ASPECTOS GENERALES

The purpose of Experiment 11 was to extend the result of Experiment 10 to cover irregular textures and to refute any alternative explanation based on the selective processing of a small number of features. Irregular textures can be characterized by their statistical properties. If segregation proceeds by a genuinely statistical representation of an extended area, then segregation should be a function of the statistical variation of a textured surface, rather than the discriminability of local elements.

Suppose that there is a parallel process which characterizes the cyclopean texture of extended regions. If this process operates analogously to that suggested for luminance textures, then it should operate on the outputs of sets of cyclopean spatial filters tuned to orientation and corrugation freijuency. The extent to which a patch of cyclopean texture selectively stimulates different sets of filters should govern its discriminability as a texture. In other words, the second-stage process should have a measurable selectivity for cyclopean orientation and size. Supposing a texture is produced by adding together sinusoidal corrugations whose orientation is selected randomly from a distribution of orientations. As the standard deviation of that distribution is increased, cyclopean spatial filters at a greater number of orientations will be stimulated. Effectively, the overall orientation of the textured surface becomes blurred. There should be a critical standard deviation at which this blurring becomes too great for the second-stage process to discriminate between textures. An analogous argument may also be applied for the dimension of corrugation frequency (or cyclopean size).

If, instead of this genuinely statistical process, perfomiance is based on a form of selective discrimination between a small number of features, the standard deviation of orientation or corrugation frequency will have little effect, provided that individual humps or hollows are still discriminable and of markedly different cyclopean orientation or size.

M ethods

With the exception of the fomiation of the 18 images for each experimental run, the methods were identical to those of Experiment 10.

The images for this experiment consisted of two different types of irregular textures: orientation textures and size textures. Both types were generated by a linear combination of 50 sinusoidal corrimations selected as follows:

(1) O r i e n ta t io n te x tu r e s : F r e q u e n c y w a s d r a w n f r o m a u n i f o r m distribution coveri ng the range 0.25 - 2.0 c/deg on a logarithmic scale (i.e. f r eque nc y was 2" where n varied uni forml y between -2 and 1). T h e peak- t r o u g h d i s p a r i t y o f e a c h c o r r u g a t i o n wa s i n v er s el y p r o p o r t i o n a l to f re que nc y, with a mean o f 4 min arc. Phase was r an do mi ze d . Or ient ati on wa s d r a w n f rom a G a u s s i a n di st ribut ion c ent red on 0 o r 9 0 d eg , t he s t a n d a r d d e v i a t i o n o f w h i c h w a s m a n i p u l a t e d to f o r m s e p a r a t e conditions-^

(2) Size textures: O r i e nt a ti o n wa s d r a w n f rom a u n i f o r m d i st r i b u t i o n c o v e r i n g the c o m p l e t e r a n g e o f or ie nt at ions . P ha se w a s r a n d o m i z e d . F r e q u e n c y was dr awn f rom a Ga us sia n distribution centr ed on 0 .4 o r 0.8 c / d e g on a l o g a r i t h m i c scale, the s ta n d a r d d e v i a t i o n o f w h i c h w a s m a n i p u l a t e d to f orm s e p a r a t e c o n d i t i o n s . S t a n d a r d d e v i a t i o n s a re e x p r e s s e d as a p e r c e n t a g e o f the d i s t a n c e b e t w e e n the t w o m e a n f r e q u e nc ie s on the l ogar ithmic scale. The pe ak-t rough di spa ri ty o f e ach c orrugati on was inversely proportional to frequency, with a mea n o f 4 mi n arc.

For orient at ion textures, each e x pe ri me n ta l run selected stimuli f ro m 9 i ma ge s centred on 0 de g and 9 images centred on 90 deg, both with the s ame s tandard deviations o f orientation. For size textures, the two sets of 9 images were centred on 0.4 c /de g and 0.8 c/deg, again with the s ame standard deviat ions. T he se t ext ures had an a p p e ar a nc e similar to that o f crumpl ed clothing or rippled sand.

T h e o b s e r v e r s in this e x p e r i m e n t we re again DK and PDL. Ea ch o b s e r v e r c o mp l et ed t wo runs for each condition. DK compl et ed 3 c o nd it io n s for both orientation and size textures at 5, 25, and 45 d e g and 10, 30 and 50% respectively. Bl oc ks consisted o f 3 r uns o f ei the r size textures o r orient at ion textures with the o r d er r a n d o m i z e d and c oun te r -b a la nc e d as for Expe riment 10. PD L compl et ed 5 c o ndi ti ons for ea ch o f the two types o f texture at 5, 15, 25, 35, and 45 deg and 10, 20, 30, 40, and 5 0%, in blocks o f 5.

