geometry & gestalt

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GESTALT THEORY © 2011(ISSN 0170-057 X)

Vol. 33, No.3/4, 383-422

Baingio Pinna

What is the Meaning of Shape?

1. On the Shape

Te shape of an object is a primary condition fundamental for our lives. Shapeis the primary visual attribute among others (color, shade, lighting) that elicitsunambiguousidentication due mainly to its constancy . Another relevantperceptual property is itsuniqueness . Indeed, it is unique and much moreinformative than any other object properties, i.e. color, shading (depth) andlighting (illumination).Shapes are not usually regarded as a creation of our brain but appearveridically ,as part of the physical world. As a matter of fact, the core meaning of shapeis one of the main interests and targets of mathematics (from topology andmathematical analysis to trigonometry and geometry) aimed to describe andstudy the main properties of shapes and the relationship among them. No otherproperty has been studied from so many different perspectives and so deeply asshape (see Palmer, 1999; Pizlo, 2008). It is useful to distinguish between shapein the mathematical sense (i.e. as an ideal object) and shape as encoded in thephysical world. In the former sense, objects are ontologically neutral and notalways perceptually possible and relevant.

1.1. Te Invention of the Square

Among all the known shapes, the square is a unique and special one. Teemergence of the square and its geometrical/phenomenal components (sides andangles) is the consequence of the way four segments go together according tothe Gestalt grouping and organization principles. Phenomenally, its singularity,homogeneity, regularity and symmetry are among the strongest of all the knownshapes. Te circle also shows unique properties, but unlike the square it ispresent in nature (e.g. the full moon and the sun). Te square is instead a human

invention. It is a pure creation of the human mind.Te invention of the wheel (i.e. the circle) is likely one of the most importantinventions of all time. It was at the root of the Industrial Revolution. Te oldestknown wheel was attributed to the ancient Mesopotamian culture of Sumeraround 3500 B.C., but it is supposed to have been invented much earlier. Ifthe potter’s wheels were the very rst wheels, the invention of the square was


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likely as important as the wheel. Te square is, in fact, a basic shape used tomeasure any kind of object, shape or space. Every shape either regular or irregularis measured in squares (m2) or in the 3-D version of the square, cubes (m3).

Te square is the unit and, more generally, the ‘brick’ of all the other shapes. Bymoving around the gaze and focusing the attention on the shapes, one noticesthat almost everything has a square shape. Most of the human artifacts are madeup of squares or its variations. For instance, houses are composed of windows,oors, tables, televisions and doors that are squares or square-like shapes. As concerns these special phenomenal properties, we will study the meaning ofshape starting from the square.

1.2. Te Shape before the “Shape”: Grouping and Figure-Ground Segregation

Gestalt psychologists were the rst to study and develop a theory of shape,considered as an emergent quality. Tey studied the shape mostly in terms ofgrouping and gure-ground segregation. (Other Gestalt approaches to shapeperception will be discussed in section 3.3.)Rubin (1915, 1921) studied the problem of shape formation in terms of gure-ground segregation, by asking what appears as a gure and what as a background.He discovered the following general gure-ground principles: surroundedness,size, orientation, contrast, symmetry, convexity, and parallelism. Rubin alsosuggested the following main phenomenal attributes, belonging to the gure butnot to the background. (i) Te gure takes on the shape traced by the contour,implying that the contour belongs unilaterally to the gure (see Nakayama &Shimojo, 1990; Spillmann, 2012; Spillmann & Ehrenstein, 2004), not to thebackground. (ii) Its color/brightness is perceived full like a surface and denserthan the same physical color/brightness on the background that appear insteadtransparent and empty. (iii) Te gure appears closer to the observer than thebackground. Wertheimer (1923, see also Spillmann, 2012) approached this problem in termsof grouping. Te questions he answered is: how do the elements in the visual eld‘go together’ to form an integrated percept? How do individual elements createlarger wholes? He studied some basic grouping principles useful to answer theprevious questions. Tey are: proximity, similarity, good continuation, closure,symmetry, convexity, prägnanz , past experience, common fate, and parallelism.It is reasonable to consider that gure–ground segregation must operate beforegrouping (Hoffman & Richards, 1984; Palmer, 1999). For example, dotelements on which grouping acts must be already segregated as a gure fromthe background, otherwise the visual system would not know which elementsto group. Nevertheless, the same elements do not possess the gural properties

of holistic organized and segregated gures; rather, they appear as elementary


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components necessary to create boundaries. Tey are not surfaces, but somethingsimilar to perceptual ‘bricks’ necessary to create something more holistic. In spiteof the apparent differences between gure-ground segregation and grouping,

what is phenomenally clear is that both dynamics are so intimately intertwinedthat a sharp distinction is likely impossible and maybe useless from a scienticpoint of view. Within Rubin’s and Wertheimer’s works, the problem of shape formation isapproached in terms of the main conditions operating in two of the processes(grouping and gure-ground segregation) underlying but preceding the formationof the shape. For example, the unilateral belongingness of the boundaries can beconsidered as a shape issue before the “shape” meaning. It talked about shapebut it did not explain its meaning. Similarly, even if the closure principle can

describe the perception of a square, it cannot say anything about its propertiesand about the way its properties assign the special meanings we have previouslydescribed. Furthermore, it cannot explain the square variations described in thenext sections.Even if Gestalt grouping and gure-ground principles are part of the problem ofshape perception, they do not face directly this problem and, more importantly,they do not answer basic questions like: what is shape? What is its meaning?

2. General Methods

2.1. SubjectsDifferent groups of 12 undergraduate students of architecture, design, linguisticsparticipated in the experiments. Subjects had some basic knowledge of Gestaltpsychology and visual illusions, but they were naive both to the stimuli and tothe purpose of the experiments. Tey were male and female with normal orcorrected-to-normal vision.

2.2. Stimuli

Te stimuli were the gures shown in the next sections. Te overall sizes of thevisual stimuli were~ 3.5 deg visual angle. Te gures were shown on a computerscreen with ambient illumination from a Osram Daylight uorescent light (250lux, 5600° K). Stimuli were displayed on a 33 cm color CR monitor (SonyGDM-F520 1600x1200 pixels, refresh rate 100 Hz), driven by a MacBook Procomputer with an NVIDIA GeForce 8600M G . Viewing was binocular in thefrontoparallel plane at a distance of 50 cm from the monitor.

2.3. Procedure

wo methods, similar to those used by Gestalt psychologists, were used.


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Phenomenological task : Te task of the subjects was to report spontaneously whatthey perceived by providing a complete description of the main visual property.Te descriptions were provided by at least 10 out of 12 subjects and were reported

concisely within the main text to aid the reader in the stream of argumentations.Te descriptions were judged by three graduate students of linguistics, naive asto the hypotheses, to get a fair representation of the ones given by the observers.Subjects were allowed to make free comparisons, confrontations, afterthoughts,to see in different ways, distance, etc.; to match the stimulus with every otherone. Variations and possible comparisons occurring during the free explorationwere noted down by the experimenter. Te selection of the stimuli with oppositeconditions and controls and the possible comparisons among the stimuli preventthe problem of generating biased experiences. Tis is clearly shown by thedifferences in the results (see next sections).Scaling task : Te subjects were instructed to rate (in percent) the descriptionsof the specic attribute obtained in the phenomenological experiments. Newgroups of 12 subjects were instructed to scale the relative strength or salience (inpercent) of the descriptions of the phenomenological task: “please rate whetherthis statement is an accurate reection of your perception of the stimulus, on ascale from 100 (perfect agreement) to 0 (complete disagreement)”. Troughoutthe text we reported descriptions whose mean ratings were greater than 80. Asconcerns these tasks and procedure see Pinna, (2010a, b; Pinna & Albertazzi,2011; Pinna & Sirigu, in press; Pinna & Reeves, 2009).

