tests between voluntary control conditions andneutral condition are given in Tab. 7.1.

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hA hApA*** hApB** hB hBpA hBpB*** sp*** sppA*** sppB***−4

−2

0

2

4

6

8Mean over median induced changes

Mea

n ov

er m

edia

n in

duce

d ch

ange

s (s

)

Figure 7.1: Changes induced by voluntary control compared to neutral observation of theNecker cube. Stars indicate significance of the one-sided Wilcoxon tests between voluntarycontrol and neutral condition after correction with the FDR method: ∗: p ≤ 0.05, ∗∗:p ≤ 0.01 and ∗∗∗: p ≤ 0.001.

hA hApA hApB hB hBpA hBpB sp sppA sppBp 0.32 1 · 10−6 0.005 0.21 0.04 4 · 10−6 6 · 10−8 3 · 10−7 9 · 10−8

padj 0.32 3 · 10−6 0.008 0.24 0.06 7 · 10−6 4 · 10−7 9 · 10−7 4 · 10−7

Table 7.1: p-values of the one-sided Wilcoxon tests for differences in median values forall experimental conditions. The second row displays the p-values adjusted for multipletesting with the FDR method.

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t̃

∆hApA −0.30∗/∗

∆hBpB −0.32∗/∗

∆sp 0.74∗∗∗/∗∗

t̃

∆hApA,rel −0.45∗∗∗/∗∗∗

∆hBpB,rel −0.49∗∗∗/∗∗∗

∆sp,rel 0.61∗∗∗/∗∗∗

Table 7.2: Correlation coefficients r for Wilcoxon tests between measures describing neut-ral and voluntarily controlled observation of the Necker cube. The left table describesabsolute measures, while the right gives relative measures gives the correlation for relativeone. Asterisks indicate p-values: ∗: p ≤ 0.05, ∗∗: p ≤ 0.01 and ∗∗∗: p ≤ 0.001; asterisksafter the slash give p-values after correction for multiple testing using the false discoveryrate method (FDR).

For the instruction to hold percept A and to avoid B, the median over alldwell times is not different from to the neutral condition. But dwell timesfor A are significantly larger than corresponding dwell times in the neutralcondition. Additionally, dwell times for percept B are significantly smaller.In the hold B condition a similar effect is observed: overall dwell times donot change, but dwell times for percept B are significantly larger than thosein the neutral condition. Dwell times for A are slightly smaller than in theneutral condition but not significantly so (p = 0.06). The effect of the speedup instruction is seen in a decrease of dwell times for perspective A and B,and hence also in all dwell times taken together. Effect sizes are very similar.The results of the correlation tests between passive and voluntary controlconditions are given in Tab. 7.2. It shows that ∆hApA and ∆hBpB correlatenegatively with median dwell times in the neutral condition, while ∆sp cor-relates positively with the median. The correlations are still significant aftercorrection for multiple testing. The same directions of correlations are foundfor the relative measures of voluntary control ∆hApA,rel, ∆hBpB,rel and ∆sp,rel,with larger correlation coefficients for the hold conditions and a smaller forthe speed up condition. In Fig. 7.2, the absolute decrease in dwell times forthe speed up condition is plotted against neutral median dwell times in orderto illustrate the relation more precisely. A clear increase of ∆sp with themedian of neutral dwell times is seen.Of the correlation coefficients between ∆hApA, ∆hBpB and ∆sp only the onebetween ∆hApA and ∆hBpB is significant, with r = 0.49, p ≤ 0.001. The ∆’sof the hold conditions are not correlated to the one of the speed up condi-tion. Again, the correlation remains significant after application of the FDRmethod.

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0 2 4 6 8 10−4

−2

0

2

4

6

8

10

Median dwell time, neutral (s)

∆ sp (

s)

Figure 7.2: Absolute decrease of dwell times in the “speed up” condition vs. median dwelltimes in the neutral condition for 58 participants.

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Of the RSLQ-D subscales, the scale for evaluating beliefs and assumptionscorrelates significantly with voluntary control, namely with the ability tohold percept B (r = 0.26, p = 0.05, uncorrected). Furthermore, the sub-scale for focussing thoughts on natural rewards correlates also with ∆hBpB

(r = 0.28, p = 0.03).Of the BIG-5 subscales, the one for conscientiousness correlates negativelywith the ability to speed up reversals, i.e. ∆sp (r = −0.28, p = 0.04), whilethe one for neuroticism correlates positively with ∆sp (r = 0.27, p = 0.04).The subscale for agreeableness correlates with ∆hApA (r = 0.30, p = 0.03),the ability to hold percept A.There are no significant correlations of the three subscales of the HAKEMP-90 questionnaire to any measure employed here to describe voluntary controlover bistable perception.After correction with the FDR method, the found correlations between per-sonality traits and voluntary control variables do not remain significant.

7.4 DiscussionFig. 7.1 shows clearly that participants were able to follow the given instruc-tions. For the hold conditions, the desired percept was increased in durationwhile the length of the undesired one was decreased, even though this effectis not significant for percept B after correction. In the speed up conditiondwell times of both percepts were significantly reduced, as expected. Hence,the employed paradigm yields the desired effects and the measures ∆hApA,∆hBpB and ∆sp defined in Eqs. 7.2, 7.6 and 7.7 quantify these adequately.Other researchers used similar approaches to quantify changes between dif-ferent instructions, i.e. by considering mean dwell times and comparing themacross conditions. So, the approach pursued here is in agreement with liter-ature.Also the results reported by other groups are very similar. Pelton and Sol-ley (1968) for example, found a significant difference in number of reversalsbetween two groups of participants, one of which was instructed to switch asmuch, the other as little as possible (i.e. always holding the current perceptas much as possible). In a more recent work van Ee et al. (2005) comparedvoluntary control between different bistable stimuli. They used “neutral”,“hold percept 1”, “hold percept 2” and “speed up” conditions, similar to thecurrent experiment. The authors report significant changes between the con-

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ditions. Similar results were described by Kornmeier et al. (2009). Thus, theeffects of voluntary control as demonstrated in the current experiment are ingood agreement with the literature.The correlation coefficients presented in Tab. 7.2 show that voluntary con-trol, both in absolute and in relative terms, is not independent of dwelltimes in the neutral condition, a finding which has not been reported so far.The correlations indicate that an increased median dwell time goes hand inhand with decreased ability to hold percepts A and B and an increase inthe ability to speed up the reversal process. This relation is particularlystrong for the speed up condition. Here, the coefficient of determinationis as high as roughly 55 % (estimating the coefficient of determination asr2 = 0.742 = 0.55). Thus, a great part of the variability of the success tospeed up reversals can be explained by neutral dwell times. For the holdconditions, only a small part, about 10 % of the variability is explained bythe neutral dwell times.These results indicate that it seems to become increasingly difficult to pro-long dwell times the higher dwell times are under passive perception. On theother hand, a speed up of reversal is the easier the higher the dwell timesare. Both effects do not seem to be only a linear scaling effect, as they arealso present when one considers relative changes of the voluntary conditionscompared to the neutral condition. More data points, especially for slowreversers, would be desirable in order to quantify the exact relation betweent̃ and ∆sp (cf. Fig. 7.2).The correlation between ∆hApA and ∆hBpB shows that both percepts of theNecker cube are not only perceived for different amounts of time but thatsuccess of voluntarily controlling them is different. This is reflected in thecorrelation coefficient between ∆hApA and ∆hBpB being much lower than 1.If it was as easy to hold percept B as it is to hold percept A, r ≈ 1 wouldbe expected. In fact, Fig. 7.1 indicates that the ability to hold B is slightlylower than the one to hold A (n.s.). Hence, the bias effect presented inChapter 6 is further substantiated by this finding, as it not only manifests inan asymmetry in neutral dwell times but also in an asymmetry in the abilityto influence percepts. Additional evidence for it is added by the fact that∆hApA and ∆hBpB correlate with different personality measures (cf. the nextparagraph and Chapter 9).Due to the exploratory nature of this study, uncorrected p-values were givenfor the tests between measures quantifying voluntary control over perceptionof the Necker cube and personality questionnaires. As these correlations do

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not remain significant after rigorous correction for multiple testing using theFDR method, they should be interpreted as trends that are worth study-ing in more detail in a conceptually more focused study. Maybe also higherstatistical power would be desirable for that. Interpretation of the currentresults should thus be conducted with special care, keeping in mind that therelations might be chance results.The findings are quite plausible, though. In fact, again an asymmetry be-tween the two percepts of the Necker cube is seen, as mentioned above in thesame section: ∆hApA and ∆hBpB do not correlate with the same measures.Actually, ∆hApA does not correlate at all with measures of self-leadership,BIG-5 or volition. Thus, the bias between percept A and B is reflected inthese results.The correlations found between ∆hBpB and the RSLQ-D subscale for eval-uating beliefs and assumptions as well as the scale for focussing on naturalrewards give some hints as to which personality aspects might play a role inthe ability to focus one’s perception on B. The subscale for evaluating beliefsand assumptions yields high values when a person has a strong tendency toevaluate their beliefs and assumptions, in particular in difficult situations. I.e.the scale operationalises a certain self-reflection with regard to the person’sbeliefs. The other correlated scale, namely the one for focussing thoughtson natural rewards, expresses how much a person adapts the internal andexternal situation in order to make a task enjoyable. I.e. the scale is a meas-ure of how well a person can adapt thoughts and action in particular withrespect to work in order to make it more pleasant. So one could say thatboth subscales require a certain self-reflection, either over beliefs or over howpleasant the situation is and what would improve it, and a certain adapta-tion, either of beliefs or thoughts or actions. This interpretation is supportedby a finding on perception and mindfulness presented in Chapter 9. It wasdiscovered that ∆hBpB is correlated to the CHIME subscale of relativity ofthoughts, i.e. the knowledge about subjectivity of experience and the pos-sibility of changing interpretations. Again this concept is strongly related toself-reflection and adaptation.Hence, the current results suggest that a high ability of self-reflection andpositive adaptation is related to the ability to focus on seeing the Neckercube from below (percept B). For future research, it would be desirable tohave a questionnaire that is centred more strongly on these qualities. Thenthe validity of the current finding could be tested directly in a more focusedapproach without the need to calculate many correlation coefficients.

