psychophysical estimation of speed discrimination. i. methodology

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2262 J. Opt. Soc. Am. A/Vol. 22, No. 10 /October 2005 Lakshminarayanan et al.

Psychophysical estimation of speed discrimination.I. Methodology

Vasudevan Lakshminarayanan

Department of Physics and Astronomy and College of Optometry, University of Missouri–St. Louis,One University Boulevard, St. Louis, Missouri 63121

Aparna Raghuram*

College of Optometry, University of Missouri–St. Louis, One University Boulevard, St. Louis, Missouri 63121

Ritu Khanna

Department of Mathematics and Computer Science, University of Missouri–St. Louis, One University Boulevard,St. Louis, Missouri 63121

Received January 3, 2005; revised manuscript received March 14, 2005; accepted March 21, 2005

Thresholds were assessed for a speed discrimination task with a pair of luminance-defined drifting gratings.The design and results of a series of experiments dealing in general with speed discrimination are described.Results show that for a speed discrimination task using drifting gratings, simultaneous presentation of thepair of gratings (spatially separated) was preferred over sequential presentation (temporally separated) in or-der to minimize the effects of eye movements and tracking. An interstimulus interval of at least 1000 ms wasnecessary to prevent motion aftereffects on subsequently viewed stimuli. For the two reference speeds tested of2 and 8 deg/s using identical spatial frequency or randomizing spatial frequency for the pair of gratings didnot affect speed discrimination thresholds. Implementing a staircase method of estimating thresholds was pre-ferred over the method of constant stimuli or the method of limits. The results of these experiments were usedto define the methodology for an investigation of aging and motion perception. These results will be of interestand use to psychophysicists designing and implementing speed discrimination paradigms. © 2005 Optical So-ciety of America

OCIS codes: 330.4150, 330.5510, 330.5020, 330.7310, 330.4300.

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. INTRODUCTIONsychophysical measures of speed perception have beentudied using such stimuli as random dots, lines, slits,pots, and drifting gratings for the past three decades.1–8

ost of the work has been concentrated on understandinghe basic mechanism of processing and modeling how hu-ans perceive speed. Studies addressed whether differ-

nt stimulus parameters like contrast, spatial frequency,emporal frequency, stimulus duration, and adaptationffect speed perception.9–14 The product of speed and spa-ial frequency defines temporal frequency of a driftingtimulus. Hence perceived speed and discrimination para-igms have also been used indirectly to address howany channels process temporal frequency.15,16 Another

ommonly used stimulus for studying temporal frequencyhannels is counterphase flicker gratings.17–20 Studies ofemporal frequency have not come to a complete consen-us on the number of channels necessary for human mo-ion perception although the most accepted model sug-ests not more than two or three channels.15–23 The firsthannel is thought to be low-pass and the second channelandpass filters. The third channel processes very highemporal frequencies.

We were interested in understanding how aging affectspeed perception. We ran experiments that helped ushoose the optimal stimulus parameters to be employed

1084-7529/05/102262-7/$15.00 © 2

n our experimental paradigm. This paper discusses theethodological issues concerning the design of the psy-

hophysical experimental paradigm, and the companionaper (Part II) focuses on the effects of aging on motionerception.The following specific questions were addressed as con-

erns on the methodology of the psychophysical experi-ents:

1. How does speed discrimination threshold depend onhe psychophysical method implemented?

2. Is there a difference in threshold between a stimu-us presented simultaneously and one presented sequen-ially (spatial versus temporal)?

3. Does interstimulus interval (ISI) play a significantole in determining speed thresholds?

4. How does randomizing spatial frequency affectpeed discrimination threshold?

. METHODSairs of drifting grating oriented vertically and moving inpposite directions were used as the stimulus. The stimu-us was generated using the Cambridge Vision Researchystems VSG2/5 graphic display card with a frame rate of

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Lakshminarayanan et al. Vol. 22, No. 10 /October 2005 /J. Opt. Soc. Am. A 2263

20 Hz. The drifting gratings were presented on squarepertures 1.5° in dimension. They were separated fromach other by 1.5 degrees. A fixation cross was presentedidway between the two apertures containing the drift-

ng gratings. One of the gratings was the standard thatoved at the same speed in a block of trials; the other

rating, the test, moved at varied speeds. Which apertureontained the standard or the test was randomized.