3. Squares, Rotated Square and Diamonds

3.1. Non-Square Shapes that Appear Like Squares

Shape illusions are only apparently in contrast with the properties previouslydescribed: unambiguous identication, constancy, uniqueness and veridicality.Tese illusions are, in fact, considered to be exceptions visible under specic andrare conditions and, thus, ineffective for real life.Te strong shape illusion, illustrated in Fig. 1a, was described like a large squarewith concave and convex sides. Tis description reveals a “distortion” that doesnot change the basic meaning of the square shape. In fact, the main shape evenif distorted is still perceived like a square. Moreover, paradoxically the distortionreinforces and strengthens the perception of the square. In fact, the square isamodally seen as the whole shape supporting the perceived distortion. Conversely,the distortion is what elicits the amodal wholeness of the square (see Pinna,2010b). Tis kind of phenomenal dynamics also occurs when the perceiveddistortion is not illusory but “real”, as shown in Fig. 1b.


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Fig. 1 Non-square shapes that appear like squares

In more intense conditions in terms of distortion (see Figs. 1c-i), where the squareand its sides or angles appear beveled, broken, crashed, gnawed, deliquescing,deformed, protruding, the main shape is again perceived as a square, whilethose specic descriptions reveal what happens to each square. Tey appear

like “happenings” of a square (Pinna, 2010b; Pinna & Albertazzi, 2011). Tesechanges and happenings can be seen as depending on or related to specic and“invisible” but perceptible causes affecting the shape and the material propertiesof the square. Tey add visual meanings but do not really change the shape of thesquare, which is perceived like the amodal invariant shape supporting all thosehappenings (see also section 5.6). From a geometrical point of view, these arenon-square shapes that appear like squares.Tese results suggest the following questions: Why do we perceive a square plus ahappening in each of these cases, instead of a set of irregular shapes, one different

from the other? What is the role of the happening and of other possible shape

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attributes in shape formation? Which properties inuence and determine themeaning of shape? An answer to the rst question was previously reported by Pinna (2010b). In the

next sections, possible responses to the other questions will be proposed. We willrst start by showing opposite conditions, where squares are perceived like non-square shapes, to understand the ways and under which conditions a square shapecan be inuenced and changed.

3.2. Squares that Appear Like Non-Square Shapes

3.2.1. Square Fig. 2a shows a square. Te gure, here illustrated, appears like a “true” square,i.e. a shape that appears like a squaretout court , a square without anything else.Tis one-word description, “square”, does not reveal any happening or any otherrelevant emerging attribute. Shape properties, like orientation, size and position,are left off, because, under these conditions, they are “invisible” or unnoticeablelike the background. Tese omitted properties are superuous. Te word “square”seems to contain, in fact, everything to recreate exactly the same gure and, thus,does not need any further information. Tis square appears like the best exampleand the model of every “square”.It is worthwhile noticing that the omissions are important information usefulto understand the phenomenology of shape perception. Related to our square,we can state that the more numerous are the omissions (invisible attributes), thebetter is the appearance as a model of this shape, or, conversely the less is theinformation described, the better is the squareness of the shape. We dene as“phenomenal singularity” the instance of a shape that does not need to be denedby attributes and that correspond to a one-word description. In other words, thephenomenal singularity isthe best instanceof a specic shape.By asking naive subjects “draw a square” and, afterwards, “choose the square thatis the most ‘square’ among those illustrated” (see Figs. 2a-c), we found that mostof them (99%) represented the square exactly like the one of Fig. 2a and chosethis gure as the best example of square among the three.Tese results suggest the following questions: What is the relationship betweenthe descriptive and the phenomenal notion of shape? More particularly, what isthe meaning of the term “square” when it denotes a singularity like the shape ofthe object perceived in Fig. 2a? By complementation, what is the meaning of thesame term when it does not refer to a phenomenal singularity but emerges withvisible attributes? What is the visual meaning of the square? What does this shapeconvey, express or reveal in the way it appears?


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3.2.2. Rotated Square Fig. 2b represents an intermediate but crucial step in answering the previousquestions. Tis gure is mostly described as a rotated square. Under these

conditions, subjects introduced spontaneously information about orientation,thus, creating a two-word description. Te rotation becomes now visible, noticeablelike a gure. Te exact orientation is, instead, not specied spontaneously inwords. Only after asking them to describe the apparent direction and degree ofrotation, our subjects reported~ 10° anticlockwise.Tese results suggest a twofold perception: a “true” square plus something thathappens to it, namely, the rotation. In other words, unlike Fig. 2a the square is,now, not only a square, but also a square with a “happening” (Pinna, 2010b)dened in terms of rotation. Te anti-clockwise rotation suggests some kind of

minimum rotation pathway starting from the “true” square of Fig. 2a.Structurally, this happening is similar to those described for Figs. 1c-i.Linguistically, the rotation is an adjective that describes the noun, which is thesquare. Phenomenally, it is what happens to the shape. Te primary role of theshape (square) in relation to the adjective (rotation) can be clearly perceivedby comparing the two following possible descriptions: “a rotated square” and“a rotation with a square shape”. Te second description appears meaninglessand odd. A rotation cannot have a shape, while the shape can have a rotation.Tis suggests a clear asymmetrical hierarchy between the two terms. Te shape

is primary, earlier in time and order than the rotation. Terefore, the shape is anoun and as such it is a word generally used to identify a class of elements. As anoun, the shape is like “a thing”, which can appear in many different ways, andthe rotation is one of this ways of being of the shape, i.e. the attribute of thatspecic thing.Tese phenomenal observations suggest the following methodological note:the asymmetrical descriptions represent a useful method of understanding theprimary role of one visual component over another, e.g. of the shape over therotation and, more generally, of something that becomes the primary thing over

another perceived like its attribute. Another example useful to understand theeffectiveness of this method is represented by the relation between shape andcolor: we say “a red square” and not “a square-shaped red”. Te distinctionbetween things and attributes can also be demonstrated through the positionof the words one relative to the other and through the phenomenal invisibility,i.e. an attribute (way of being of a thing) can be invisible or unnoticed like abackground much more than a thing.Despite this asymmetry, rotation and square dene themselves reciprocally. Terotation is dened by the shape, i.e. the rotation can be perceived if and only

if the square as a singularity is also perceived. Conversely, the rotation denes


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3.3. Te Role of the Frame of Reference in Shape Perception

More recent and complex explanations of the square/diamond illusion are basedon object-centered reference frames. Rock (1973, 1983; see also Clément &Bukley, 2008), starting from previous Gestalt studies (Asch & Witkin, 1948a,1948b; Koffka, 1935; Metzger, 1941, 1975), suggested that the perceivedshape is a description relative to a perceptual frame of reference, i.e. the visualsystem prefers gravitational axes over retinal or head axes. In other words, Rockconsidered Mach’s square/diamond illusion as a clear evidence that a shapeis perceived in relation to an environmental frame of reference where gravitydenes the reference orientation, at least in the absence of intrinsic axes in theobject itself. If the environmental orientation of the gure changes with respectto the two gures, the description of one shape does not match the description

stored in memory for the other shape, therefore the observer fails to perceive theequivalence of the two gures.Te stimulus factors important in determining the intrinsic reference frameare: gravitational orientation; directional symmetry (Pinna, 2010b; Pinna &Reeves, 2009); axes of reectional symmetry, congural orientation (Attneave,1968; Palmer, 1980) and axes of elongation (Marr & Nishihara, 1978; Palmer,1975a, 1983, 1985; Rock, 1973). Tese factors rule the relation between shapeand orientation as it happens in other phenomena (e.g., the rod-and-frame andKopfermann’s effects; Davi & Prott, 1993; Kopfermann, 1930; see also Marr &

Nishihara, 1978; Palmer, 1975b, 1989, 1999; Witkins & Asch, 1948).Tese explanations contain some serious limits especially within the context ofphenomenology. More particularly, they cannot account for the reason why weperceive a square, a diamond or a rotated square without invoking names anddescriptions stored in memory. More specically, they do not say anything aboutwhat changes phenomenally inside the shape properties when axes of reection,gravitation and other factors change and about which shape properties switchwhen a square switches to a diamond.Tese limits are accompanied by the following questions: why are two names/descriptions (square and diamond) stored so differently? Are they stored as differentnames because they are perceived differently or are they perceived differentlybecause they are stored in memory with different names/descriptions? Tese lastquestions are not trivial because they are related to the important problem ofthe primary role of visual perception over the higher cognitive processes (seeKanizsa, 1980, 1985, 1991). Tis implies that the difference between square anddiamond can be accounted for within the domain of vision alone and in terms ofperceptual organization of shape attributes.In addition to these issues, the previous hypotheses cannot explain what shapes,such as squares, diamonds or rotated squares, are, and, even more generally, they


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do not say anything about what a shape is. Tey only state that in the case of thesquare/diamond illusion some factors inuence the switch from one shape toanother. Even if these factors are likely really effective, they cannot explain the

meaning of shape. As a consequence, on the basis of these factors what determinesthe perception of a square and a diamond is not accounted for.