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The results on the BIG-5 scales on the other hand suggest that the abilityto hold percept A is related to the personality dimension of agreeableness,indicated by a corresponding correlation. The scale expresses how compas-sionate and cooperative a person believes themselves to be. Again, a findingin terms of mindfulness (Chapter 9), namely a correlation between ∆hApA

with the FFA subscale for acceptance, seems to support the current result.That concept of acceptance expresses how well a person can positively acceptadverse experiences and have a compassionate attitude towards own short-comings and those of others. This is certainly a very good basis for beingagreeable towards other people. Hence, a relation between the ability to holdpercept A and agreeableness seems plausible. Thus, it is promising to furtherexplore it using corresponding personality concepts.Furthermore, the ability to speed up perception, ∆sp is correlated positivelywith neuroticism and negatively with conscientiousness. Conscientiousnessindicates efficient, organised behaviour and self-discipline, i.e. the desire todo a task well. Neuroticism on the other hand denotes emotional lability, thetendency to experience unpleasant emotions and a low impulse control. Asthe careful conduction of a task usually takes a certain amount of time andcannot be sped up arbitrarily, it makes sense that people with high scores inconscientiousness can only speed up perceptual reversals to a certain degree.Low impulse control and emotional instability might be related to percep-tual instability and hence an affinity to speed up reversals. Furthermore,a principal component analysis (PCA) of the 5 scores of the BIG-5 ques-tionnaire for all participants showed that conscientiousness and neuroticismpoint in almost opposite directions in the space spanned by the two principlecomponents. Hence, the opposite correlations of the conscientiousness andneuroticism scores with the ability to speed up reversals are reasonable.Finally, the lack of correlations between the scores of the HAKEMP-90 andthe ability to influence bistable perception shows that action-control as ahigh-level psychological concept is not related to control over perception ofthe Necker cube. In more detail, this means that none of the three subscalesof the questionnaire, namely “orientation for action after failure”, “orientationfor action in action planning” and “orientation for action during action”, over-lap significantly with the ability to hold or speed up the reversal process ofthe Necker cube. This might be explained by the fact that the HAKEMP-90operationalises more general schemes of action, i.e. how immersed a persongenerally is in a task or how they cope with repeated failure. These scalesmight be too abstract and general as to capture the ability to influence

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bistable perception.In general, it seems advisable to use the results presented here as the basis forfurther explorations of the relations between bistable perception, neutral andvoluntarily controlled, and personality. A report by Paunonen and Ashton(2001) indicates that focusing on more narrow personality facet measuresmight increase the explanatory power of the relations found. The authorsfound that more narrow personality facets predicted a variety of behavioursmuch better than the BIG-5 factors. Thus, further research utilising thisapproach might bring more light to the understanding of inter-individual dif-ferences in bistable perception in terms of personality.In conclusion, in this chapter voluntary control over perception was success-fully reproduced and quantified with the most relevant measures. It wasshown that a great part of the inter-individual variability in the ability tohold one particular percept can be explained by the length of neutral dwelltimes. Furthermore, the perceptual bias presented in Chapter 6 was alsodiscovered in form of a different ability to hold both percepts of the Neckercube. In terms of personality, it was found that the ability to hold percept Ais positively correlated with agreeableness. The ability to hold percept B cor-relates with self-leadership, while the ability to speed reversal up correlatesnegatively with conscientiousness and positively with neuroticism. Actioncontrol, as operationalised by the HAKEMP-90 questionnaire, is not relatedto voluntary control.

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8. Perception & Personality

In the last chapter results on the relation between voluntary control overbistable perception of the Necker cube and personality were reported. Thischapter, on the other hand, is focused on relations between personality anddwell times for passive perception of the ambiguous figure.

8.1 Studies Linking Bistability and PersonalityIn contrast to voluntary control over bistable perception, there are quite afew reports relating neutral perception of the Necker cube with personalitytraits. These vary in their methodological approach and quality. In manystudies, especially the older ones, it was not dwell times that were measuredbut only the number of reversals. Hence, in the following short overview ofthe literature, mostly number of reversals will be cited as measure of bistableperception. Mostly questionnaires were used in order to assess personalitytraits.According to Beer (1989) the number of reversals for the Necker cube isnot related to the concept of ambiguity tolerance, but correlates negativelywith rigidity. Kidd and Cherymisin (1965) only considered the very firstreversal time for different ambiguous figures and found also that long timesgo hand in hand with high values in rigidity and furthermore in anxiety andfield-dependence. Field-dependence is a concept of cognitive style, indicat-ing how much a person relies on external information in contrast to theirinner knowledge and analysis. It is important to note that testing for thefirst reversal of an ambiguous figure is strongly dependent on instruction,as being uninformed about reversibility leads to an absence of reversals inmost cases (Rock and Mitchener, 1992). As Kidd and Cherymisin (1965) donot give details of either instructions or the used ambiguous figures, theirfindings should be used carefully. Frederiksen and Guilford (1934) found

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that intraversion/extraversion as well as impulsiveness was not related tobistable perception of the Necker cube. By dividing their participants, whosaw different ambiguous figures including the Necker cube, into two groupsof slowest and fastest reversers, Bergum and Bergum (1979b) found thatthe high reversal group scored significantly higher in self-rated creativity. Ina different study Bergum and Bergum (1979a) compared a group of archi-tecture students and one of business administration students with respectto creativity and reversals. The former rated themselves as more creative,original and visually oriented compared to the second and also reversed sig-nificantly more often. These findings were supported by a study of Klintman(1984) who showed that participants that rated high in a original thinkingtest also had high reversal rates.Overall, these results demonstrate that bistable perception of the Neckercube is related to personality in several ways. This underscores the top-down component of the reversal process.Goal of the experiments and analyses described here was to gain a more gen-eral overview over the relations between personality and bistable perception.For that, several personality questionnaires were used. A rough overviewwas aimed at by using the BIG-5 inventory. It encompasses the personalitydimensions of openness, conscientiousness, extraversion, agreeableness andneuroticism. It was hypothesised furthermore that a high degree of sen-sation seeking might be related to reversal frequency. Even though Beer(1989) had not found a relation between ambiguity tolerance and the num-ber of reversals, a re-evaluation with a newer conceptualisation of ambiguitytolerance by (Dalbert, 1999) and in particular a better controlled visual ex-periment1 seemed worthwhile. In the light of the correlation between firstdwell time and anxiety reported by Kidd and Cherymisin (1965), it wasof interest to determine whether a relation to anxiety would also be foundfor measures describing the whole reversal process. For that the State andTrait Anxiety Inventory (STAI, Laux et al. (1981)) was chosen as it wouldprovide two measures to operationalise anxiety, one for the current situationand one relating to personality trait. Finally, the two questionnaires oper-ationalising action-control (HAKEMP-90, Kuhl (1994)) and self-leadership(RSLQ-D, Andreßen and Konradt (2007)) employed to study relations ofpersonality and voluntary control over bistable perception (Chaper 7) were

1Beer (1989) used oral reports of reversals which do not allow for precise analysis ofdwell times.

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used here again in order to probe for potential relations to neutral perceptionof the Necker cube.The following section will detail the methods applied to that end.

8.2 Operationalisation of Personality TraitsPotential links between personality and perception were explored by testingfor correlations between questionnaire scores and measures describing pass-ive, bistable perception of the Necker cube. For that, questionnaire data of28 participants (mean age 30.6± 10.9 years, 12 male) for the HAKEMP-90,the STAI, the BSSS and the ambiguity tolerance questionnaires was used.For the RSLQ-D and the BIG-5 questionnaires, data from 58 participants(29.0 ± 9.5 years, 27 male) was used. The details of the experiment onbistable perception of the Necker cube are given in Sec. 3.3. Note, that fail-ure to understand the instructions for this experiment resulted in the lowernumber of usable data sets (28 and 58, respectively) compared to the overallavailable data (33 and 65, respectively).For the HAKEMP-90, three scores were calculated, namely the score for“orientation for action after failure” (“Handlungsorientierung nach Misser-folg”, HOM), the score for “orientation for action in action planning” (“Hand-lungsorientierung bei der Handlungsplanung”, HOP) and the one for “orient-ation for action during action” (“Handlungsorientierung bei der Tätigkeit-sausführung”, HOT). The STAI has two subscores, namely the score for stateanxiety and the one for trait anxiety. BSSS and ambiguity tolerance (“Un-gewissheitstoleranz”, UGT) only have one score each.In order to describe bistable perception, mean and median dwell times werecalculated for each participant. Furthermore, the parameters of the lognor-mal fits as well as its mode and variance were used as measures to operation-alise bistable perception.For all combinations between the questionnaire scores and the measures ofbistable perception, Spearman correlation coefficients and p-values were cal-culated.

8.3 ResultsNone of the scores for action-control, anxiety, sensation seeking and ambi-guity tolerance correlates significantly with measures describing the central

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tendency (mean and median) of dwell time distributions or with the meas-ures describing the fitted distributions (distribution parameters, mode andvariance).One subscale each of the self-leadership questionnaire and of the BIG-5 in-ventory, on the other hand, correlates with measures of passive bistable per-ception.2The RSLQ-D subscale of self-reward (“Selbstbelohnung”) correlates negat-ively with mean dwell times (r = −0.29, p = 0.03), the parameter µ of thelognormal fit (r = −0.26, p = 0.05) and its variance varlog (r = −0.33, p =0.01). The scale for conscientiousness of the BIG-5 correlates negatively withthe mode of the lognormal fit (r = −0.27, p = 0.04).These results do not remain significant after correction for multiple testingwith the FDR method.

8.4 DiscussionThe lack of correlations found for several of the personality scales employedin the described experiments indicate which personality aspects are not re-lated to passive bistable perception of the Necker cube.The fact that none of the HAKEMP-90 scores is correlated with dwell timemeasures of the neutral condition is in agreement with a corresponding lackof correlations for the voluntary control conditions as described in Chapter 7.This further supports the finding that action-control as operationalised hereis not strongly related to bistable perception.The report of a positive relation between the length of the first dwell timeand anxiety by Kidd and Cherymisin (1965) can be well reconciled with thelack of a correlation in the current experiments. First, the length of the ini-tial dwell time is strongly dependent on the given instruction, which was notdetailed in the cited study. Measures describing dwell times of continuousobservation of the Necker cube are very likely to capture different aspectsof bistable perception than only the first percept. The instructions of thecurrent experiment were ambiguous as to whether participants should indic-ate their first percept or the first reversal they experienced. So, the lengthof the first dwell time was not reliably determined as it was not of interestfor the current study. Hence, a direct comparison to the results of Kidd and

2Note that correlations of RSLQ-D scores with measures quantifying voluntary influ-ence were presented in Chapter 7.