The average luminance of the grating was �72 cd/m2.he luminance from the background (display) was70 cd/m2. Tests were conducted in a dark room (except

or the luminance from the display). Stimuli were pre-ented for 500 ms except in experiment 2 (see below)here both 500 ms and 1000 ms durations were used. Forll the experiments listed below the subjects gave theiresponse after the stimulus was presented, that is, asoon as the stimulus disappeared from the screen. Thisas followed by an ISI (between trials) of 1000 ms afterhich the next presentation began (except for experimentwhere ISI was varied from 250 ms to 2000 ms). Feed-

ack on performance was not provided to the subjects af-er each trial. Sufficient practice trials were given beforehe experiments were run to obtain threshold. Informedonsent was obtained from all subjects prior to the start ofhe experiments.

. RESULTS AND DISCUSSION. Experiment 1: Psychophysical Methodshree different psychophysical procedures were used tostimate threshold (see Gescheider24).

. Staircase Technique (ST)n this procedure subjects had to respond in a two-lternative forced-choice (2AFC) whether the grating onhe left or right of fixation were moving faster. A two-own–two-up staircase method was used to control thepeed difference between trials. Two consecutive correctesponses were required to reduce the speed differenceetween the test and the standard grating, and two con-ecutive incorrect responses were required to increase thepeed difference between the test and the standard. Theest grating speed was 25%–50% faster than the standardrating at the start of the trial; this was sufficient for theest grating to appear faster than the standard. The stepize for the correct response was 3% of the standard andhe step size for the incorrect response was 1.5% of thetandard. The staircase terminated after eight reversalsere obtained and the last six were averaged for thresh-ld.

. Method of Adjustmentn this procedure subjects matched the speed of the testrating to the speed of the standard. The standard was al-ays presented to the left of fixation and the test grating

o the right. Subjects could control the speed of the testrating, decreasing or increasing the speed to match thetandard. Both standard and test grating were presentedimultaneously on the screen for 500 ms; subjects couldhen control the speed of the test grating. This was fol-owed by an ISI of 1000 ms before the start of the nextrial.

. Modified Method of Limitsn the classic method of limits, the stimulus parametertudied is generally presented in an ascending or de-cending order, which could give cues on the progressionf the task. Interleaving of the ascending and the de-cending trials generally avoids this. In our study, weodified this procedure by implementing a combination

f the method of constant stimuli and the method of lim-ts. In this modified method, we presented trials in ran-om order as in the method of constant stimuli, thenorted the results in ascending/descending order to esti-ate threshold as one would with the method of limits.he standard grating moved at a specific speed. The testrating moved faster than, slower than, or equal in speedo the standard grating. The speed of the test grating wasandomized during the experiment. The results were thenroken down and analyzed separately in ascending or de-cending order to measure the speed threshold. Transi-ion between a correct to an incorrect response was aver-ged for threshold (indicating the zone of uncertainty).he average of three separate runs provided the overalliscrimination threshold for this method.

. Discrimination Thresholdsiscrimination thresholds were expressed as a Weber

raction, �v /V, where �v is the absolute difference be-ween the estimated speed discrimination threshold andhe speed of the standard grating, and V is the speed ofhe standard grating. All subjects in the study alwaysverestimated test speeds.

. Subjectsxperiments were conducted on 16 adults 20–30 years ofge. All subjects had corrected or uncorrected visual acu-ty of 20/20 or better.

. Resultsepeated-measures analysis of variance (ANOVA) onpeed discrimination thresholds obtained by the three dif-erent psychophysical methods used showed a significantithin-subject effect for psychophysical methods

�F1,15�=12.145;p�0.01�. Post hoc analysis with theonferroni criterion showed that the significant differ-nces among psychophysical methods was mainly due tohe differences between the staircase technique and theethod of adjustment �p�0.001�. No significant differ-

nce was found between the other methods (Fig. 1).

. Discussionhe different methodologies used have inherent advan-

ages and disadvantages:

a. Method of Adjustment: In this procedure thresholdsend to be higher due to the tendency of subjects to stop athe first subjective perception of equality. Hence the re-ults are heavily dependent on the subject’s criterion.ubjects with stricter criterion had similar thresholdsmong the three methods. Subjects with a lax criterionenerally showed overestimation of threshold, as preci-ion was not a requirement.