4. Doubts about the Role of Frame of Reference 4.1. On the Second Order Square/Diamond Illusion

Te limits of these hypotheses can be highlighted even more effectively throughsome new phenomenal conditions useful to understand the meaning of shape.Teir rationale is the following: if the perceived shape is a description relativeto a perceptual frame of reference, then results analogous to those achieved withthe square/diamond illusion are expected to be attained through second ordervariations of squares and diamonds.In Fig. 3a, the square and the diamond of Figs. 2a and 2c and the rotated squareof Fig. 2b are changed by making the sides concave. Under these conditions thetwo main effects previously described, i.e. the square/diamond switch and the sizedifference between the horizontal and vertical conditions, are strongly reduced oreven absent. Tey appear more easily like the same gure with different amountof rotation.


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Fig. 3 Second order variations of a square, a rotated square and a diamond

In Fig. 3b, the angles are now rounded. Te two main effects of the square/diamond illusion are clearly absent. Tey are also absent in the further conditionsillustrated in Figs. 3c-g, where the changes involve the whole shapes. In Figs. 3h- j, only one angle of each shape has been changed, but again the square/diamond

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and the size difference effects are very weak or absent. Tese results demonstratethat under these conditions the vertical/horizontal and gravitational axis do notdene the reference orientation and, thus, do not inuence shape perception.

4.2. Te Square/Diamond Illusion with Polygons

A second set of conditions that weaken the previous hypotheses and, at the sametime, contribute to an understanding that the meaning of shape is related to theorientation of polygons. If the rotation of a square by 45 deg induces the square/diamond illusion, similar results are expected by rotating polygons.In Fig. 4, several polygons in two orientations with a different number of sidesare illustrated. Te polygons do not show any kind of difference in the twoorientations. Furthermore, they do not have different names stored in memoryand, nally, they do not show a clear size change like the one reported in thesquare/diamond illusion.

Fig. 4 Polygons and the square/diamond illusion

Why does only the square induce this kind of illusion, while other polygons donot? Te octagon, shown in two orientations, with the sides or with the angles


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along the vertical/horizontal axis (see Fig. 5), is useful when answering thisquestion. Under these conditions, the two gures appear different: one attenedand the other pointed. Sides or angles emerge more strongly in one but not in the

other condition andvice versa . Te vertical/horizontal alignments strengthen thesalience of the sides and the angles. (It is worthwhile clarifying that, among theprevious polygons, the one geometrically and phenomenally closer to the octagonis the hexagon, where sides and angles are as well placed both on the vertical andon the horizontal axis.) Although the two octagons show the difference previouslydescribed, they do not have different names stored in memory and do not showa clear size difference like the square/diamond illusion.

Fig. 5 Flattened and pointed octagons

A new effect emerging in these gures is an illusion of numerosity: the numberof angles and sides is perceived higher in the octagon with the angles along thevertical and horizontal axes. Tis phenomenon is likely related to the phenomenalasymmetry between the emergence of the sides and the angles. Tis asymmetry

will be dealt in greater depth in the next section.

5. Inside the Shape: What is a Shape?

5.1. What are Squares and Diamonds? Sidedness and Pointedness

o understand why the second order variations illustrated in Fig. 3 are notinuenced in the two main properties of the square/diamond effect, it isnecessary to go back to the properties emerging in the two octagons, which helpthe understanding of the meaning of the square and the diamond.

In geometry, a square is dened as a regular quadrilateral, namely a shape withfour equal sides and four equal angles. Sides and angles are the components of asquare that emerge more easily within the gradient of visibility, i.e. the gradient ofphenomenal vividness of different visual attributes that do not pop out with thesame strength (Pinna, 2010a). If a square shape is made up of sides and angles,then it shows phenomenal properties such as “sidedness” and “pointedness” relatedto these components. Tese two properties are only apparently equipollent. Tesquare/diamond illusion demonstrates the vividness asymmetry between theseproperties. In the square the sidedness appears stronger than the pointedness,

while the diamond shows more strongly the pointedness. Te perceived strength


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of one or of the other property is inuenced by the vertical/horizontal andgravitational axis that plays by accentuating the sidedness against the pointednessin the square and,vice versa , the pointedness against the sidedness in the diamond.

On the basis of these properties, it appears clear why the second order variationsof Fig. 3 are not involved in the square/diamond illusions. In fact, in all theconditions illustrated sidedness and pointedness are not in contrast but either thesidedness or the pointedness are attenuated or emphasized, thus weakening onlyone of the two effects. Tis entails that one of the two singularities is weakened,therefore appearing as a rotation of the other.Te two properties can also account for the reason why we perceive a rotatedsquare in Fig. 2b. Tis is due to the strength of the sidedness being higher thanthe one of the pointedness.

Similarly, the numerosity illusion of Fig. 5 can be considered as related to theshape attribute that denes the number of elements in the octagon. We suggestthat this gure, similarly to the other polygons, is mostly dened by the sidednessand thus by the number of sides. More specically, to answer a question like“what polygon is this?” spontaneously we count at a glance the number of sidesbut not the number of vertices. Te importance of the two properties in deningthe shape appears in fact asymmetrical. Terefore, because in the pointed octagonof Fig. 5 the sidedness is weakened while the vertices are perceived with a strongervividness, the numerosity of the sides is determined taking into account or starting

from the angles or vertices, which induce an increasing of number of sides or asummation effect due to the numerosity fuzziness of the sides together with theangles. Te calculation at a glance of the number of sides can include also somevertices that pop out more strongly than the sides.Tese phenomenal reports suggest that, all else being equal, the perceived shapecan change or switch from one shape to another by accentuating the sidednessor the pointedness independently from the vertical/horizontal and gravitationalaxes. A demonstration of this expectation is illustrated in Fig. 6, where, despitethe congural orientation effects (i.e. the perception of local spatial orientation

determined by the global spatial orientational structure) studied by Attneave(1968) and Palmer (1980), rows of gures are perceived as rotated squares or asdiamonds according to the position of the small circle placed near the sides ornear the angles of the gures (see also Pinna, 2010a, 2010b; Pinna & Albertazzi,2011). While in Figs. 6a and 6c, the geometrical diamonds are phenomenallyperceived as rotated squares, in Figs. 6b and 6d, the geometrical diamonds areperceived more strongly than in the control (Fig. 6e) as diamonds.


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Fig. 6 Rotated squares or diamonds?

5.2. On the Difference between a Square and a Rotated Square

It is worthwhile clarifying that a diamond and a square rotated by 45 deg as shownin Fig. 6 are different shapes, not only because they have two different names, but,mostly, because they show opposite phenomenal properties: pointedness in thediamonds and sidedness in the rotated squares. Tis shape switch is not a minordifference but a variation of the perceptual meaning of shape (see Pinna, 2010b).Pointedness and sidedness are like the underlying shapes of the shape, a second

level shape (meta-shape), i.e. the meanings of the perceived shapes, and, more

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particularly, of the diamond and square or of the two octagons illustrated in Fig.5. Tese phenomenal remarks are corroborated by the results of Fig. 7, where theinner rectangles accentuate the sidedness or the pointedness of both the checks

and the whole checkerboards, thus eliciting respectively the perception of rotatedsquares or diamonds in the same geometrical gures. Tis result demonstrateslocal and global effects of the accentuation.