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Cherymisin (1965) was not possible. Secondly, here the STAI questionnairewas used while the authors of the cited study used the Taylor Manifest Anxi-ety Scale. As a study directly comparing these questionnaires seems not tobe available, it cannot be judged how the two scales differ.There are no studies that tested for potential relations between the concept ofsensation seeking and bistable perception. Thus, the current results demon-strate for the first time that sensation seeking behaviour is not related toperception of the Necker cube. Because of the brevity of the employed scale,an analysis in terms of the four sub-traits of sensation seeking was not per-formed. From the current results, it cannot be excluded that one of thesemight be related to bistable perception.The lack of a correlation between ambiguity tolerance and bistable percep-tion found by Beer (1989) was confirmed in the current study. Thus, it can beconcluded that also with a different questionnaire and state-of-the-art meas-urement and analysis methods for bistable perception there is no relationbetween ambiguity tolerance and passive bistable perception.The lack of correlations between measures describing bistable perceptionof the Necker cube and anxiety, sensation seeking and ambiguity toleranceprovide useful indications in the search for personality aspects or traits thatare related to bistable perception. These findings narrow down the potentialcandidates for related concepts and hence indirectly advance the search forthem. Thus, the results presented above can be of use for further investiga-tions of the perception-personality connection.Regarding the correlations that were indeed found, similarly as in Chapter 7,uncorrected p-values were reported in the previous section, with results notbeing significant any more after rigorous correction using the FDR method.Hence, special care should be taken in the interpretation of the followingresults which can serve as a basis for further research.The three correlations to the self-leadership scale for self-reward are depend-ent to a high degree. Both the parameter µ and the variance varlogn arestrongly correlated with the mean dwell times: r = 0.97 and 0.88, respect-ively (p ≤ 0.001 in both cases). Thus, the correlations of mean dwell timesand µ are almost equivalent, showing that a strong tendency towards self-reward and the application of self-rewarding behaviour go hand in hand withshort dwell times. The correlation to varlogn indicates furthermore, that inthis case dwell times do not vary so much. That three correlations point al-most in the same direction is a good indicator of the reliability of the result.Compared to personality traits, self-leadership and its subscales is a more

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flexible concept that can be more easily changed (Neck and Houghton, 2006)but which is related to personality, though (Houghton et al., 2004). Thecorrelation found here thus indicates the relation of bistable perception tomore flexible traits like self-leadership. A further research direction could beto explore how the relation between perception and self-reward would evolvewhen the latter would be changed by training.The relation between self-reward and small dwell times seems to be relatedto the finding that high creativity also goes hand in hand with small dwelltimes (Bergum and Bergum (1979a), Bergum and Bergum (1979b) and Klint-man (1984)). Self-leadership was shown to be conducive to innovative workbehaviour (de Stobbeleir et al., 2011). In particular, Curral and Marques-Quinteiro (2009) found a positive correlation between self-reward and innov-ation at work. As the concepts of creativity and self-reward are related, thecurrent correlation is in good agreement with the negative correlation be-tween creativity and dwell times.The correlation between conscientiousness and the mode of the lognormal fitindicates that an observer of the Necker cube who rates high in conscien-tious behaviour would reverse most often within a short time. Maybe con-scientiousness is associated with a high processing speed or fast perceptualfeedback loops that lead to a frequent occurrence of short dwell times. Thisis a finding that should be re-evaluated either with a more focused designin order to increase the effect strength or when the shape of the dwell timedistribution has been associated with more personality trait so that a bet-ter interpretation is possible. The fact that conscientiousness only correlateswith the modal but not with median or mean dwell times could have two dif-ferent meanings. First, it might be a chance finding, as the other measuresof central tendency of the dwell time distribution are not related. On theother hand does the mode describe a different aspect of the distribution, asit is always smaller than median and mean for a right skewed distribution. Itmight be that the relation found here, is very specific, indicating an aspectof the lower part of the distribution which is not strongly related to meanand median.In summary, the experiments described in this chapter identified several per-sonality traits that are very likely not related to bistable perception, namelyaction-control, anxiety, sensation seeking and ambiguity tolerance. Self-rewarding behaviour as an aspect of self-leadership, on the other hand, wasfound to correlate negatively with dwell times – a finding that is probablyrelated to the correlations between number of reversals and creativity. Fur-

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thermore, conscientiousness seems to be related to the mode of the lognormaldistribution. These results further validate and advance the undertaking ofexplaining inter-individual variations of dwell times in terms of personalitytraits.

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9. Mindfulness & Perception

Mindfulness is a concept originating from Bhuddist psychology and philo-sophy, referring to a certain quality of the mind. Its beneficial effects inmedicine have been described early by John Kabat-Zinn (e.g. Kabat-Zinn(1982)). Subsequently the concept was received into Western psychology.In this chapter results on relations between bistable perception of the Neckercube and mindfulness will be presented.

9.1 Mindfulness in Science and PerceptionMindfulness found its way into Western psychological research because sci-entists and meditation practitioners wanted to explore its beneficial effectson both mental as well as physical health. This endeavour has lead to a grow-ing and successful research field in psychology. For reviews of the effects ofmindfulness in general and Mindfulness Based Stress Reduction (MBSR) onhealth see Baer (2003) and Praissman (2008). Furthermore, research showsthat mindfulness does indeed have effects on perception. Two studies are ofparticular interest for bistable perception. In a study with Tibetan Bhud-dist monks on binocular rivalry, Carter et al. (2005) found that dwell timeswere increased extremely for a majority of the participants after and dur-ing one-point meditation, while only a few reported prolonged dwell timesafter compassion meditation. In the same article the authors also report pro-longed disappearance durations in motion induced blindness. These resultswere obtained with highly trained monks who had 5 to 54 years of training.Sauer et al. (2012) studied the effects of mindfulness on perception of theNecker cube. The authors compared mean dwell times between a group ofexperienced meditators with at least 5 years of daily practice and a groupof non-meditators. They found no differences for neutral perception of theNecker cube but a significant prolongation of dwell times in a hold condition.

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Both studies indicate that there is indeed a relation between mindfulness andvisual perception. Goal of the present study was to explore whether thesedifferences could also be detected in an unbiased group of participants, i.e. agroup that was not screened for meditation experience.As indicated by the results of Carter et al. (2005) there are several aspectsnot only of meditation but also of mindfulness. Bishop et al. (2004) gavean operational definition for mindfulness in which they distinguished twocomponents: (1) self-regulation of attention so that it is maintained on im-mediate experience and (2) an orientation towards one’s own experiencescharacterised by curiosity, openness and acceptance. Bergomi et al. (2012)even discerned nine aspects of mindfulness based on their summary of existingmindfulness scales and incorporated them into the CHIME-β questionnaire.Building on these results the authors created the Comprehensive Inventoryof Mindfulness Experience, CHIME, incorporating the following eight as-pects of mindfulness without relying on technical expressions of meditationor Bhuddism: (1) awareness towards internal experiences (inner awareness),(2) awareness towards external experiences (outer awareness), (3) acting withawareness (acting with awareness), (4) accepting and non-judgemental ori-entation (acceptance), (5) decentering and nonreactivity (decentering), (6)openness to experiences (openness), (7) relativity of thoughts (relativity) and(8) insightful understanding (insight). Another mindfulness questionnaire,the Freiburg Mindfulness Inventory (FMI), has been designed by Walachet al. (2006), which, in a short version discerns “acceptance” and “presence”also without requiring participants’ knowledge of the Bhuddist backgroundof mindfulness.Both the CHIME and the FMI questionnaire were used in the current studyto explore mindfulness in an unbiased group of participants. For that, theproperty of both questionnaires that they do not utilise technical terms ofmeditation or Bhuddism was very important. It was hypothesised that neut-ral dwell times would not be correlated to mindfulness scores, as Sauer et al.(2012) did not find a corresponding difference between meditation expertsand non-meditators. The same study and the one of Carter et al. (2005),on the other hand, suggested that there might be relations between mind-fulness and voluntary control over perception of the Necker cube. These twohypotheses were tested in the following way.

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9.2 Methods65 healthy participants (age 28.8 ± 9.1 years, 31 male) with normal or cor-rected to normal vision took part in this experiment.As part of the NC-pers study, they completed the voluntary control experi-ment for bistable perception (described in detail in Chapter 7) and two mind-fulness questionnaires, the FMI (Freiburg Mindfulness Inventory, Walachet al. (2006)) and the CHIME (Comprehensive Inventory of Mindfulness Ex-periences by Bergomi and co-workers in preparation, personal communica-tion). The voluntary control experiment consisted of four sessions of bistableperception of the Necker cube with varying instructions, each of 3-minutelength, during which participants indicated reversals with two buttons onthe computer keyboard. After a session of neutral, i.e. passive observation ofreversals, a condition with instructions to hold percept A and avoid perceptB, one with instruction to hold B and avoid A and one with instructions tospeed up reversals followed in randomised order. Different conditions wereseparated by breaks of half a minute.All in all 7 of the 65 data sets had to be excluded due to the amount of dwelltime data being insufficient after correction for multiple, consecutive pressesof the same button. Hence, data of 58 participants (29.0±9.5 years, 27 male)was used.From dwell time data of the neutral condition, mean and median dwell timeswere calculated. Parameters of the lognormal distribution were estimatedwith maximum likelihood estimation. From these, the mode position and thevariance were determined. Furthermore, the three measures best describingvoluntary control over bistable perception of the Necker cube were calculated:∆hApA,∆hBpB and ∆sp (for a deduction of these see cf. Chaper 7). From theanswers of the questionnaires, the overall score of the FMI, the scores of itstwo subscales for acceptance and presence, as well as the scores of the eightsubscales of the CHIME were calculated.Subsequently, correlations between the ten mindfulness subscales (two fromFMI plus eight from CHIME) and the three measures of the voluntary controlexperiment as well as the six describing measures passive bistable perceptionwere calculated.Furthermore, the three measures of the FMI (overall score plus subscales)were tested for correlations with the CHIME subscales.All correlation tests were performed using the Spearman test. Multiple test-

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ing was corrected using the False Discovery Rate method (FDR). Due to theexploratory nature of the study, mostly uncorrected p-values will be given inthe next section, though.