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b. Staircase Technique: Since a 2AFC was adopted,his technique forces the observer to choose a response.ubjects were not given the “equal” option, though sub-

ects often did report that grating speed appeared equals the test grating speed approached threshold. Thoughhe subjects reported that the gratings appeared to beoving at equal speed, on a forced choice they were still

ble to discriminate accurately above guessing or chanceevels. The disadvantage is that subjects can be influ-nced by the progression of trials. That is, subjects be-ome aware of the increasing difficulty of the trials.uessing could influence reversals at or near threshold as

rials could be long and tiresome.c. Modified method of limits: In this methodology trials

re generated from a randomized pool, and hence subjectsannot judge the progression of the trial. Three differentresentation modes were used. The disadvantage ob-erved with this method is that subjects might be re-ponding to sequential speed discrimination rather thanimultaneous speed discrimination; that is, they mightot give their response comparing the test to the standardut might compare the test with a previous trial’s testrating speed and ignore the standard. Using longer in-erstimulus intervals could probably have limited thisossibility.

McKee4 reported that for a stimulus composed of a ver-ical slit and for velocities ranging from 2 to 8 deg/s thepeed discrimination thresholds could be obtained to anccuracy of 5% in humans. Orban et al.6 obtained similaresults where velocity judgments could be made at 5–7%ccuracy for velocities ranging from 4 to 64 deg/s. Simi-ar results were also obtained for drifting gratings andandom dot patterns.5,25–27 In our study, on average thepeed discrimination thresholds ranged from 10–13% forspeed of 2 deg/s. Thresholds are slightly higher thanhat is reported in the literature as the number of sub-

ects in our study was higher, and previous studies hadwo or three well-trained psychophysical subjects, hencehe variability between subjects was low.

ig. 1. Differences observed in the speed discrimination task forhe different psychophysical methods (standard speed, 2 deg/s).rror bars denote � standard error.

. Conclusionur results show that the staircase technique estimated

ower thresholds than other psychophysical procedures.he goal of this experiment was to identify a psychophysi-al procedure that would give a consistent estimate of thehreshold when used as a test to assess the ability of sub-ects to discriminate speed at various reference speed lev-ls. As the test was to be administered to subjects olderhan 60 years of age, choosing the appropriate procedureas very important. Psychophysical procedures can be

ime-consuming and stressful. Considerable compromiseas to be made on the number of trials and the total du-ation of the psychophysical methodology employed with-ut decreasing the sensitivity of the test. Our resultshow that the staircase technique was the appropriateethod of assessment as it estimated the lowest thresh-

ld and was not affected by the criterion of the observer.

. Experiment 2: Sequential versus Simultaneousresentationere the stimulus paradigm was similar to that of experi-ent 1 for the simultaneous presentation. For sequential

resentation only the grating (either the standard or theest) to the left of the fixation appeared for 500 ms. Thisas followed by the grating to the right of the fixation for00 ms. During any one interval, only one of the gratingatches was seen (left or right), hence eliminating the in-uence of motion aftereffects on subsequently viewedtimuli on the same visual field. After both temporalvents, the task for the subject was to state whether therating in the first interval or the second interval wasoving faster [two-interval-alternative-forced-choice pro-

edure (2AFC)]. The psychophysical methodology wasimilar to the staircase technique in experiment 1 (2own 2 up 2AFC procedure).

. Subjectsata were collected from 14 normal subjects with a meange of 24.12±3.11. All subjects had corrected or uncor-ected visual acuity of 20/20.

. Resultsepeated-measures ANOVA on speed discrimination

hresholds showed significant within-subject differencesetween sequential presentation and simultaneous pre-entation when stimulus duration was 500 ms at p0.05 for both speeds 2 and 8 deg/s. They were not sig-

ificantly different from the simultaneous presentationhen the stimulus duration was 1000 ms for both speeds.equential presentation recorded lower thresholds com-ared with simultaneous presentation at 500 ms. Theariability in the test results was much lower for the se-uential presentation than for the simultaneous (Fig. 2).