Fig. 7 Rotated squares or diamonds in both the checks and the whole checkerboards


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Sidedness and pointedness can also be accentuated in the two grids with thesame geometrical shape as shown in Fig. 8. Again, the single elements of the grid(each single inner diamond shape) and the global shape of the grid are perceived

as rotated squares or diamonds by virtue of the accentuation of sidedness orpointedness.

Fig. 8 Rotated squares or diamonds in both the components and the whole grids

Tese results suggest that the shape of an object depends on its inner properties,on their accentuation due to other elements (disk or empty circles) present in


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the visual eld. Terefore, shape perception is the result of the organization of itsinner attributes, whose gradient of visibility can be changed according to accentsplaced in a spatial position that enhances the vividness of one shape attribute

against the other.It is worthwhile showing Kopfermann’s effect demonstrating the dependence ofan object shape on the frame of reference (Kopfermann, 1930; see also Antonucciet al., 1995; Gibson, 1937; Wikin & Asch, 1948). Te effect is shown in Fig. 9 inthe four classical versions. Under these conditions, the square and the diamondof Figs. 9a-b, when included within a rectangle obliquely oriented are perceivedrespectively as a diamond and as a rotated square (see Figs. 9c-d).

Fig. 9 Kopfermann’s effect

Figs. 10a and 10b demonstrate the stronger role of the accentuation of thesidedness or the pointedness over the larger reference frame. Due to the blackdot and to the inner small rectangle, the geometrical shapes are now restored,i.e. the diamond and the rotated square perceived in Figs. 9c-d are switched intoa rotated square and a diamond demonstrating the ineffectiveness of the largerframe of reference.

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Fig. 10 Kopfermann’s effect annulled

5.3. On the Accentuation of Shape Properties

Sidedness and pointedness can be accentuated in many ways (see Pinna, 2010a,2010b; Pinna & Albertazzi, 2011). A powerful accentuation factor is the reversedcontrast shown in Fig. 11. Due to this factor, the same geometrical octagonsappear rotated in opposite directions, clockwise or anticlockwise (Figs. 11a-b).Tey are also perceived pointed with different strength and at different locationsof the gures depending on the position of the white components (Figs. 11c-d).By comparing Figs. 11a-b and 11c-d, the visual differences between the sidednessand the pointedness emerge very clearly. Te difference in salience of sides andangles is seen very clearly also in Figs. 11e-f, where a slightly concave and convexeffect of the sides can be perceived.Tese differences are also accompanied by the illusion of numerosity describedin section 4.2. It is worthwhile noticing that it is not the geometrical orientationwhich denes the numerosity, in fact it is kept constant, but the emergence of the

sidedness or of the pointedness due to their accentuation.

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Fig. 11 Accentuation of sidedness and pointedness in octagons

In Fig. 12, the accentuation of the sidedness and pointedness through thereversed contrast induces diamond-shaped (Fig. 12a) or grand piano-like (Fig.12b) gures in the same geometrical objects.

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Fig. 12 Diamond-shaped or grand piano-like gures in the same geometrical objects

In Fig. 13, the accentuation, due to the arrangement of black and white sides of eachsquare, produces a directional symmetry and elicits several phenomena: (i) a globaland local rectangle illusion, i.e. the geometrical squares, both locally (each singlesquare) and globally (the square made up of squares), are perceived like rectangleselongated in the direction perpendicular to the black sides; (ii) the orientation ofeach element appears polarized (upwards in Fig. 13a and downwards in Fig. 13b);(iii) the elements are grouped in columns and rows and a global waving (up &

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down or left & right) apparent motion is clearly perceived when the gaze followsthe tip of a pen moved across the patterns illustrated in Figs. 13c and 13d.Tese results are likely related to the fact that the black side not only enhances

the salience of the sidedness, but also denes the base of each check. Tis suggeststhat the phenomenal accentuation of one shape property manifests vectorialproperties. More particularly, the accent placed on the black side appears, underthese conditions, as the starting point of the oriented direction. Te white sideof each check, opposite to the black one, is perceived as the tip of the arrow oras the terminal point of the oriented direction induced by the accent. Finally.the magnitude of the vector depends on the magnitude of the accent, here keptconstant. Briey, the accents behave like Euclidean vectors considered in thesame acceptation used in physics.

Fig. 13 Te accentuation, due to black sides, produces a directional symmetry and manifestsvectorial properties

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Tese results demonstrate that the accentuation of one shape property againstthe other can induce different kinds of dimensional, direction and even motioneffects, which suggest a theory of shape, considered like an overall holder

containing many shape attributes that compete or cooperate and whose strengthcan be changed or accentuated in many ways.Other effects induced by the accentuation and by its vectorial properties are thetilt and straighten up effects of Fig. 14. Te dot seems to tilt further the shapeby pulling the top left-hand corner of the parallelogram in Fig. 14-left and topush the whole gure in the right-vertical direction, thus, straightening up theparallelogram in Fig. 14-right.

Fig. 14 ilt and straighten up effects

Another kind of accentuation is induced by the missing parts or cuts of sidesand angles shown in Fig. 15, thus inducing the switch from the diamond to therotated square shape both in the 2D and 3D conditions. It is worthwhile noticingthat the 3D appearance of the cube with the missing corner is weaker than theone of the cube with the cut side (see also Fig. 16). Tis is likely due to thedirectional symmetry induced by the cut, which favors the vertical organizationof lines that camouages the whole 3D perception.


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Fig . 15 Diamond and the rotated square shapes both in the 2D and 3D conditions

By introducing white sides or white dots within the same shape near the corneror next to one side, the cube appearance can be either weakened or optimized (cf.the control at the bottom) as shown in Fig. 16.


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Fig. 16 Te vertical organization weakens the 3D appearance of the cubes

5.4. Other Shape Properties: Te Pointing

Te shape properties are not restricted to the sidedness and pointedness. Giventhe vectorial attributes previously described and the relations between sides andangles and also between what appears as the base of a shape and its height, thepointing is another signicant shape property, which can be strongly inuencedby the accentuation. If the pointing is a shape attribute, then it is expected tocreate and dene the perceived shape.

In Fig. 17a, the horizontal alignment of equilateral triangles induces the pointing


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of the triangles in the direction of their alignment. Tis is due to the conguralorientation effect studied by Attneave (1968), Palmer (1980, 1989) and Palmer& Bucher (1981).

Figs. 17b-c demonstrate that the pointing of the triangles can be deviated orredirected by the small rectangles and circles placed inside each triangle,respectively in the top left and bottom left-hand directions. Tese results areunexpected on the basis of the congural orientation effect (see also Pinna,2010a, 2010b).

Fig. 17 Te pointing and the shape of triangles can be inuenced by the accentuation

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More important than these conditions are the following ones of Figs. 17d-e, wherethe pointing clearly inuences the shape of the triangles, thus demonstratingthat the pointing is a shape property. Geometrically the triangles are isosceles,

nevertheless due to the pointing induced by the two kinds of accentuation(rectangles and circles), they are perceived like scalene triangles. More in details,because the perceived pointing is not in the direction of the angle created bythe two longer sides, this induces an asymmetrical effect that propagates anddetermines the whole shape of each triangle making it appear as scalene.Tese results suggest that the pointing and all the other meta-shape attributeshere studied are the main attributes responsible for the shape formation. Teycan explain what a shape is.Variations in the pointing of sides or vertices, due to the accentuation, clearlyinuence the shape of gures as shown in Fig. 18. Under these conditions, therows of irregular quadrilaterals are perceived as different shapes, difficult torecognize as the same gures. By determining the shape, the accent determinesalso the orientation of each specic shape and therefore the shape-relatedinformation about its rigidity and surface bending in the 3D space. Te bendingregion is easily and immediately perceivable and its location changes in relationto the accent position within the gure. Tese results suggest the kind of visualorganization and the new conditions illustrated in the following section.