9.3 ResultsBetween the measures describing neutral bistable perception and the mindful-ness subscales, there is only one significant correlation. Namely, the CHIMEsubscale of relativity of thoughts correlates negatively with the parameter σof the lognormal distribution (r = −0.27, p = 0.04).Each of the three measures of voluntary control over bistable perceptioncorrelates significantly with at least one mindfulness subscale. Uncorrectedp-values for these correlations are given here. The ability to hold percept A,operationalised by ∆hApA, is related to the subscale for acceptance of the FMI(r = 0.33, p = 0.013). The ability to hold percept B, ∆hBpB, is correlatedto the CHIME subscales for awareness towards external experiences (r =0.27, p = 0.042) and relativity of thoughts (r = 0.42, p = 0.001). The abilityto speed up perceptual reversals, ∆sp, shows a correlation to the CHIMEsubscale for awareness towards external experiences (r = 0.32, p = 0.014).1These correlations do not remain significant after correction using the FDRmethod.The FMI correlates with seven of the eight subscales of CHIME. A table withcorrelation coefficients is given in Tab. 9.1. Fhe overall FMI score has thehighest correlations with acceptance, decentering and insight. The accept-ance subscale of FMI has the highest correlations for the same four CHIMEsubscales. The FMI presence subscale correlates highest with decentering,outer awareness, acceptance, inner awareness and insight. The opennesssubscale of CHIME shows no significant correlations to the FMI. All correl-ations remain significant after correction for multiple testing using the FDRmethod.

1Note that very similar results were obtained when using relative instead of absolutechanges of dwell times: ∆hApA,rel and acceptance: r = 0.32, p = 0.015, ∆hBpB,rel andrelativity of thoughts: r = 0.35, p = 0.008 and ∆sp,rel and awareness towards external ex-periences: r = 0.33, p = 0.011. Awareness towards external experiences does not correlatesignificantly to ∆hBpB,rel (r = 0.20, p = 0.13).

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CHIME FMI FMIacc FMIpresinner awareness 0.240 0.115 0.372∗∗/∗∗

outer awareness 0.281∗/∗ 0.111 0.447∗∗∗/∗∗∗

acting with awareness 0.439∗∗∗/∗∗∗ 0.461∗∗∗/∗∗∗ 0.278∗/∗

acceptance 0.668∗∗∗/∗∗∗ 0.730∗∗∗/∗∗∗ 0.382∗∗/∗

decentering 0.630∗∗∗/∗∗∗ 0.589∗∗∗/∗∗∗ 0.527∗∗∗/∗∗∗openness 0.150 0.104 0.175relativity 0.275∗/∗ 0.188 0.304∗/∗

insight 0.511∗∗∗/∗∗∗ 0.488∗∗∗/∗∗∗ 0.346∗∗/∗

Table 9.1: Correlation coefficients for Spearman correlation tests between the subscalesof the FMI and CHIME questionnaires (∗: p ≤ 0.05, ∗∗: p ≤ 0.01 and ∗∗∗: p ≤ 0.001;asterisks after the slash refer to FDR-adjusted p-values).

9.4 Mindfulness Relates to Perceptual VolitionAs expected, there are no clear direct correlations between mindfulness andneutral dwell times. The finding of a negative correlation between σ and theCHIME scale for relativity of thoughts is ambiguous. It might indeed hint ata relation to the shape of the dwell time distribution. In this case, it wouldbe difficult to judge the implications of this finding, as there only very sparsereference points as to what the parameters of the distribution of inverse timesrepresent. On the other hand it could also be a chance result, as there are noother correlations supporting it. A study with higher statistical power wouldbe needed to explore this relation in more detail. For that a larger numberof participants would be necessary. Furthermore, also a greater amount ofdwell time data would be desirable, i.e. longer measurement periods.The results on correlations between mindfulness and voluntary control overbistable perception of the Necker cube are in good agreement with the res-ults of Sauer et al. (2012) and also Carter et al. (2005). Sauer et al. (2012)used an unspecific hold instruction, i.e. participants were asked to alwayshold the current percept. The current design goes a bit further than that asit differentiates between the two perspectives. The results show that a highdegree of self-reported mindfulness goes hand in hand with greater success inholding both perspective A and perspective B. But it also becomes clear thatdifferent aspects of mindfulness are related to voluntarily influencing eitherpercept. A high degree of acceptance (FMI) is related to success in holdingperspective A, while for perspective B awareness towards external experi-

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ences and relativity of thoughts are relevant. The awarness towards externalexperiences is furthermore related to the ability to speed up perception.These results show (1) that relations between mindfulness and perceptioncan not only be detected between experts and laypersons but also via theinter-individual differences in an unbiased sample, (2) that the asymmetryin the ability to hold percept A compared to hold percept B as detailed inChapter 7 is also reflected in different aspects of mindfulness and (3) thatalso the ability to speed up perception is correlated to one aspect of mind-fulness.These findings shall be discussed in more detail in the following. The cor-relation between acceptance as operationalised by the FMI and ∆hApA isin good agreement with the correlation between agreeableness and ∆hApA

described in Chapter 8. In the FMI, acceptance is understood as a non-judgemental, compassionate stance towards oneself and one’s surrounding.Examples of statements used which are rated with a Likert-type scale are“Ich kann darüber lächeln, wenn ich sehe, wie ich mir manchmal das Lebenschwer mache.” (“I can smile when I realise how I sometimes make my lifedifficult.”) or “Ich nehme unangenehme Erfahrungen an.” (“I accept uncom-fortable experiences.”). Agreeableness in the BIG-5 questionnaire includesstatements like “Ich bekomme häufiger Streit mit meiner Familie und meinenKollegen.” (“I often argue with my family and colleagues.”, negatively codedstatement) and “Ich versuche stets rücksichtsvoll und sensibel zu handeln.”(“I always try to act considerately and sensitively.”). It is reasonable to as-sume that an accepting state of mind is conducive to being agreeable whileprobably an agreeable person will also manifest the characteristics of accept-ance.Also for ∆hBpB we find supporting correlations in terms of mindfulness andpersonality. ∆hBpB correlates with both relativity of thoughts and the eval-uating beliefs and assumptions scale of RSLQ-D (cf. Chaper 7). The formerscale posts items like “Es ist mir im Alltag bewusst, dass sich eigene Mein-ungen, die ich zur Zeit sehr ernst nehme, deutlich verändern können.” (“Inmy everyday life I am aware that my own beliefs which I take very seri-ously at the moment can change considerably.”) and the latter items like “InSituationen, in denen ich auf Probleme treffe, prüfe ich, ob meine Überzeu-gungen angemessen sind.” (“In situations in which I encounter problems Icheck whether my opinions are appropriate.”). Both scales query how criticaland flexible a person operates with their beliefs.Thus, the correlations of ∆hApA and ∆hBpB with mindfulness and personality

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or self-leadership measures reinforce each other. It is hence very unlikely thatthese correlations are due to chance effects, even though they do not remainsignificant after correction for multiple testing. Still, the results could bestrengthened by conducting a study with a more focused design drawing onless correlation tests and a higher number of participants.As also mentioned in Chapter 7 the different correlations for the ability tohold percept A compared to the one to hold percept B are related to thebias effect discussed in Chapter 6. The bias effect describes the fact thatdwell times for percept A are significantly longer than those of percept B.It was argued in Chapter 6 that this preference might be due to many shortprimings in everyday life by cube-like things which are seen from above. Itwould be of great interest to find out whether an accepting attitude in thesense of mindfulness is related to a higher susceptibility to priming of perceptA. Answering this question would require another experiment. If this wasthe case, acceptance would be a bridging concept for both the bias effect andvoluntary control over percept A. Additionally, by acknowledging the biaseffect, the correlation of relativity of thoughts with ∆hBpB is conceptuallyexplicable. Because the perspective as seen from above is the more dominantone and as it is probably constantly reinforced by priming, a shift or relativ-isation has to occur in order to inverse the bias, i.e. to make percept B thedominant one and thus realise the hold B instruction. This line of thoughtmight also support the correlation between ∆hBpB and the awareness towardsexternal experiences. As percept A is more dominant, an increased externalawareness might be able to overcome the priming by mentally directing theperceptual focus on those aspects of the Necker cube that favour percept B.This heightened awareness is unlike to further support percept A by the sameamount as it is already favoured perceptually.In the same way as the hold B condition may be understood as reversingthe bias effect, the hold A condition can be conceived as reinforcing it. Itcould be hypothesised that such a reinforcement is facilitated by an attitudeof acceptance.The correlation between ∆sp and the awareness towards external experiencesis also a plausible result and thus not very likely to be only due to chance.The scale for awareness towards external experiences evaluates agreementwith statements like “Ich nehme Farben und Formen in der Natur deutlichund bewusst wahr.” (“I perceive colours and forms in nature clearly andconsciously.”). It is reasonable that an affinity and ability to perceive withsuch a heightened awareness should be related with the ability to produce

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and follow fast reversals between the percepts of the Necker cube.Thus, the results presented here add on to the findings by Sauer et al. (2012)in that they show similar results in an unbiased group of participants andfurthermore are able to reflect the asymmetry in perception and mindfulnessbetween the two percepts of the Necker cube. Additionally, they demonstratea relation of mindfulness to the ability to speed up reversals – a finding whichhas not been reported so far.Finally, the results on the correlations between the two mindfulness question-naires used here demonstrate how they are related to each other. As shownin Tab. 9.1 the overall score of the FMI has the highest loadings on accept-ance, decentering, insight and acting with awareness, in decreasing strengthof correlation. Thus, the FMI is a mixed conceptualisation of these fouraspects of mindfulness. The acceptance subscale of the FMI also has highloadings on the same four aspects and very low ones on the other aspects ofthe CHIME. But here, the subscale for acceptance of the CHIME clearly hasthe highest loading (r = 0.73). This is confirms that both questionnaires aimat the same understanding of acceptance. For the presence subscale of theFMI, the relation is not as clear. Here, the strongest correlation is with theCHIME subscale for decentering (r = 0.53). But the other correlation coeffi-cients are not small, except to one to the scale for a openness. Nevertheless,as the greatest gap is between strongest and second strongest correlation,it can be said that presence in the FMI loads strongest on decentering buthas significant loadings on outer awareness, acceptance, inner awareness andinsight. Thus, the FMI presence scale is more mixed in terms of the aspectsdistinguished with the CHIME questionnaire. One should note that usuallya higher number of participants is desirable for the validation or compar-ison of a new questionnaire, hence the results presented here are more of anapproximate nature.