. Discussionrevious studies by Verghese and Stone28 andhompson29 did not find significant difference between se-uential and simultaneous presentation. Differences ob-erved in our study could be a result of tracking due toonger stimulus duration. In simultaneous presentationor the same duration there are two grating patches onhe screen, but in sequential there is only one. Hence in

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he sequential presentation, there is no uncertainty fromhe subject, if he is losing fixation, as to which grating torack as only one grating patch is visible. Moreover theifference between the sequential and simultaneous pre-entation decreased to nonsignificant results at 1000 ms.here is a possibility that eye movements and trackingould have resulted in better performance in the sequen-ial as well as the simultaneous presentation at 1000 ms.

. Experiment 3: Effect of Interstimulus Intervalrevious studies by Smith and Edgar10 and Clifford andenderoth12 have shown that adaptation to a moving pat-

ern decreases the perceived speed. The visual systemails to represent veridically the absolute speed of thetimulus. A study by Goldstein1 has also shown that thepeed of a constantly moving grating is perceived to de-rease as a function of stimulus duration. The purpose ofxperiment 3 is to investigate the effects of ISI on a speediscrimination task, i.e., to assess whether subsequentrials were influenced by the previous trials. The stimulussed for this experiment was similar to that in experi-ent 1. The speed discrimination was tested for two ref-

rence speeds 4 and 8 deg/s. The spatial frequency wascycles/deg. The ISI was varied at 250, 500, 1000, and

000 ms.

. Subjectsata were collected from three experienced psychophysi-

al subjects. One was the author and the other two ob-

ig. 2. Comparison between simultaneous and sequential presendeg/s. Lower plots, standard speed 8 deg/s. At 500 ms stimulus

oth standard speeds tested. No significant difference in thresholus duration.

ervers were naïve to the purpose of the study. The re-ults of this study are a subset of findings from a studynvestigating the effects of ISI as a function of spatial fre-uency and speed.30 Hence the number of subjects wasmall compared with those in the other experiments re-orted in this paper.

. Resultshe triangles in Fig. 3 illustrate the results obtained for aeference speed of 2 deg/s. ANOVA indicated that for a ref-rence speed of 4 deg/s significant differences were ob-ained for ISI at p�0.00. An ISI of 250 ms had signifi-antly higher thresholds compared with an ISI of 1000 or000 ms at p�0.05. The circles in Fig. 3 illustrate the re-ults obtained for a reference speed of 8 deg/s. ANOVA in-icated a significant difference for ISI at p�0.05. An ISIf 250 ms resulted in higher thresholds compared with000 or 2000 ms at p�0.05 for both.

. Conclusionn ISI of 1000 ms or greater resulted in lower thresholdsompared with an ISI of less than 1000 ms. These resultsre probably indicative of the effects of afterimages onpeed thresholds at ISIs less than 1000 ms.30

. Experiment 4: Constant versus Random Spatialrequencyrevious studies have shown that speed discrimination

hresholds could be aided by such factors as spatial fre-

mode on speed discrimination task. Upper plots, standard speedion, sequential mode had better threshold than simultaneous forobserved between the two presentation modes at 1000 ms stimu-

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uency, temporal frequency, and contrast.10,16,29 Subjectsould utilize differences that occur in perceived spatialrequency and temporal frequency as a cue to perform theask rather than estimating true speed differences. Ex-erimentally the only variable that is different betweenhe two gratings (if spatial frequency is kept constant) ishe speed and hence the temporal frequency, since that isproduct of speed and spatial frequency. It has been ob-

erved that identical gratings moving at different speedsan look very different on the basis of other factors. Forxample, the faster-moving grating of the same spatialrequency appears to have lower contrast and higher spa-ial frequency.3 This phenomenon, rather than simplypeed information, could be used to determine which grat-ng is moving faster.