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Fig. 18 Rows of irregular quadrilaterals are perceived as different shapes

5.5. Te Headedness and the Organic Segmentation

Tere is a special kind of shape formation never studied before, which subsumes

a meta-shape property that we call “headedness”. Tis property is shown in theirregular wiggly object of Fig. 19a that assumes an organic appearance similar toan amoeba or to some kind of living creature with a head and upper and lowerlimbs, moving in the direction dened by the shape component perceived as thehead of the organism. Te object shapes up slowly and appears reversible, i.e.the same component can assume different roles (head, limb), therefore changingthe whole organic segmentation and, as a consequence, the direction of theperceived motion, the structure, the weight and all the other static and dynamiccharacteristics of the organism.

Tis organic segmentation can be reshaped, similarly to the ways previously


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shown in the case of the squares, through the accentuation of one componentagainst the others in the function of head, thus favoring the emergence of theheadedness shape property. Figs. 19b-e demonstrate that by changing the spatial

position of the small circle the organism changes its shape, appearing each timeas a different creature. Te component dened by the circle becomes the head. As such, all the organic properties change accordingly to what is perceived as thehead, i.e. to the headedness property. For instance, the organisms of Figs. 19b-c or 19d-e are perceived moving in opposite directions. Te limbs appear alsototally different and so on.

Fig. 19 Different organic segmentations of undulated gures

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Figs. 19f-c demonstrate that not all the components can assume the function ofhead. Te accentuation of the bottom components cannot induce so strongly asin Figs. 19b-e the headedness property. Tis likely depends on the position of the

head, usually placed sideways or at the top of a living being. However, the term“usually” does not necessarily mean that the position of the head is totally due topast experience, but that the head should be structurally located in certain spatialcomponents and not in others in order to show the strongest headedness propertynecessary to inuence at best the entire shape. Against the headedness and organic segmentation, it can be argued that theseresults are due to the fact that the lled circle behaves or is reminiscent of aneye, thus eliciting cognitive processes that have nothing to do with the shapeformation within the visual domain. Te counter-arguments to this issue are

illustrated in the conditions of Fig. 20, where the positions of the small circleand the different shapes of the accentuation reject this objection in favor of thespontaneous organic segmentation as part of the problem of shape formationwithin the perceptual domain and depending on the headedness property. Figs.20f-g shows how different shapes of the inner components can create organicsegmentation by putting together different wiggly components that create notonly a head within a body but also a face with different components (nose, mouthand so on).


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5.6. Te Happening as a Further Shape Property

In the light of these results, we can now go back to the conditions illustrated inFig. 1, by reviewing the phenomenal notion of “happening”. It can, in fact, beconsidered as another meta-shape attribute among the others. Every happeningis a discontinuity that accentuates one or more properties of the main shape.Tis discontinuity gives a meaning to the shape in the same way as we haveshown in the previous sections, or like, for example, in the diamond and therotated squares of Fig. 15. Te missing portion of the side or of the angle impartsdifferent meanings to the shape by eliciting a diamond or a rotated square shape.Furthermore, in the same way as the happening (the geometrical discontinuity)imparts a meaning to the shape, the shape imparts a meaning to the discontinuity.For instance, the object illustrated in Fig. 1c is the result of a complex kind

of shape formation and meaning assignment that we spontaneously dene “abeveled square”. Geometrically, there is neither a “square”, nor a “beveling”, oran “a” but two vertical, two horizontal and one oblique segment forming a closedgure with the oblique segment placed in the top right-hand portion of the gureconnecting the horizontal and vertical segments, shorter than the other two. Tiscomplex geometrical description is strongly simplied by giving a visual meaningto that shape, i.e. a beveled square. Differently from these phenomenal results,good continuation, prägnanz and closure principles group the sides of the gureto form a pentagon. Te discontinuous component, i.e. the oblique segment,gives a meaning to the other sides, that become a square, and, at the same time,the square assigns a meaning to the discontinuity that appear like a beveling (seealso Pinna, 2010a, 2010b).Te notion of happening also suggests a more interesting aspect of the meaningof shape. Shape not only implies boundary contour formation or geometricalorganization like square vs. diamond. It also contains more complex propertiesas suggested by Rubin introducing depth and chromatic attributes (see section1.2). Figs. 1c-i clearly demonstrate that there are also material properties thatcan inuence and assign different meanings to the shape. In fact, when, forexample, it is broken, the material properties strongly determine its shape. If asquare is made up of glass, when its shape is broken, it will be different from asquare made up of pottery or fabric. Te shape of the break changes accordingto the material property. Conversely, the shape of the broken square suggests itsmaterial properties. Te beveled square indicates only a small number of materialattributes (paper, metal, etc.) and, at the same time excludes many others. Teyare reciprocally determined in the same way we have seen in the case of thediamond and the rotated square.For a more exhaustive analysis of the notion of “happening” see Pinna (2010a,2010b) and Pinna & Albertazzi (2011).


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6. Discussion and Conclusions

In the previous sections, following the methods traced by Gestalt psychologists,we studied the meaning of shape perception starting from the square/diamondillusion, which represents a problem for the invariant features hypothesis and forany model of shape formation. Teories based on the role of frame of reference indetermining shape perception were discussed and largely weakened or refuted inthe light of a high number of new effects, demonstrating the basic phenomenalrole of inner properties in dening the meaning of shape.On the basis of these effects, several shape properties were demonstrated. Teyare: (i) the sidedness and the pointedness, related to the sides and angles in thecase of squares, diamonds and polygons; (ii) the pointing involved mostly inthe triangles; (iii) the headedness, i.e. the appearance like a head of a particularcomponent within an irregular shape, in the case of a new kind of visualorganization that we called “organic segmentation”; nally, (iv) the happening,i.e. the something that happens to a gure. Many other shape properties remainto be studied.Tese shape properties were demonstrated to underlie the whole notion of shapeand to appear like second level shape meanings. Tey can be considered liketransversal or elemental meta-shapes common to a large number of shapes bothregular and irregular. Tey are like meaningful primitives, phenomenally relevant,of the language of shape perception.Tis suggests that the meaning of shape can be understood on the basis of amultiplicity of meta-shape attributes. Terefore, the notion of shape can bephenomenally represented like a whole visual “thing” that contains a specic setof phenomenal primitive properties. In other words, the shape can be consideredlike the holder of shape attributes. As a holder it expresses and manifests the stateof organization of the inner meta-shapes. Within the shape like a holder, the shape attributes are not placed all at thesame height within the gradient of visibility, i.e. some emerge more stronglythan others depending on a number of factors that can inuence their vividnessand thus their visibility. Among them, we studied some known factors like thehorizontal/vertical axes, the gravitational orientation, the congural orientationand the large reference frame. We also demonstrated their limits and showed thereason of their effectiveness under specic conditions. Within the hypothesis ofthe shape like a holder, their effectiveness depends on the accentuation of onespecic meta-shape attribute. Terefore, in the case of a square, the horizontal/vertical organization of the sides accentuates the sidedness, while in the case ofthe diamond the pointedness is accentuated by the same factor. Tis entails thata rotated square is perceived when the sidedness is stronger than the pointedness;otherwise we would have perceived a rotated diamond.


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the more reason for the notion of happening. In fact, in the case of the beveledsquare, the square appears as the amodal whole object and the beveling as themodal part of it. Te square is the result of the amodal wholeness completion of

something perceived as its visible modal portion. Te square is perceived and notperceived at the same time and its amodal whole completion occurs “beyond” thebeveling. Tis implies that the amodal completion can be considered as a subsetor as an instance of the more general problem of amodal wholeness. In the case ofthe beveled square, the amodal wholeness corresponds to the amodal prägnanz.Tis suggests that every shape manifests an ideal condition where one meta-shapeattribute emerges much more than others. In other words, each shape indicatesamodally its starting or converging point of singularity. Terefore, we are able toperceive how a gure can be changed or accentuated to obtain the best condition

under which the shape becomes a singularity. It is worthwhile noticing that, onthe basis of our results, the gradient of visibility of the shape attributes indicatesthat, when one attribute emerges, the others remain invisible or in a second planeof visibility.In conclusion, the meaning of shape, here suggested, allows its extension toconditions never included in the notion of shape so far. Tey are, for example,the material properties, previously considered as shape attributes (see section5.6), but also gures like those illustrated in Fig. 21, known as “Maluma- akete”(Köhler, 1929, 1947; see also Ramachandran & Hubbard; 2001), where two

opposite attributes are perceived, curviness and pointedness, and where a largeset of further opposite properties – smoothness and sharpness, jaggedness androundedness – are related to these ones.