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10. Temporal Processing

The most interesting aspect of bistable perception of the Necker cube isclearly its temporal dynamics. One way to better understand it, is to studyit directly by exploring the dwell time distribution. A second promising ap-proach is to examine potential relations to processes and concepts knownfrom research on time perception and temporal processing. While the firstapproach was pursued in Chapters 4 to 6, some results of the second willbe presented in this chapter. Later, in Chapter 12, some theoretical consid-erations concerning the universality of cognitive temporal processes will bediscussed.

10.1 Time Perception, Reaction and AttentionDue to the temporal nature of bistable perception it is very likely to berelated to other aspects of temporal processing. Furthermore, bistable per-ception certainly has some top-down components (Long and Toppino, 2004),as for example demonstrated in the voluntary control that participants canexercise over perception (cf. van Ee et al. (2005) and Chapter 7). Attentionalprocesses have been shown to be part of this top-down influence (e.g. Reis-berg and O’Shaughnessy (1984), Kohler et al. (2008)). These thoughts ledto the inclusion of tasks operationalising both attention and temporal pro-cessing in the NC-pers study. It was to the goal to find out how temporal andattentional processes are related to both neutral and voluntarily controlledperception of the Necker cube.Time perception can be categorised in three levels of temporal processing inhuman beings (Wittmann, 2011). The functional moment is a basic temporalbuilding block of perception of the order of miliseconds, defining simultaneityand succession. In the experienced moment time of up to a few seconds isintegrated, creating the experience of nowness. Thirdly, the mental presence

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encompasses multiple seconds over which cognitive and emotional processesare maintained. For bistable perception both the functional moment and theexperienced moment might be important. In fact, these two timescales havebeen linked theoretically in the Necker-Zeno model (Atmanspacher et al.,2008, 2004). Repeated or periodic perceptual processes in the range of thefunctional moment might be involved in triggering perceptual reversals. Asimple Go/Nogo reaction time paradigm was used in order to probe this tem-poral range. A temporal integration task (Szelag et al., 1996) based on theperception of metronome beats aimed at the second time range, namely theexperienced moment. This is also the range, into which Necker cube reversaltimes fall.Diverting attention has been shown to slow down perception of percep-tual (Reisberg and O’Shaughnessy, 1984) and binocular rivalry (Alais et al.,2010). The latter study compared the effect for binocular with that for theNecker cube. It was found that attention had a greater effect for perceptualthan for binocular rivalry. This indicates a high-level, top-down influence ofattention. There are at least three distinct differences between attentionalprocesses and bistable perception, though, as pointed out by Leopold andLogothetis (1999). First, voluntary control over attention is larger than thatover bistable perception. Secondly, attention can enhance processing of avisual object while in bistable perception the perception can change com-pletely. Third, attentional shifts can be much faster than the shortest dwelltimes. On the basis of these findings, it was the goal to find out in which wayinter-individual differences in attention were related to differences in bistableperception of the Necker cube. A common attention task, namely the d2task (Brickenkamp, 2002), was used to operationalise attention. This taskcaptures several aspects of attention in a visual paradigm and is thus wellsuited to compare to bistable visual perception.

10.2 Exploring Links in Time ScalesAs described above, temporal processing was operationalised via an attentiontask, a reaction time task and a temporal integration task. All three tasksas well as the voluntary control experiment for bistable perception of theNecker cube (as detailed in Chapter 7) were completed by 65 participants.Data sets of 58 participants (29.0± 9.5 years, 27 male) were used for furtheranalysis, with 7 being excluded because of insufficient data for the Necker

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cube experiment.To operationalise attention, the d2-attention task was utilised in pen andpaper form. The test consists of 14 rows of the letters “d” and “p”. Aboveand below these letters are one to four short vertical strokes. Participantswere asked to cross out as many d’s with two strokes in each line withoutmissing any. They had 20 s for each line. They also were presented with ashort practice.For the analysis the first and the last line of the test were not considered.The remaining twelve lines were evaluated in four blocks of three lines. Thenumber of attended targets were determined by counting the number of tar-gets (crossed-out or not) per line up to and with the right-most crossed-outtarget. The concentration performance was calculated as the sum of theblock-wise differences between the number of attended target objects perblock and the number of confusions per block, i.e. the number of instanceswhere a non-target object was marked. The percentage of errors was determ-ined by dividing the total number of errors (confusions and omissions) by thetotal number of attended target objects. The total number of target objectswas determined as the sum of all attended targets over all twelve lines.As reaction time task, a simple Go/Nogo task was used. Participants werepresented with a random sequence of 50 visual stimuli. Half of the stimuliwere the left image in Fig. 10.1, the other half the right one. Participantswere asked to press the space-bar on the computer keyboard as quickly aspossible for the right image but not for the left. They were instructed totry and not make any errors, i.e. missing to press the space-bar or pressingwhen the left image was shown. Times of image appearance and participantresponse were recorded with Psychtoobox-3. Note that both images are re-arrangements of the Necker cube line drawing in order to make this stimuluscomparable to the Necker cube in terms of luminosity and contrast. As mostparticipants made no or only very few mistakes in this task, error rate wasnot taken into account and reaction time was calculated as the mean reactiontime for all correct space-bar presses.The temporal integration task as described by Szelag et al. (1996) was usedhere with small adaptions. Metronome beats (auditory clicks) were presen-ted at frequencies of 1, 2, 3, 4 and 5Hz (beats per second). The duration ofclicks was about 1ms. Stimulus sequences of clicks were presented via speak-ers for 10 s. Participants could adjust sound volume to a comfortable level.They were asked to listen to the equally spaced beats of the metronome andto integrate beats into larger units consisting of 2, 3 or more beats. To do

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Figure 10.1: Stimuli for the Go/Nogo task. Participants were asked to react as quickly aspossible to the right stimulus and not at all to the left one.

so, they were instructed to accentuate mentally every second, third, fourthetc. beat, thus creating a subjective rhythm for themselves, e.g. 1-2-3-4, 1-2-3-4, etc. Participants reported how many clicks they could integrate into oneperceptual unit by pressing the corresponding number key on the keyboardof a computer after each sequence. Each of the 5 different frequencies werepresented 5 times in randomised order. This resulted in a total of 25 tri-als. Subsequent trials were interrupted by breaks of 6 s to prevent carry-overeffects. A break of two minutes was given after half of the trials. At thebeginning of the task, participants were given a few practice trials in orderto familiarise themselves with it.For all metronome frequencies, median integration times were calculated foreach participant. The integration time is the number of beats a participantintegrated into one unit multiplied by the time between successive beats(which is the inverse of the metronome frequency). Here, the median wasused, and not the mean, as there is only a small number of data points perparticipant and frequency, namely 5, making the median the more robustmeasure. Additionally, the range of integration times was calculated perparticipant as the difference between the median integration time for 1Hzand 5Hz. Finally, mean and standard deviation for median values over allparticipants were calculated and plotted vs. frequency, in order to comparethe current results with those of Szelag et al. (1996) who showed a similarplot.The measures from these three tasks were tested for correlations with meas-ures of neutral and voluntarily controlled bistable perception, using Spear-man correlation coefficients. For the neutral condition, these were mean andmedian dwell times, as well as parameters, mode and variance of the lognor-

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mal distribution. The voluntary control conditions were described by thethree measures ∆hApA, ∆hBpB and ∆sp introduced and detailed in Sec. 7.2.

10.3 ResultsOf the three scores from the d2 attention task only the number of atten-ded target objects shows significant correlations. This score correlates neg-atively with mean (r = −0.39, p = 0.002) and median dwell times (r =−0.35, p = 0.008) of the neutral condition, as well as with the mode t0,logn(r = −0.35, p = 0.008), the parameter µ (r = −0.37, p = 0.004) and thevariance varlogn (r = −0.35, p = 0.007) of the lognormal distribution. Theseresults remain significant when corrected with the FDR method for multipletesting1. There are no significant correlations to the measures describingvoluntary control over bistable perception.The mean reaction time in the Go/Nogo task did not correlate with anymeasure of bistable perception of the Necker cube.The frequency dependency of the integration times in the temporal integ-ration task is very similar to the one found in Szelag et al. (1996). Theintegration times decrease with increasing frequency, starting slightly below3 s for 1Hz and coming down to a value just above 1 s. The plot is shown inFig. 10.2.Of the measures of the temporal integration task, the range of integrationtimes correlates positively with the parameter σ (r = 0.29, p = 0.03) andthe variance varlogn (r = 0.34, p = 0.01) of the lognormal distribution. Itfurthermore correlates negatively with the ability to hold percept A (∆hApA,r = −0.26, p = 0.05). The median frequency for 1Hz also correlates posit-ively with the parameter σ (r = 0.35, p = 0.006) and the variance varlogn(r = 0.37, p = 0.005) of the lognormal distribution, but not with ∆hApA.Median integration times for the other metronome frequencies do not showany significant correlations to measures of bistable perception.

10.4 DiscussionThe correlations between neutral bistable perception of the Necker cube andthe number of attended target objects in the d2 attention task are very clear

1Note that this proceeding is very conservative, as some of the tested measures arehighly dependent.

