Experiment 1 Fixed Disparity

In previous experim ents the speed illusion has been m easured by observing a single expansion field (as opposed to a stereo pair). T herefore disparities w ere alw ays zero (where view ing was binocular), consistent with a fixed depth plane. (Radial expansion in a fixed depth plane is consistent with a deform ation event, fo r ex am ple an in flatin g balloon). T o p ro v id e ben ch m ark figures for the m agnitude o f the illusion w ith zero and non-zero disparities its strength at a

range o f depth planes was m easured, sim ilar to those that w ould be present in later experim ents.

5.3.1 Methods

Observers

T hree subjects took part in the study, all o f w hom w ere chosen to be naive to the aim s o f the experim ent because o f the subjective nature o f the judgem ent they had to m ake. Each had norm al, or corrected to norm al visual acuity and good stereo-acuity.

Each observer perform ed at least 4 (observer M C), m ore usually 6 (observers AC & SK), blocks o f trials, com prising 40 trails per block.

The ability o f the volunteers to discrim inate m otion-in-depth was confirm ed in a separate experim ent. A forced choice procedure was used to establish if subjects could tell w hen a dynam ic disparity R D K 'receded' (crossed disparity o f 20 pixels to uncrossed disparity o f 20 pixels) or 'approached' (The dots were static, i.e. there was no relative m otion am ong them ). Tw o subjects scored better than 95% correct on this task, w hile SK perform ed m uch better than chance at 76% correct. W hile this low er perform ance suggests poorer stereo-m otion perception for SK the subsequent pattern o f experim ental results for this observer was sim ilar to that o f the others.

Stimuli

T he dots (D ifference o f G aussian) used had a centre spatial frequency o f 1.6 cycles per degree o f visual angle at the view ing distance o f 1 m eter em ployed. E ach dot subtended approxim ately 0.573 degrees o f visual angle. O ne hundred dots occupied each window, which was curtailed at a radius o f 3.33 degrees by a

2 raised cosine function. The dot density was therefore 4.8 dots per degree .

The ‘standard’ radial pattern m oved at a fixed speed at all times, nom inally 2.98 degrees/s. (As the speed o f each dot was scaled according to its eccentricity from the centre o f the dot field to produce smooth expansion the m edian speed o f the dots was 0.997 degrees/s. T herefore dots m oving at 2.98 degrees/s w ere only seen at the outer extrem ity o f the w indow ). T he speed o f dots in the rotation pattern was varied according to a Q uest algorithm (W atson & Pelli, 1983). Q uest selected speeds from the range: (0.298..26.26) degrees/s in logjo steps. T he speed o f dots in the rotation pattern was sim ilarly scaled w ith eccentricity to generate a rigid rotation that was locally m atched to the radial pattern.

Stim uli w ere view ed through a W heatstone m irror stereoscope to allow the introduction o f binocular disparity to the im age. To this end each m ovie actually com prised two windows o f anim ation with sim ilar, but non-identical images (see figure 5.3). Each field o f dots was displayed w ithin a rectangular black border that served as a reference fram e, found to be effective in producing a strong perception o f m otion-in-depth (Erkelens & C ollew ijn, 1985). This fram e was presented prior to the com m encem ent o f the experim ental trials, and subjects w ere required to fuse the rectangular fram es w hile view ing the display through the stereoscope. (Pre-trial fusion has been show n to im prove the form ation o f a stereoscopic percept (Uttal, D avis & W elke (1994)). The front surface m irrors w ere arranged so that only the appropriate m onocular im age was seen by each eye. O bservers w ere asked to fixate a small black line located m idw ay along the top border o f the reference fram e. The anim ation was therefore centred 2.86 degrees from fixation. Once fusion was obtained the subject started the block o f trials by pressing one o f the response keys used to record their judgem ents: buttons 1 and 3 o f the keyboard's num eric keypad. The two fields o f dots within each rectangle were identical to each other, but were placed in different locations relativ e to their reference fram es. On a given trial each field o f dots w as displaced up to 30 pixels from the centre o f their reference fram es. The direction o f this displacem ent in one h alf im age was opposite to that o f its partner, giving a m axim um o f 1.43 degrees o f relative disparity. The displacem ents used w ere: 0, 10, 20, 30 pixels. Each o f these displacem ents (except 0) was used to produce

a crossed and an uncrossed disparity resulting in seven unique conditions o f relative disparity: 0, ±0.238, ±0.477 and ± 0.714 degrees o f visual angle. The m etric distances in depth im plied by these changes w ere as follows. For crossed disparities, the dots appeared to float at a depth o f (12.2, 21.7, 29.4) cm closer to the observer than the fixation plane. For uncrossed disparities the values w ere (16.1, 38.5, 71.5) cm behind the fixation plane.

Procedure

Participants were asked to discrim inate betw een two com plex m otion patterns on the basis o f their apparent speed, their task being to nom inate which anim ation appeared faster. (N o in struction w as given regarding w hich dim ension o f m otion, lateral or in depth, should be judged-observers w ere allow ed to select their own criteria). Tw o tem poral intervals each contained a lOOOmS m ovie depicting a field o f dots travelling in either a radial or a rotational m otion. The radial pattern was alw ays expanding, how ever the rotating pattern was varied random ly betw een clockw ise and anti-clockw ise directions. T he inter-stim ulus interval w as approxim ately lOOOmS, during w hich the next anim ation was calculated. Radial motion was the ‘fixed’ anim ation, i.e. its speed did not vary.