Fig. 21 Maluma and akete


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SummaryTe aim of this work is to answer the following questions: what is shape? What is itsmeaning? Shape perception and its meaning were studied starting from the square/diamond illusion and according to the phenomenological approach traced by gestaltpsychologists. Te role of frame of reference in determining shape perception wasdiscussed and largely weakened or refuted in the light of a high number of new effects,based on some phenomenal meta-shape properties useful and necessary to dene themeaning of shape. Te new effects studied are based on the accentuation of the followingmeta-shape attributes: sidedness and pointedness (in the case of squares, diamondsand polygons); the pointing (in the triangles); the headedness (in irregular shapes); thehappening (in deformed shapes), i.e. the something that happens to a gure. Everyhappening is a discontinuity that accentuates one or more properties of the main shapeand gives a meaning to the shape.Te phenomenal results demonstrated that the accentuation of the meta-shape propertiesoperates like Euclidean vectors. On the basis of these results we suggested that the meaningof shape could be understood on the basis of a multiplicity of meta-shape attributesthat operate like meaningful primitives of the complex language of shape perception.Terefore, the notion of shape can be represented like a whole visual “thing/holder” thatcontains a specic organized set of phenomenal primitive properties, i.e. the state oforganization of the inner meta-shapes.Keywords: Shape perception, Gestalt psychology, perceptual organization, visualmeaning, visual illusions.

Zusammenfassung

Ziel der vorliegenden Arbeit ist die Beantwortung folgender Fragen: Was ist Formund was ist deren Bedeutung? Die Wahrnehmung von Form und Bedeutung wurdeerstmals anhand einer Quadrat-Rauten- äuschung (Pinna) mit Hilfe der von derGestaltpsychologie entwickelten phänomenologischen Methode untersucht. DieRolle des Bezugssystems für die Wahrnehmung einer Form wird diskutiert, jedochangesichts zahlreicher neuer Effekte größtenteils herabgestuft oder gar widerlegt. Dieseneuen Effekte gehen auf einige für die Denition der Form-Bedeutung förderlicheund notwendige phänomenale Meta-Form-Eigenschaften zurück. Sie beruhen auf der Akzentuierung folgender Eigenschaften: anschauliche Erstreckung von Kanten undEcken (im Fall von Quadraten, Rauten und Polygonen); anschauliche Ausrichtung (bei

Dreiecken); anschauliche Gerichtetheit (bei unregelmäßigen Formen); Bezogenheit aufein dynamisches Ereignis (bei deformierten Formen), also auf das Etwas, das mit einerForm geschieht. Jedes Ereignis stellt eine Störung dar, die eine oder mehrere (implizite)Eigenschaften der zugrunde liegenden Form isoliert und verstärkt und dadurch der Formeine Bedeutung zuweist.Die Beobachtungen zeigen, dass die Meta-Form-Eigenschaften sich wie euklidischeVektoren verhalten. Aufgrund der Ergebnisse vertreten wir die Auffassung, dass man dieBedeutung einer Form auf der Grundlage einer Vielzahl von Meta-Form-Eigenschaftenverstehen kann, die sich ihrerseits wie bedeutungshaltige Primitiva der komplexen Spracheder Formwahrnehmung verhalten. Der Begriff der Form kann daher wie ein holistischer

“Ding- räger” aufgefasst werden, der eine spezisch organisierte Anzahl grundlegender


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phänomenaler Eigenschaften enthält, nämlich den Zustand der Organisation der innerenMeta-Formen.Schlüsselwörter:Formwahrnehmung, Gestaltpsychologie, Wahrnehmungsorganisation,visuelle Bedeutung, Wahrnehmungstäuschung.

References Antonucci, G., Fanzon, D., Spinelli, D., & Zoccolotti, P. (1995): Visual factors affecting the rod- and-frame

illusion: the role of gap size and frame components. Perception, 24, 1119-1130. Asch, S. E, & Witkin, H. A. (1948a): Studies in space orientation: I. Perception of the upright with displaced

visual elds. Journal of Experimental Psychology 38, 325-337. Asch, S. E., & Witkin, H. A. (1948b): Studies in space orientation: II. Perception of the upright with displaced

visual elds and with body tilted. Journal of Experimental Psychology 38, 455-477. Attneave, F. (1968). riangles as ambiguous gures. American Journal of Psychology 81, 447-453.Clément, G., & Bukley, A. (2008): Mach’s square-or-diamond phenomenon in microgravity during parabolic

ight. Neuroscience Letters 447, 179-182.Davi, M., & Proffit, D.R. (1993): Frames of reference and distinctive gural characteristics affect shape percep-

tion. Journal of Experimental Psychology: Human Perception and Performance 19, 867-877.Gibson, J.J. (1937): Adaptation, after-effect and contrast in the perception of tilted lines: II. Simultaneopus

contrast and the areal restriction of the after-effect. Journal of Experimental Psychology 20, 553-569.Goldmeier, E. (1937): Über Ähnlichkeit bei gesehenen guren. Psychologische Forschung 4, 146-208.Hoffman, D.D., & Richards, W.A. (1984): Parts of recognition. Cognition 18, 65-96.Huppe, A., (1984): Prägnanz. Ein gestalttheoretischer Grund-begriff. Munchen, Prol Verlag.Kanizsa, G. (1975): Te role of regularity in perceptual organization. In Flores D’Arcais, G.B (eds.), Studies in

Perception, Festschrift for Fabio Metelli, Firenze, Giunti-Martello, 48-66.Kanizsa, G. (1980): Grammatica del vedere. Bologna, Il Mulino.Kanizsa, G. (1985): Seeing and thinking. Acta Psycologica 59, 23-33.Kanizsa, G. (1991): Vedere e pensare. Bologna, Il Mulino.Kanizsa, G., & Luccio, R. (1986): Die Doppoldeutigkeiten der Prägnanz. Gestalt Teory 8, 99-135.Kanizsa, G., & Luccio, R. (1989): Fenomenologia della formazione di un ordine autonomo della percezione.

Rivista di Psicologia 3, 28-46.Koffka, K. (1935): Principles of Gestalt Psychology. Routledge and Kegan Paul, London, UK.Köhler, W. (1920): Die physischen Gestalten in Ruhe und im stationären Zustand. Eine naturphilosophische

Untersuchung. Vieweg, Braunschweig.Köhler, W. (1929): Gestalt Psychology. New York: Liveright.Köhler, W. (1938): Te place of value in a world of facts. New York, Liveright.Köhler, W. (1947): Gestalt Psychology, 2nd Ed. New York: Liveright.Kopfermann, H. (1930): Psychologische Untersuchungen über die Wirkung zweidimensionaler Darstellungen

körperlicher Gebilde. Psychologische Forschung 13, 293-364.Mach, E. (1914/1959): Te Analysis of Sensation. Chicago, Open Court USA.Marr, D., & Nishihara, H. K. (1978): Representation and recognition of the spatial organizationof three-dimensional shapes. Proceedings of the Royal Society of London 200, 269-294.Metzger, W. (1941): Psychologie: die Entwicklung ihrer Grundannhamen seit der Einführung des Experiments.