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and robust. First, it should be noted that these correlations are highly de-pendent. To illustrate that, Spearman correlation coefficients between meandwell time, t̄, and the other measures of neutral bistable perception werecalculated: median dwell time, t̃: r = 0.97, mode of lognormal fit, t0,logn:r = 0.88, parameter µ of lognormal fit: r = 0.98 and variance of the lognor-mal fit, varlogn: r = 0.89. All these correlations are highly significant. Hence,the correlations of the number of attended targets with the listed measures allpoint in the same direction. They show that short dwell times, and the cor-respondingly small variance, go hand in hand with a high rate of processingletters in the d2 task. The similar correlations and the very low p-valuesindicate a very robust finding.The speed of processing visual information could to be the concept connect-ing both processes. It can be understood within models of bistability thatincorporate adaptation. In these models, with continuous sensual input, cer-tain neural cycles are excited until they satiate at which point a perceptualreversal takes place. For more details on these models cf. Sec. 2.1. Whenprocessing speed is high in an individual, satiation, and hence the perceptualinversion, will be very likely to occur earlier. Note, that at this point nohypothesis is given of how this concept of processing speed would be incor-porated on a neural level. On the other hand, a high processing speed willalso lead to a high number of targets attended in the d2 task, irrespectiveof error rate in that task. Thus, this finding points towards a common tem-poral structure in visual processing. This is an important finding as it helpsto create a conceptual bridge between bistable perception and temporal pro-cessing.The lack of a correlation between the measures of bistable perception and themean reaction time provides another piece of information for relating bistableperception to temporal processing in general. It indicates that perception ofthe Necker cube does not use the same temporal processing structures as asimple reaction time task – at least not to a large extend. In other words, themechanisms that enable a person to react quickly do not make them switchmore often – or less for that matter.The findings on temporal integration, on the other hand, suggest that theremight be another relation to bistable perception. First, the temporal integ-ration vs. frequency plot (Fig. 10.2) demonstrates that the task was correctlyreproduced after Szelag et al. (1996). The integration times for the differentfrequencies are very similar to those in the cited study. Standard deviationsin the current plot are considerably smaller than in the original article which

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was based on a lower number of participants. Furthermore, half of the groupof Szelag et al. (1996) had a much higher average age (ca. 58 years). Thus,the integration times found here can be used with good confidence for furtheranalysis.The correlations calculated for the median integration time at 1Hz, t̃int,1Hz,are similar to those found for the range of integration times, t̃int,range. In fact,t̃int,1Hz is highly significantly correlated with t̃int,range (r = 0.91, p < 0.001).This is because the range is the difference between t̃int,1Hz and t̃int,5Hz. Thefurther information added by t̃int,5Hz that the range represents might not becrucial here, as all the higher metronome frequencies from 2 to 5Hz do notcorrelate with any measure of bistable perception. So the main contributionseems to come from the integration time at 1Hz, for which the also the cor-relation coefficients are higher.The correlation between the variance of the lognormal fit and t̃int,1Hz indic-ates that long integration times go hand in hand with a large variance. Asthe skewness of the lognormal distribution increases monotonically with σ,which is also large for long integration times, this means that long integra-tion times are associated with a strongly right-skewed dwell time distributionwith a large variance.2 Thus, large dwell times occur more frequently whilethe most frequent dwell times, those around the mode, remain more or lessstable. This interpretation is supported by a trend towards positive cor-relations of mean dwell times to t̃int,range and t̃int,1Hz (r = 0.25 and 0.24,respectively; p = 0.06 in both cases). So this finding suggests a positiverelation between dwell times and integration times. This could be indicativeof a common temporal processing. In other words, there are at least partlyoverlaps between temporal processing and the reversal process.The negative correlation of the integration time range with ∆hApA might beat least partly related to the increased difficulty to prolong already long dwelltimes. In the sense that a large range, associated with long dwell times, willgo hand in hand with a low ability to prolong percept A.To better understand the results presented here and in order to increase theirexplanatory power, it would be very interesting to further study bistable per-ception and temporal integration with respect to two aspects. (1) How willdwell times be related to integration times at lower metronome frequen-cies and (2) how are integration times at 1Hz distributed within one person?

2The skewness of a distribution indicates how asymmetric it is, with a positive skewness,as for the lognormal distribution, indicating a long tail to the right.

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The first question is likely to put the metronome task into a parameter regionwhere the time scales match much better with those of bistable perception.At 1Hz the relevant time scale of the metronome task is 1 s, at 2Hz it is0.5 s and so forth. I.e. with increasing metronome frequency the individualtemporal units, i.e. beats, get smaller and smaller compared to the mean re-versal times. Even for very fast reversers, these are usually not smaller thanroughly 1.5 s. Thus, it might be that for lower frequencies, i.e. larger dur-ations between beats, the correlations to dwell times will become stronger.Metronome frequencies of 0.5, 0.25 and 0.125Hz would be good choices forthis approach, probing time scales of 2, 4 and 8 s, respectively, thus accessingtypical dwell time ranges. If the correlations found in the current study wasconfirmed, it would be interesting to get a higher number of data points atone frequency for which integration times correlate strongly with dwell timesand study the distribution of these integration times. Maybe similarities orclear differences to the distribution of dwell times could be found that wouldallow for a comparison of the two processes.In conclusion, the results presented in this chapter identified two temporalconcepts that are related to and seem to play a role in bistable perception ofthe Necker cube: processing speed and temporal integration. While a highprocessing speed goes hand in hand with short dwell times, a high degree oftemporal integration co-occurs with long dwell times. Reaction time, on theother hand, seems to be based mainly on other processes than those involvedin bistable perception.

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11. (Un-)Related Processes

In this chapter, similarities and differences of other perceptual and cognitiveprocesses to bistable perception of the Necker cube will be presented.First, an acoustic analogue to the Necker cube will be introduced and thetemporal dynamics of its perception will be described. Second, an experimentexploring potential relations of visual bistable perception to working memorywill be presented.

11.1 The Verbal Transformation Effect

11.1.1 Acoustic Multistable PerceptionThere are at least two different categories of bistable acoustic stimuli: aud-itory streaming stimuli and verbal transformation stimuli.Auditory streaming is characterised by an alternation of high and low fre-quency tones. Pressnitzer and Hupé (2006) presented repeated ABA patternsof high (A) and low frequency (B) tones. This leads to perception of eitherone stream (ABA-ABA) or two streams (A-A-A and -B—B-) for listeners.The verbal transformation effect was already reported byWarren and Gregory(1958). The authors used an endless loop of a recording of a word like “say”.The perception of the word would abruptly change to “ace” and back again.Radilova et al. (1990) studied this effect for three different reversible words,one of which was used in the current study described in the next sections.For auditory streaming Pressnitzer and Hupé (2006) found strong similaritiesto perception of visual plaids, a monocular rivalry stimulus, but no correla-tion between the amount of switches in both categories (r ≈ 0.40, p = 0.06).The authors compared dwell time distributions for both percepts using nor-malised dwell times. They reported characteristics of the gamma and thelognormal distribution, without a formal goodness of fit analysis. Also, they

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did not find a significant difference between acoustic and visual normaliseddwell times with a Kolmogorov-Smirnov test. In the same study, volun-tary control over bistable percepts in both modalities was quantified. Againno correlation was found between the two categories. These findings wereinterpreted as an indication that both forms of bistable perception sharecommon principles, which are implemented at least partly independently forboth modalities. Presenting auditory streaming stimuli simultaneously withvisual plaids or apparent motion stimuli, Hupé et al. (2008) found that per-ceptual switches co-occur independently in both modalities.Kondo et al. (2012) compared the number of switches for bistable perceptionof the Necker cube to both auditory streaming and the verbal transformationeffect, but did not consider the distribution of dwell times. They found sig-nificant correlations between visual and acoustic bistability with correlationcoefficients of roughly 0.30. Furthermore, significant correlations of reversalsfor visual plaids to auditory streaming were found (0.30 ≤ r ≤ 0.58). Prob-ably, the interactions were significant in this study but not in Pressnitzer andHupé (2006) because of the higher number of participants in the former.Here a detailed examination of the temporal dynamics of verbal transform-ation for the syllable pair “au” and “gen” utlilised in Radilova et al. (1990)will be presented. Furthermore, comparisons to bistable perception of theNecker cube will be made.

11.1.2 MethodsThe verbal transformation effect was studied using a loop of the computer-generated syllables “au” and “gen” (Radilova et al., 1990). The 23 Germanspeaking participants of the NC-dist study heard this loop via two computerloudspeakers for 3 minutes. A description of the acoustic transformationeffect was given beforehand but no training session. In order to minimisea potential bias towards one or the other word, the syllable sequence wasslowly faded in, i.e. the volume of the stimulus was increased from inaudibleto a comfortable level. Participants were asked to passively listen to thesyllable sequence and indicate perceptual reversals from “Augen” to “genau”and vice-versa with two buttons in a similar way as in the experiment onvisual bistable perception of the Necker cube. Computer-generated stimuliwere used in order to keep the stimulus emotionally neutral.The first half minute of recorded dwell times was discarded in order to ac-count for possible adaptation in the beginning of the presentation, as no

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training was given. Subsequently, dwell time data was corrected for mul-tiple, successive presses of the same button in the same way as for the visualbistable perception data (cf. Sec. 3.4). In this way, the amount of data pointsof two participants was reduced so much that they had to be excluded fromfurther analysis, resulting in a data set of 21 participants (25.6 ± 8.0 years,12 male).In order to explore the possibility of an overlap between visual and acousticbistable perception, the dwell time distribution for the verbal transformationeffect was analysed in the same way as for the Necker cube. The gamma, thegamma rate, the lognormal, the lognormal rate, the Weibull and the Rayleighdistributions were fitted to the data using the maximum likelihood method.As for visual bistable perception, goodness of fit was quantified using SSEand pKS. The details of the fitting and evaluating procedure were identicalto the ones described in Secs. 4.4 to 4.6.Additionally, Spearman correlation coefficients for mean and median dwelltimes as well as for the mode of the lognormal distribution between visualand acoustic bistable perception were calculated for the 21 data sets availablefor both experiments. For the Necker cube experiment, these three measureswere calculated from data of the first cube shown in the experiment (coveringa visual angle of 4 ◦). These first measurements on the Necker cube are mostsimilar to the corresponding acoustic experiment as no long-term adaptationwas possible (which cannot be completely excluded for later measurementsof the other cube sizes). For both the Necker cube and the verbal transform-ation effect data, the mode was calculated from the lognormal fits as theseprovided the best fit quality and descriptiveness for both types of dwell timedata (cf. next section).

11.1.3 ResultsBoxplots of the measures of goodness of fit for dwell times of the verbaltransformation effect are shown in Fig. 11.1. The order of fit performance issimilar compared to dwell times in the visual modality. In terms of SSE thelognormal rate and the gamma rate distribution provide the best fit, withmaybe a slight advantage of the lognormal rate fit. Next best fits are thelognormal, then the gamma, the Weibull and lastly the Rayleigh distribu-tion. Considering the pKS-values, the lognormal rate distribution yields thebest fit, followed by the lognormal, the gamma rate, the gamma, the Weibulland the Rayleigh distributions. The amount of data sets for which the mod-

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ified K-S test rejects the Null hypothesis at the 0.05-level is smallest for thelognormal rate fit (2; 10%), followed by the lognormal and the gamma ratedistributions for both of which 5 fits (24%) were rejected. For the gammadistribution 7 fits (33%) were rejected, for the Weibull 12 (57%) and for theRayleigh 15 (71%).Neither for mean, for median dwell times nor for the mode of the lognormaldistribution was there a significant correlation across the two types of exper-iments. Correlation coefficients and p-values are r = 0.01, p = 0.95 (mean),r = 0.14, p = 0.54 (median) and r = 0.16, p = 0.49 (mode of lognormaldistribution), respectively.