B etw een trials the referen ce fram e and fix atio n m ark w ere co n tinuously d isp lay ed to allow p articipants to m aintain fusion. S ubsequent trials w ere triggered once the observer's response was made.

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Figure 5.3 A stereo pair showing an expanding stimulus. Each image shows a field of dots travelling in the directions indicated by the arrow s. By view ing through a W heatstone stereoscope, only one image is seen by each eye. Each im age contains exactly the same spatial arrangem ent of dots, but those in the right panel are displaced to the right relative to the surrounding black fram e. The mark on the top edge o f the windows is the point that subjects were asked to fixate during a trial.

5.3.2 R esults

P s y c h o m e tric fu n c tio n s w e re fitte d w ith a c u m u la tiv e G a u ssia n fu n c tio n w h e re th e m e a n a n d s ta n d a rd d e v ia tio n o f th e fu n c tio n w e re v a rie d to o b ta in a le a s t s q u a r e s o p tim is a tio n b e tw e e n th e d a ta a n d th e f itte d c u rv e . T h e p o in t o f s u b je c tiv e e q u a lity (P S E ) w as e stim a te d fro m th e fitte d c u rv e by c a lc u la tin g the in v e rse o f th e c u m u la tiv e G a u ssia n at th e p o in t w h e re su b je c ts ju d g e d th e ra d ia l p a tte rn fa ste r w ith a p ro b a b ility o f 50% .

3 .5

AC

c 2. 5 0 1 2 ■D 0) 0) CL t/5 u n c ro s s e d dis p a rity ba seline # — c ro s s e d d is p a rit y • z e ro d is p a rit y 0 . 5 A) d i s p a r i t y ( d e g r e e s ) 1 .5 B) ■o 0 0 Q. Crt 0. 3

MC

5 2 5 1 u n c ro s s e d dis p a rity baseline « — c ro s s e d d is p a rit y • z e ro d is p a rit y 0 •D 0 CL 0 . 5 d i s p a r i t y ( d e g r e e s ) 1 .5 4

SK

5 3 5 2 5 1 u n c ro s s e d d is p a rit y ba seline a — c ro s s e d d is p a rit y • z e ro d is p a rit y 5 0 C) 0 . 5 1 d i s p a r i t y ( d e g r e e s ) 1.5

Figure 5.4 Results of Experiment 1. The magnitude of the speed illusion is shown for three observers separately (figures 5.4A, B, C). Plotted on the y-axis is the speed of the dots of a rotating pattern (as a factor of the radial speed) that provided a perceptual match to the (fixed speed) radial pattern. The speed illusion is shown as a function of the amount of fixed horizontal disparity on the x-axis, and is shown separately for each of the three observers. The two curves shown on each graph are for crossed and uncrossed disparities, and results for zero disparity are plotted separately on the figure, see legend. The horizontal line shows the dot speed expected if subjects had perceived a match (in retinal speed) terms between rotation and radial patterns.

Figure 5.4 sum m arises the data from the three observers. Each graph shows data for one subject, plotting the point o f subjective equality (PSE) on the y-axis as a function o f the relative disparity condition on the x-axis. The two curves on each graph rep re sen t crossed d isp arity (nearer than the p lane o f fix atio n ) and uncrossed disparity. T he solid line show n for reference is the retinal speed m atch, i.e. the FSE that w ould be obtained if subjects saw a rotational pattern w ith nom inal m ean dot speed o f 0.997 degrees/s as the same global speed as the radial pattern (whose mean dot speed was alw ays 0.997 degrees/s). V alues above this line indicate that subjects needed a faster rotation to provide a perceptual m atch to the radial pattern.

It can be seen from the graphs that in the zero disparity condition the speed illusion is evident, and consistent with previous studies w here disparities w ere zero due to view ing o f a single pattern o f m otion (not a stereo pair). C om paring b etw een su bjects, first, it is app aren t th at the speed illusion is subject to individual differences. Subject M C requires in excess o f a 60 % increase in the dot speed o f a rotation pattern to m atch the expanding pattern. Subjects A C and SK require a greater increase o f over 100%. These biases are consistent w ith previous w ork, but are larger than reported elsew here, possibly reflecting the effect o f stereoscopic view ing, which has not previously been explored.

T he zero disparity condition acts as a benchm ark against w hich to com pare perform ance to non-zero disparities. The data show no evidence that fixing the stim ulus at constant depths using non-zero disparity affects the apparent speed exaggeration. D espite the addition o f up to 1.43 degrees o f relative disparity, there is no sign o f a consistent change in the speed illusion in any o f the subjects. This was confirm ed statistically with a repeated m easures, one way analysis o f variance, F(5 j2)=0.981, p>0.05.

In sum m ary, placing the R D K 's dot field at a constant depth does not dim inish the size o f the speed illusion. Therefore, any effect found in later experim ents is not due to an artefact o f the view ing conditions necessary to induce stereoscopic fusion.

In document Complex motion processing (Page 144-151)