Dresden, Steinkopff.Metzger, W. (1963): Psychologie. Darmstadt, Steinkopff Verlag.Metzger, W. (1975a): Gesetze des Sehens. Kramer, Frankfurt-am-Main.Metzger, W. (1975b): Die Entdeckung der Prägnanztendenz. Die Anfänge einer nicht-atomistischen Wahr-

nehmungslehre. In Flores D’Arcais, G.B (eds.), Studies in Perception, Festschrift for Fabio Metelli, Firenze,Giunti-Martello, 3-47.

Metzger, W. (1982): Möglichkeiten der Verallgemeinerung des Prägnanzprinzips. Gestalt Teory 4, 3-22.Nakayama, K., & Shimojo, S. (1990): owards a neural understanding of visual surface representation. Cold

Spring Harbor Symposia on Quantitative Biology LV, 911-924.Palmer, S. E. (1975a): Te effects of contextual scenes on the identication of objects. Memory & Cognition

3(5), 519-526.Palmer, S.E. (1975b): Visual perception and world knowledge: Notes on a model of sensory-cognitive interac-

tion. In D. A. Norman & D. E. Rumelhart (Eds.), Explorations in cognition, 279-307. San Francisco: W.H. Freeman.


38/44


420

Palmer, S.E. (1980): What makes triangles point: Local and global effects in congurations of ambiguous trian-gles. Cognitive Psychology 12, 285-305.

Palmer, S.E. (1983): Te psychology of perceptual organization: A transformational approach. In J. Beck, B.Hope, & A. Baddeley (Eds.), Human and machine vision, 269-339. New York: Academic Press.

Palmer, S.E. (1985): Te role of symmetry in shape perception. Special Issue: Seeing and knowing. Acta Psy-chologica 59(1), 67-90.

Palmer, S.E. (1989): Reference frames in the perception of shape and orientation. In B. E. Shepp & S. Balleste-ros (Eds.), Object perception: Structure and process, 121-163. Hillsdale, NJ: Erlbaum.

Palmer, S.E. (1999): Vision Science: photons to phenomenology, Cambridge, Massachusetts, London, Eng-land, Te MI press.

Palmer, S.E., & Bucher, N.M. (1981): extural effect in perceiving pointing of ambiguous triangle. Journal ofExperimental Psychology: Human Perception & Performance 8(5), 693-708.

Pinna, B. (1993): La creatività del vedere: verso una Psicologia Integrale. Padova, Domenighini Editore.Pinna, B. (1996): La percezione delle qualità emergenti: una conferma della ”tendenza alla pregnanza”. In

Boscolo P., Cristante F., Dell’Antonio A. e Soresi S., (eds.), Aspetti qualitativi e quantitativi nella ricercapsicologica, Padova, Il Poligrafo, 261-276.

Pinna, B. (2005): Riessioni fenomenologiche sulla percezione delle qualità emergenti: verso una riconsiderazi-one critica della teoria della Pregnanza. Annali della Facoltà di Lingue e Letterature Straniere dell’Universitàdi Sassari 3, 211-256.

Pinna, B. (2010a): What Comes Before Psychophysics? Te Problem of ‘What We Perceive’ and the Phenome-nological Exploration of New Effects. Seeing & Perceiving 23, 463-481.

Pinna, B. (2010b): New Gestalt principles of perceptual organization: An extension from grouping to shape andmeaning. Gestalt Teory 32, 1-67.

Pinna, B., & Albertazzi, L. (2011): From grouping to visual meanings: A new theory of perceptual organization,288-344. In L. Albertazzi, G. van onder, D. Vishwanath, (eds.), Information in Perception, MI Press.

Pinna, B., & Reeves, A. (2009): From Perception to art: How the brain creates meanings. Spatial Vision 22,225-272.

Pinna, B., & Sirigu, L. (in press): Te Accentuation Principle of Visual Organization and the Illusion of MusicalSuspension. Seeing & Perceiving.

Pizlo, Z. (2008): 3D shape: its unique place in visual perception. Cambridge, MA: MI Press.

Ramachandran, V.S., & Hubbard, E.M. (2001): Synaesthesia: A window into perception, thought and lan-guage. Journal of Consciousness Studies 8(12), 3-34.Rausch, E. (1952): Struktur und Metrik gural-optischer Wahrnehmung. Frankfurt, Kramer.Rausch, E. (1966): Das Eigenschaftsproblem in der Gestalttheorie der Wahrnehmung. In W. Metzger, & H.

Erke (hrsg.), Wahrnehmung und Bewußtsein, “Handbuch der Psychologie”, Bd 1/1, 866-951, Hogrefe,Göttingen.

Rock, I. (1973): Orientation and form. New York: Academic Press.Rock, I. (1983): Te logic of perception. Cambridge, MA: MI Press.Rubin, E. (1915): Synsoplevede Figurer. Kobenhavn, Glydendalske Boghandel.Rubin, E. (1921): Visuell wahrgenommene Figuren. Kobenhavn, Gyldendalske Boghandel.Schumann, F. (1900): Beiträge zur Analyse der Gesichtswahrnehmungen. Zur Schätzung räumlicher Grössen.

Zeitschrift für Psychologie und Physiologie der Sinnersorgane 24, 1-33.Spillmann, L. (Eds.) (in press): Max Wertheimer: On Motion and Figure-Ground Organization. MI Press.

Spillmann, L., & Ehrenstein, W.H. (2004): Gestalt factors in the visual neurosciences. In L. Chalupa & J. S. Werner (eds.). Te Visual Neurosciences. Cambridge, MA, MI Press, 1573-1589. Wertheimer, M. (1912a): Über das Denken der Naturvölker. Zeitschrift für Psychologie 60, 321-378. Wertheimer, M. (1912b):Untersuchungen über das Sehen von Bewegung. Zeitschrift für Psychologie 61, 161-

265. Wertheimer, M. (1922): Untersuchungen zur Lehre von der Gestalt. I. Psychologische Forschung 1, 47-58. Wertheimer, M. (1923): Untersuchungen zur Lehre von der Gestalt II. Psychologische Forschung 4, 301-350. Witkin, H.A., & Asch, S.E. (1948): Studies in space orientation, IV. Further experiments on perception of the

upright with displaced visual elds. Journal of Experimental Psychology 38, 762-782.


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Announcements - Ankündigungen

On the occasion of the 100 th anniversary of the pivotal publica on byMax Wertheimer on the phi-phenomenon in 1912,

Wertheimer’s symposiumat the convention of the German Society of Psychology

Bielefeld, 24 th to 27 th September 2012 will take place.

The symposium will be hosted by Viktor Sarris (University of Frankfurt)and Horst Gundlach (University of Würzburg) in coopera on with the GTA

– Society for Gestalt theory and its applica ons.

The preliminary agenda contains contribu ons by Michael Wertheimer(University of Colorado at Boulder), Lothar Spillmann (Neurocentrum,University medical center Freiburg), Riccardo Luccio (University of Trieste),and Jürgen Kriz (University of Osnabrück).

Aus Anlass des 100jährigen Jubiläums der entscheidenden Publika onvon Max Wertheimer zum Phi-Phänomen im Jahre 1912 ndet ein

Wertheimer-Symposiumauf dem Kongress der Deutschen Gesellschaft für Psychologie

Bielefeld, 24. – 27. September 2012

sta .

Das Symposium wird in Koopera on mit der GTA - Gesellscha fürGestal heorie und ihre Anwendungen, von Viktor Sarris (UniversitätFrankfurt) und Horst Gundlach (Universität Würzburg) veranstaltet.

Vorges ehen sind Beiträge von Michael Wertheimer (University of Coloradoat Boulder), Lothar Spillmann (Neurocentrum, UniversitätsklinikumFreiburg), Riccardo Luccio (University of Trieste) und Jürgen Kriz(Universität Osnabrück).

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GTA – SymposiumHelsinki

29. September 2012

In the anniversary year of Gestalt Theory, the GTA – Society for GestaltTheory and its Applica ons – hosts a scien c symposium in Finland forthe rst me.

Inte rac ng with Finnish academics, various topics focusing on GestaltTheory will be covered.