11.1.4 DiscussionThe comparisons of the different distribution functions with boxplots showthat the lognormal rate fits yield the best quality, followed by the lognormaldistribution and the gamma rate distribution. This is a clear parallel to thevisual perception of the Necker cube. Also, the percentage of rejected fitsis very similar to visual perception. As the lognormal and the lognormalrate fit are equivalent, the lognormal distribution seems to provide the bestcompromise between fit quality and descriptiveness as it characterises dwelltimes and not rates, which do not have a direct perceptual correspondent (cf.also Sec. 4.6.2).Thus, the temporal dynamics of acoustic and visual bistable perception arevery similar. This finding is in good agreement with the results of Press-nitzer and Hupé (2006) who also found similar dwell time distributions forboth modalities. The authors did not approach this question by consideringthe goodness of fit of the dwell time distributions, though. Thus, the currentwork is the first rigorous test of goodness of fit for a verbal transformationeffect stimulus.The correlation tests on the other hand, show that there are also considerabledifferences in reversal behaviour between the two modalities. At least part ofthe reversal process in bistable perception is implemented independently forvisual and acoustic perception. This must be the case because a fast reverserfor the Necker cube is not necessarily a fast reverser for verbal transformationand vice versa. The results of the correlation tests are somewhat at variancewith the results of Kondo et al. (2012), who found significant correlationswith correlation coefficients around 0.30 between the number of switches intwo verbal transformation tasks and perception of the Necker cube. In the

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current study, though, the correlation coefficients are essentially zero. Therewere some differences in the experimental setup on the Necker cube thatmight be responsible for these differences. Kondo et al. (2012) used a singlebutton design for reporting, which in principle should not influence the res-ults. Furthermore, several short trials were used leading to a total lengthof observation of more than double the time used in the current study. Thevisual angle was the same in both studies. Even though probably no practicesessions were used in the study of Kondo et al. (2012), it is not likely thatshort adaptation effects in the beginning of the measurement would accountfor the different results to the current study, as the overall measurementperiod was very long so that a potential initial adaptation in the experimentof Kondo and co-workers should be leveled out by the later data. Lastly,for the acoustic experimetn, the verbal transformation stimuli were differentfrom the current one. Most of the different verbal interpretations these stim-uli could take were words from the Japanese language. This is probably themost pronounced difference in experimental design between both studies andmight in itself account for the differences in results.Furthermore, there is also a marked difference in analysis of dwell time data.Kondo et al. (2012) excluded the data of 8% of the participants because thesereported a large number of reversals in particular for the verbal transforma-tion effect. This might have a strong effect on the correlations between dwelltimes in both modalities. No such correction was performed in the currentstudy.In conclusion, in the current study it was shown that the lognormal distri-bution produces the best combination of fit quality and descriptiveness forthe verbal transformation effect dwell time data of the Augen/genau stimu-lus. Lognormal rate and gamma rate distributions yield good and acceptablefits, respectively. This shows a clear similarity to bistable perception of theNecker cube, suggesting a certain overlap in the processes involved in bistableperception for the visual and the acoustic modality. Parts of the processingleading to perceptual reversals are very likely to occur independently for bothmodalities, though, as there was no correlation between dwell times for thevisual and acoustic modality.

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11.2 Working Memory

11.2.1 “Memory” in Bistable PerceptionThere are several hints that memory plays a role in bistable visual perception.Using spectral analysis, Gao et al. (2006) found that dwell times of bistableperception of the Necker cube behave as 1/f noise and show long-range cor-relations. This points towards a “memory” effect perception of the Neckercube, meaning that a long dwell time is more likely to be followed by a longdwell time and vice versa. Studying intermittent presentation of bistablestructure from motion and binocular rivalry stimuli, Pearson and Brascamp(2008) report on memory traces stabilising percepts over long blank phases.Brascamp et al. (2009) even find periodic alternations in a discontinuouspresentation paradigm. Thus, there are two, maybe different indirect reportson memory in bistable perception.As a much more direct finding, Allen et al. (2011) reported correlations be-tween working memory capacity and bistable perception of the Necker cubeincluding its voluntary control. The authors found that working memorycapacity correlated positively with dwell times when viewing a Necker cubeneutrally or when trying to minimise reversals. A negative correlation wasfound when trying to speed reversal up or to hold one specific percept. Inthe latter case the correlation was between working memory capacity andthe percept that was not held. In their study working memory capacity wasoperationalised using a reading span task based on Daneman and Carpenter(1980). Unfortunately, no details of the methods of their experiments norquantitative results were given by Allen and co-workers in their abstract pub-lication.In order to gain a more detailed description of these memory effects andextend them by using a second memory task, working memory capacity wasstudied for correlations with bistable perception of the Necker cube.

11.2.2 Working Memory in Bistability?In order to explore potential overlaps between the cognitive processes in-volved in bistable perception and working memory, two measures quantifyingworking memory capacity were tested for correlations to measures describingbistable perception, both in the neutral and in the voluntary control condi-tions.

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32 participants completed the experiment on voluntary control over bistableperception, as well as two tests on working memory: the backward digitspan task and the reading span task. As described in detail in Chapter 7,the bistable perception experiment comprised of four conditions, each threeminutes long, in which participants indicated perceptual reversals of a Neckercube using two buttons. The first condition was always the “neutral” one,where participants were asked to observe the Necker cube passively. In theother three conditions, participants were instructed to try and hold one per-spective of the Necker cube and avoid the other (implemented in both possiblepermutations) or to speed up perceptual reversals as much as possible.Backward digit span and reading span tasks were implemented as in Oberaueret al. (2000). The backward digit span task comprised of different series ofdigits presented on a computer screen. Participants were asked to repeateach series in reversed order by typing its digits on the keyboard at the endof the series. Each digit of a series was presented for 1000ms. Two series withthree and four digits served as a practice session. After that, fifteen serieswere presented, starting with four digits and increasing by one digit everythree series up to eight digits. The total number of correct digits recalledfrom all fifteen series was calculated as an overall score.In the reading span task, which was based on Daneman and Carpenter (1980),several series of sentences were presented on the computer screen. Each sen-tence was displayed for 3 s and was followed by a 1 s inter-stimulus-intervaltill the next sentence appeared. Participants were asked to rate each sentenceas “true” or “false” during the corresponding four-second-interval. At the endof each series, participants were asked to recall the last word of each sentencein the series in the order of presentation. There were two practice series andfifteen test series. The experiment started with three sentences per series andincreased by one sentence after every third series, up a series length of sevensentences. The sentences used abided by the following criteria: short andsyntactically simple, trivially true or false and the last word being a familiarnoun of less than four syllables. A score was calculated in the same way asfor the backward digit span task.For the correlation tests, mean and median dwell times were calculated fromdata of the neutral condition of the Necker cube experiment, as well as mode,distribution parameters and variances of the lognormal dwell time fit. Fur-thermore, the three measures quantifying voluntary control over perceptionof the Necker cube described in Chapter 7 were used: ∆hApA, ∆hBpB and ∆sp.After dwell time data preparation (cf. Sec. 3.4), data sets of 28 participants

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(mean age 30.6± 10.9 years, 12 male) were available.Spearman correlation coefficients and p-values were calculated between thesemeasures of bistable perception and the two test scores describing workingmemory capacity.

11.2.3 ResultsThe two scores quantifying working memory capacity do not correlate signi-ficantly with any of the measures describing bistable perception of the Neckercube and voluntary control over it. All p-values are larger than 0.2, correla-tion coefficients are all smaller than 0.26.

11.2.4 Working Memory Does Not Work BistabilityThe results do not support a relation between bistable perception and work-ing memory capacity (WMC) as operationalised by the reading span taskand the backward digit span task. Neither neutral dwell times nor the abil-ity to hold either percept or to speed up reversals correlated with these twomeasures of memory. These findings are at odds with the positive correla-tions of WMC with dwell times in the neutral condition and the negativecorrelation with dwell times in the speed up and hold conditions found byAllen et al. (2011). It is not clear how this discrepancy can be explained asvery few experimental details are given in the cited study. Only the length ofthe measurements, namely 3 minutes, and the usage of a fixation cross werestated by the authors. Size of the stimulus and exact reporting condition arenot known. Furthermore the number of participants was not given, nor wereeffect strengths and p-values, or how the reading span test was implemented.Maybe, no effects were found in the current study because of some differencesin these unspecified parameters in the study of Allen and co-workers.The hints for memory effects stated in Gao et al. (2006), Pearson and Bras-camp (2008) and Brascamp et al. (2009), on the other hand, are not con-crete enough to directly contradict a lack of correlations between WMCand bistable perception. Maybe intermediate-term memory and not workingmemory is the right concept to capture these processes. Thus, the currentresults show that further research and other conceptualisations of memoryare necessary in order to study its suggested relations to bistable perceptionof the Necker cube.

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12. Bistability within 3 s?