The purpose of this experiment was to randomly varyhe spatial frequency of the standard and the test gratingnd ask the subjects to ignore the differences that occurue to changes in spatial frequency and comment only onhe speed difference between the two. McKee et al.5

howed that randomizing contrast and spatial frequencyid not affect the speed discrimination thresholds forrifting gratings moving at 5 deg/s and hence concluded

ig. 4. Speed discrimination threshold plotted for constant or radeg/s or 8 deg/s. Spatial frequency, 2 cycles/deg. Significant dif

dentical and randomized spatial frequency condition.

ig. 3. Weber fractions for speed discrimination plotted as aunction of ISI for standard speed of 4 deg/s (triangles) anddeg/s (circles). Thresholds for an ISI of 250 to 500 ms are sig-ificantly different from those for 1000 ms and above.

hat the human system can decode speed separately.mith16 showed that when spatial frequency was fixed atcycle/deg or randomized around 1 cycle/deg, speed dis-

rimination thresholds were similar for slower velocities�8 deg/s� but differences increased at middle and highelocities. He concluded that at slower velocities, dis-rimination was based on the speed of the drifting grat-ngs but for higher velocities, temporal frequency cuesere used to aid the speed discrimination task.16 We usedspatial frequency of 2 cycles/deg and the stimulus

rifted at 2 or 8 degree/s (temporal frequency of 4 and6 Hz, respectively). As the combination of stimulus pa-ameters was different from that used in earlier studies,specially at the faster velocity where the temporal fre-uency would be 16 Hz, we estimated the differences thatould occur from constant or randomized spatial fre-uency on speed discrimination thresholds.

. Stimuliethodology and stimuli were similar to those used in ex-

eriment 1; however, the spatial frequency was random-zed between 1.5–2.5 cycles/deg. The standard moved atither 2 or 8 deg/s and the subject had to determinehich grating was moving faster. The stimulus durationas always 500 ms.

. Subjectsor the speed of 2 deg/s there were 16 subjects; fordeg/s there were 9. All subjects were corrected am-etropes or emmetropes with visual acuity of 20/20 or

etter.

. Resultsepeated-measures ANOVA for the speed of 2 deg/s re-ealed that speed discrimination thresholds did not varyignificantly when the spatial frequency was kept con-tant or randomized within a block of trials �p�0.05�.epeated-measures ANOVA for the speed of 8 deg/s alsohowed no significant difference in the estimated speedhreshold between constant and randomized spatial fre-uency �p�0.05� (Fig. 4).

zed (20%) spatial frequency of drifting gratings. Standard speed,es were not observed for speed discrimination threshold between

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. Conclusionor speeds of 2 and 8 deg/s the results show that the dis-rimination task is not affected by randomizing spatialrequency. This implies that spatial frequency or its con-equential partner the temporal frequency does not pro-ide cues in the discrimination process of judging speedifferences.

. SUMMARYe have described four experiments to evaluate the speed

iscrimination threshold of human observers. The experi-ents compared three different psychophysical proce-

ures using different standard speeds and compared theffects of simultaneous versus sequential presentation asell as fixed and randomly varying spatial frequency. Re-

ults obtained from these experiments have been used tone-tune the methodology used to assess differences inpeed perception as a function of age (Part II, Raghuramt al.31)

Here we identified that the staircase methodology isppropriate to estimate threshold, identical spatial fre-uency can be used, and the ISI of 1000 ms would be ap-ropriate to control for any motion aftereffect. Though se-uential estimation provided better thresholds with lessariability, simultaneous discrimination was preferred foretter control over eye movements and tracking. The re-ults presented here are of general interest and will be ofse to researchers involved in psychophysical measure-ents of human motion perception. We have identified

arious parameters that should be taken into account inhe formulation of a motion perception experimentalaradigm.

. DEDICATIONobert Oppenehimer said, “Knowledge should ennobleot merely those who seek and find it, nor their immedi-te colleagues; it should add to the civility and wondernd the nobility of the common life.” Russ DeValoisought this goal in all things. He was a very specialan—an inspiring researcher and collaborator, an under-

tanding colleague, a great scientist and teacher, and,ost important, a good friend who will be long remem-

ered by those whose lives he touched. This and the com-anion paper are dedicated to the life and achievementsf Russ. He is missed!

CKNOWLEDGMENTShis work was supported in part by a grant from the Uni-ersity of Missouri Research Board.

*Corresponding author. Current address: Departmentf Ophthalmology and Vision Sciences, University of Illi-ois at Chicago, 1855 West Taylor Street, Chicago, Illinois0612. E-mail: [email protected].

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psychophysical estimation of speed discrimination. i. methodology

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