Contribu ons on the following topics are planned: Gestalt Theory -

History and Modern, Gestalt Theory in Finland, Gestalt Theory in Art andCulture, Gestalt Theory in Educa on, Gestalt Theory in Psychotherapy,Gestalt Theory and Design.

Im Jubiläumsjahr der Gestal heorie veranstaltet die GTA - Gesellscha fürGestal heorie und ihre Anwendungen, erstmals ein wissenscha liches

Symposium in Finnland.Gestal heore sche Schwerpunkte aus verschiedenen Themenberei-chen werden in Interak on mit nnischen Wissenscha lern behandelt.

Geplant sind Beiträge u.a. zu folgenden Themen:Gestal heorie - Geschichte und Aktualität, Gestal heorie in Finnland,Gestal heorie in Kunst und Kultur, Gestal heorie in Bildung undErziehung, Gestal heore sche Psychotherapie, Gestal heorie undDesign.

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Te InternationalSOCIETY FOR GESTALT THEORY AND ITS APPLICATIONS

invites submissions for the

WOLFGANG METZGER AWARD 2013Tis award is named after Wolfgang Metzger, a student of Max Wertheimer and one ofthe leading members of the second generation of the Berlin Gestalt School.

In the rst period of this award it was granted by decision of the board of directors of theG A to eminent people in Gestalt science and research for outstanding achievements.In 1987, the award went to Gaetano Kanizsa and Riccardo Luccio (Italy), in 1989 toGunnar Johansson (Sweden).

Since 1999 the award has been granted every second or third year by the board ofdirectors of the G A based on an international public award contest and a screeningand review of the submittals by an international scientic Award Committee. Te rstprize winners since 1999 were: Giovanni Bruno Vicario, Italy, and Yoshie Kiritani, Japan; Peter Ulric se, USA; Fredrik Sundqvist, Sweden; Cees van Leeuwen, NL/Japan;Baingio Pinna, Italy.

Applicants for the Metzger Award 2013 must submit a scientic paper (in Englishor German) inspired by Gestalt theory and that contributes to the research or theapplication of Gestalt theory in the physical sciences, the humanities, the social sciences,the economic sciences, or any other eld of human studies. Hence, the paper could dealwith a subject from psychology, philosophy, medicine, arts, architecture, linguistics,musicology or other elds of research or application of research as long as it is inspiredby a Gestalt theoretical approach.

Te rst prize winner will receive € 1000, will be invited as the award speaker to the 18thinternational Scientic Convention of the G A in 2013, and the paper will be publishedin the international multidisciplinary journal Gestalt Teory (www.gestalttheory.net/gth/) in the submitted version or in an adapted form.Members of the Award Committee for the 2013 contest are: Geert-Jan Boudewijnse(Montreal/Canada; chair), Silvia Bonacchi (Warsaw/Poland), Hellmuth Metz-Göckel(Dortmund/FRG), Baingio Pinna (Sassari/Italy), Fiorenza occafondi (Parma/Italy), N.N.

Submittals for the Metzger Award 2013 are due by September 2012.Te submission must be sent as a Word or a PDF document to the Metzger Award committeeat: [email protected]. More information about the international Societyfor Gestalt Teory and its Applications as well as the Wolfgang Metzger Award 2013 can

be found on the website of the Society: www.gestalttheory. net/424


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Die internationaleGESELLSCHAFT FÜR GESTALTTHEORIE UND IHRE ANWENDUNGEN

lädt ein zu Einreichungen für den

WOLFGANG-METZGER-PREIS 2013Dieser Preis ist nach Wolfgang Metzger benannt, Schüler von Max Wertheimer undführendem Vertreter der zweiten Generation der Berliner Schule der Gestalttheorie.

In einer ersten Periode wurde der Preis über Beschluss des Vorstandes der G A an

verdiente Persönlichkeiten für herausragende Beiträge zur Anwendung der Gestalttheoriein Wissenschaft und Forschung verliehen: 1987 ging der Metzger-Preis in diesemSinn an Gaetano Kanizsa und Riccardo Luccio (Italien), 1989 an Gunnar Johansson(Schweden).

Seit 1999 wird der Preis international öffentlich ausgeschrieben und vom G A-Vorstandauf Grundlage der Begutachtungsergebnisse und Empfehlungen eines internationalenwissenschaftlichen Preis-Komitees vergeben. Die ersten Preise gingen seither anGiovanni Bruno Vicario (Italien) und Yoshie Kiritani (Japan), Peter Ulric se (USA),Fredrik Sundqvist (Schweden), Cees van Leeuwen (NL/Japan), Baingio Pinna (Italien).

Für Bewerbungen um den Metzger-Preis 2013 ist ein wissenschaftlicher Beitrag (inEnglisch oder Deutsch) einzureichen, der zur Überprüfung und Weiterentwicklungder Gestalttheorie in Forschung oder Anwendung in den Naturwissenschaften,den Humanwissenschaften, den Sozial- und Wirtschaftswissenschaften oder aufeinem anderen Gebiet beiträgt. Einreichungen können also beispielsweise aus derPsychologie, Philosophie, Medizin, Kunst, Architektur, den Sprachwissenschaften, derMusikwissenschaft oder auch aus anderen Fachgebieten kommen, solange sie sich in derBehandlung ihres Temas kompetent auf die Gestalttheorie beziehen.

Die Gewinnerin bzw. der Gewinner des Metzger-Preises 2013 erhält ein Preisgeld von€ 1000 und wird zum Preisträgervortrag bei der 18. internationalen Wissenschaftlichen

Arbeitstagung der G A im Jahr 2013 eingeladen. Die eingereichte Arbeit oder derPreisträgervortrag wird in der internationalen multidisziplinären ZeitschriftGestaltTeory (www.gestalttheory.net/gth/) veröffentlicht.

Mitglieder des Metzger-Preis-Komitees 2013 sind: Geert-Jan Boudewijnse (Montreal/Kanada; Vorsitz), Silvia Bonacchi (Warschau/Polen), Hellmuth Metz-Göckel (Dortmund/D), Baingio Pinna (Sassari/Italien), Fiorenza occafondi (Parma/Italien), N.N.

Einsendeschluss für den Metzger-Preis 2013 ist September 2012.Einreichung als Word- oder PDF-Dokument an das Preis-Komitee: [email protected]. Weitere Informationen über die G A und den Wolfgang-Metzger-Preis: www.gestalttheory.net/

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Fax: + 43 1 985 21 19-15 | Mail: verlag@krammerbuch at

Das vorliegende Buch beschreibt die Beziehungen zwischen Gestalttheorieund Person und ist die Frucht der Arbeit einer Gruppe von Psychologen, diesich mit folgenden Aspekten der Person befassten: die Person und ihr Ich;die Person in Aktion; die Person in Beziehung; die Entstehung der Person;die Person in Dialog; die Person und die Zentrierung. Der hauptsächlicheZugang zur Untersuchung dieser Aspekte ist ein relationaler oder feldthe-oretischer, dem zufolge die Faktoren, die das Verhalten bestimmen, nicht

nur aus dem innerpersonalen System abgeleitet werden können, sondernauch von den Beziehungen zwischen Individuum und der konkreten Situa-tion, in das es eingebettet ist, abhängen. In der Person-Umwelt-Beziehunghaben die Gestalttheoretiker besonders die Ausdrucks- und Wesensquali-täten aufgewertet, die aus dem Objekt-Pol das Ego anzielen. Die Theoriedes psychischen Feldes konnte seine Fruchtbarkeit sowohl in den Untersu-chungen zur Allgemeinen und Sozial-Psychologie zeigen, als auch in jenenzur Entwicklungspsychologie. In den letzten Jahrzehnten setzte sich dasFeldmodell auch im psychoanalytischen Umfeld durch.

Das Buch ist sowohl für Studierende als auch für Forschende und Therapeu-ten von Interesse.

Gestaltpsychologie und PersonEntwicklungen der GestaltpsychologieHerausgegeben von Giuseppe Galli

154 Seiten, € 18,--ISBN 978 3 901811 43 2

geometry & gestalt

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