Pöppel (1997) proposed a low-frequency mechanism creating perceptual unitsof about 3 s. The author suggested that this binding mechanism was operat-ive, among other situations, in bistable perception and that the dwell timeswere examples of the resultant perceptual units. In the following, it will beargued and supported with empirical data that this description neglects twoimportant characteristics of dwell times in bistable perception, namely (1)their intra-individual and (2) their inter-individual variation. This is the casefor both visual and acoustic bistability. The proposed binding mechanismis hence not well suited to describe bistable perception due to its lack tocapture the stochastic nature of bistable perception.In Pöppel (1997) the author stated: “Spontaneous alteration rates of am-biguous figures support the notion of temporal integration. If stimuli can beperceived with two perspectives (for example, the Necker cube [. . . ]), thereis an automatic shift of perceptual content after 3 s. [. . . ] Such a perceptualshift also occurs when interpreting ambiguous auditory material, such as thephoneme sequence CU-BA-CU, where one hears either CUBA or BACU.”Pöppel posited a “low-frequency mechanism [that] binds successive events upto 3 s into perceptual units” (Pöppel (1997)). He proposed that the timebetween successive perceptual switches in bistable perception is an exampleof such a perceptual unit. This statement neglects the characteristic intra-individual and inter-individual variation of dwell times.As described in Chapters 1 and 4, intra-individual variation is an expressionof the stochastic nature of bistable perception: perceptual switches betweenthe two alternatives of a bistable stimulus do not occur always after the sametime interval. Rather dwell times show an unimodal statistical distributionwith a finite width. Both the lognormal rate, the lognormal and the gammarate distribution seem to fit well to empirical data (Brascamp et al. (2005),Zhou et al. (2004), as well as Chapter 4). Fig. 12.1 shows an example of

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Figure 12.1: Left: Binned frequency of dwell times (green) with lognormal fit (blue) forone observer of the Necker cube and a measurement period of 3minutes. Right: Part ofthe dwell time sequence corresponding to the plot on the left. Dwell times in s.

a lognormal fit to empirical data of perception of the Necker cube for oneobserver of the NC-dist study as well as part of the corresponding measuredsequence of dwell times (for experimental details cf. Sec. 3.3). One can seeconsiderable variations in the dwell times, even in this short part of a meas-urement.The same holds true for acoustic bistable perception of a looped syllable se-quence of “au” and “gen” which can be heard as “Augen” or “genau” (“eyes”and “exactly” in German). Listening to the syllable loop, one’s perceptionalternates between these two German words, an phenomenon called verbaltransformation effect (cf. Sec. 11.1). Here, dwell times also vary significantly,as shown in Fig. 12.2 which displays again a fitted lognormal distributionand part of the corresponding dwell time sequence for the same person as inFig. 12.1.Thus, Pöppel’s proposal is at odds with the intra-invididual variation ofdwell times in two respects: first, it does not account for the variation in it-self, as the perceptual units in the model are taken to be of the same length.Secondly, even if one was to assume a certain statistical variation in thelength of these perceptual units, dwell times with lengths of up to a dozenseconds would not be explicable in this model. For bistable perception of

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yFigure 12.2: Left: Binned frequency of dwell times in the verbal transformation effect(au-gen syllable loop) with lognormal fit for the same observer as in Fig. 12.1. Themeasurement period was 3minutes. Right: Part of the dwell time sequence correspondingto the plot on the left. Dwell times in s.

the Necker cube, apart from our own data described above, different articles(e.g. Borsellino et al. (1972), Brascamp et al. (2005)) show that dwell timesrange from roughly 0.5 s to about a dozen seconds.Furthermore, dwell time characteristics also vary between different observersfor both visual and acoustic bistable perception. If one takes the most ob-vious single measure of bistable perception for one individual, namely meandwell time, for different observers, again, a range of values is found for bothvisual bistable perception of the Necker cube and the verbal transformationeffect. Experimental data displaying this variation is shown in the boxplotsof mean dwell times in Fig. 12.3, corresponding to data sets of 21 observers ofthe NC-dist study. They viewed the Necker cube and listened to the syllableloop for 3 minutes each. Other publications on the perception of the Neckercube support these findings. They report different ranges of dwell times overobservers, depending on experimental protocol, stimulus characteristics orsample of observers. E.g., Beer (1989) find mean dwell times between 1 and3 s, Borsellino et al. (1972) between 1 and 7 s, Dugger and Courson (1968)between 3.4 and 4.2 s and Gao et al. (2006) between 1.2 and 7.2 s. Again,neither this variation in itself is explained by Pöppel’s model nor is the oc-

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currence of dwell times significantly larger than 3 s in most of the studies.It should be kept in mind that dwell times of one observer can be influencedby several stimulus parameters. This constitutes a bottom-up effect (cf.Secs. 1.3.2 and 2.1 as well as Long and Toppino (2004)). It is not clear, howsuch variations can be reconciled with the assumption of a person-specific,universal mechanism (i.e. over different modalities, perceptual channels etc.)for the creation of equi-temporal perceptual units corresponding to perceptsof a bistable stimulus. This is an important point, as the universality of the3 s-units seems to be central to Pöppel’s model.Furthermore, it was shown in Sec. 11.1 that, while there are large similaritiesin terms of dwell time distributions between visual and acoustic bistability,there must also be an independent part of processing in both modalities due

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to the lack of correlation between visual and acoustic dwell times. This isanother finding that speaks against a central binding mechanism as sugges-ted by Pöppel.Another interpretation of the characteristics of bistable perception as presen-ted above is feasible, while retaining a central binding mechanism. Thestochasticity could be incorporated into the binding process itself, so thatvarying multiples of a fundamental temporal unit of at the most 0.5 s (theapproximate lower bound for perceptual dwell times) would constitute per-ceptual units and hence describe the times between perceptual switches. Amodel along these lines has been proposed with the Necker-Zeno model ofbistable perception (Atmanspacher et al. (2004) and Atmanspacher et al.(2008)). In this conceptualisation, modality-specific processing could occurindependently at later stages.In summary, the idea of an internal binding mechanism producing perceptualunits of roughly 3 s is badly suited to describe bistable perception both inthe visual and the acoustic domain, as it fails to incorporate intra-individualvariations of dwell times from roughly 0.5 s to up to about a dozen secondsas well as individual mean dwell times with values significantly higher than3 s.

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13. Summary & Conclusion

Two empirical psychophysical studies were presented that aimed at improv-ing the description of the temporal dynamics of bistable perception of theNecker cube and its classification in terms of cognitive processes and per-sonality traits. A strong focus was laid on better understanding the stronginter-individual differences in bistable perception.Temporal dynamics and several low-level or bottom-up aspects of bistabiltywere described for the first time for the Necker cube. It was demonstratedthat the initial phase of adaptation which has been reported in the literat-ure with somewhat varying characteristics can be avoided with appropriateinstructions and a short training phase. Furthermore, fit quality of sev-eral dwell time distributions was compared, amongst others, with a modifiedKolmogorov-Smirnov test and found superior for the lognormal distributioncompared to the gamma distribution. The effect of cube size was shown notto be significant for the range of 1 to 6 ◦ of visual angle, in which many studieson the Necker cube are situated. Methodological challenges of testing for ahysteresis effect for the Necker cube were indicated. Additionally, a percep-tual bias effect was analysed quantitatively for the first time, demonstratinga preference to see the Necker cube from above. This bias was shown to bereflected also in voluntary control over perception of the cube and in correl-ations to personality traits and self-reported mindfulness.In terms of the classification of bistable perception of the Necker cube, volun-tary control over perception was studied as a measure with considerable inter-individual differences. Voluntary control over perception was reproduced asreported in several studies. It was shown that neutral dwell times predictthe ability to slow down reversals to a low extend but the ability to speedup them up to a high extend. The psychological concept of action-controlwas found not to be directly related to voluntary control of reversals. Self-leadership and the personality traits of conscientiousness and neuroticism,

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on the other hand, were found to correlate to voluntary control over percep-tion. Furthermore, for the first time, it was possible to demonstrate thatvoluntary control over reversals is positively related to different aspects ofmindfulness in a group of observers unscreened in terms of meditation ex-perience. Several personality traits were found to be not directly related tomeasures of bistable perception: action-control, anxiety, sensation seekingand ambiguity tolerance. One aspect of self-leadership, self-reward, and thepersonality trait of conscientiousness, on the other hand, are correlated neg-atively to dwell times. Processing speed in an attention task was found tobe clearly related inversely to dwell times, suggesting a common mechanismof temporal processing. Furthermore, evidence for a positive correlation oftemporal integration to dwell times was discovered. General reaction times,on the other hand, were not related to dwell times. Also, it was demonstratedthat inter-individual differences in working memory are very unlikely to playa role in bistable perception. Finally, bistable perception was compared be-tween the visual and the auditory modalities with the verbal transformationeffect. Similar temporal dynamics were found. In particular, a goodness offit analysis was conducted and it was shown that dwell times of the acousticbistable stimulus were fitted better with a lognormal distribution than witha gamma distribution. On the other hand, evidence for at least partiallydifferent processing of bistability in both modalities was found in form of theabsence of correlations across modalities in terms of the measures of dwelltimes.On a theoretical note, a universal 3-s-binding mechanism proposed by Pöppelwas found not to be suitable to encompass bistable perception as it neglectsintra- and inter-individual differences of dwell times.Hence, both major goals of this work were achieved. The understanding ofthe temporal dynamics of bistable perception was improved and several rela-tions of bistable perception to cognition and personality traits were unveiled.The analyses also suggested new hypotheses and possibilities for future re-search. Hopefully, the continuation of research in this direction will even-tually lead to a more complete picture of bistability and in particular to abetter understanding of the individual differences in its temporal dynamics.

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Curriculum Vitae

Jannis Wernery

Collegium Helveticum,ETH Zürich & University of Zürich,Schmelzbergstr. 258092 Zürich+41(0)44 632 7501wernery@collegium.ethz.ch

Date of birth: 12 July 1984

Place of birth: Bad Säckingen, Germany

Nationality: German

Education

2003 Abitur at Klettgau Gymnasium Tiengen, Tien-gen, Germany

2003-2008 Studies of Physics at ETH Zürich completed witha Diploma in Physics of ETHZ

2005-2006 Studies of Physics at the University of Edinburgh,Scotland

June & July 2006 Research internships at the groups for solid statephysics of Dr. Paul Clegg and Dr. Jason Crain ofthe University of Edinburgh on molecular spectro-scopy and particle solutions

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Summer 2007 Research internship at the nanophysics group ofProf. Klaus Ensslin of ETHZ on atomic forcemicroscopy

March - July 2008 Diploma thesis at Prof. Mark Sherwin’s groupat UC Santa Barbara, California, using terahertzFTIR spectroscopy to study quantum posts, a newsemiconductor nanostructure

December 2008 - May2013

PhD at Collegium Helveticum, Laboratory forTransdisciplinary Research, on bistable percep-tion of the Necker cube

Research Fields and Interests

Visual and bistable perception (psychology), time perception, cognitive basesof mathematics, philosophy of science

Languages

German (native), English, French

Publications

Wernery, J., 2011. Für einen Empirismus der Würde. In: Sigg, H., Folkers,G. (Eds.), Güterabwägung bei der Bewilligung von Tierversuchen. Collegi-umsheft 11, Collegium Helveticum, Zürich, pp. 119-121

Wernery, J., Kornmeier, J., Candia, V., Folkers, G., Atmanspacher, H., 2011.Dwell time distributions for the bistable perception of the Necker cube. Per-ception 40 (ECVP Abstract Supplement), 172.

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