Results

T h e results for the orientation textures are presented in f igure 6.5. T h e results for the size textures are presented in figure 6.6. Percent correct is plotted against presentation t i me f or etich o f the s epar at e s ta n d a r d d e v i a t i o n s o f o r i e n t a t i o n a n d c o r r u g a t i o n frequency.

^ ^ B e c a u s e o n c m a u o n i s i i o i a C D i u i i u i o i i s s u a k ' ( i . e . V I c l e g e o r r c s p o n c l s t o -<S9 c l e g ) t h e t a i l s o f t h e G a u s s i a n d i s t r i b u t i o n w e r e t e r m m a t e d a t a n o f f s e t f r o m t h e m e a n o f ± 9 0 d e g . W i t h t h e s t a n d a r d d e v i a t i o n s e m p l o y e d h e r e , t h e d i s t o r t i o n o f t h e d i s t r i b u t i o n p r o d u e e d l»y t h i s l i m i t a t i o n i s n e g l i g i b l e .

For ail bill the very largest standard deviat ions pe rf o rma n ce is a b o v e c ha nc e for both o bs erver s at short presentation times, even d o w n to 75 mse c f or o b s e rv e r D K in the o r i e n t a t i o n t ask, a l t h o u g h there is still a c o n s i d e r a b l e d i f f e r e n c e in t he level o f p er fo r ma n ce o f the two observers. Thi s c onfi rms and e xt en ds the f indi ngs o f E xp er imen t 10. T h e b o u n d a r y b e tw e e n t w o s u r f a ce s can r ea di ly be p e r c e i v e d by p r e- a t t e nt i v e segregation o f c yc lope an textures, on the basis o f both orientation and size. In the present e x p e r i m e n t excel lent segregati on was obt ai ned with very irr egular c y c l o p e a n textures. T h e i n tr o sp ec t io ns whi ch r esulted f r om v i ew i n g t hese i r r eg ul ar t ex tu res we r e again consistent with viewing two separate and h o m og en e ou s rectangles o f b u m p y surface.

100 D K 90 i u g o 100 1000 P resentiiiion tim e (m s e c ) 100 P D L 90 u 2 7 0 ^ 6 0 - i 100 1000 P resentation tim e (m s e c )

F i g u r e 6.5. D ata f o r seg r e g a tin g ir r e g u la r o r ie n ta tio n textures. Perform ance is again above chance at very short presen ta tio n times. Performance is highly dependent on the standard deviation o f orientation within the texture and shows little im provem ent with presentation time, suggesting that the statistics o f the image govern the ability to segregate the textures.

100 D K 9 0 -

i

8

Presentation time (msec)

100 P D L t)

Ë

Presentation time (msec)

F ig u r e 6.6. D a m f o r se g re g a tin g Irregular size textures. P e r fo rm a n c e is a g a in a b o v e chance a t very sh o rt p r e se n ta tio n tim es. P e r fo r m a n c e is highly d e p e n d e n t on the s ta n d a r d d e v ia tio n o f c o r r u g a tio n f r e q u e n c y within the texture a n d sh o w s gra d u a l im provem ent with p resen ta tio n time.

It wa s a rg ue d f o l l o w i n g E x p e r i m e n t 10 that the a g r e e m e n t in p e r f o r m a n c e b et we en different tasks, and the difference in p e rf o rma n ce be twe en observer s, suggest ed that an i mp o rt an t f act or in that e x p e r i m e n t was t he t ime t aken to fuse the i ma g e. T h e flat ter f un ct i on s g e ne ra te d in the present e x p e r i m e n t , e s p e ci al l y with the orie nt at ion textures, do not point to fusion as a factor. T h e surfaces o f E x pe r i m en t 10 wer e o f greater p e a k - t r o u g h d ispa rit y and had l ar ger s ur fa ce slants t han the t e xt u r e s in t he p re se nt experi ment , which may have m ad e them liarder to fuse.

Does this successful perception of the border between two irregular cyclopean textures represent genuine statistical characterization of three-dimensional texture? Comparison of performance across different standard deviations reveals that there is a marked influence of the standard deviation in both the orientation and size tasks. This is the case even for segregation of surfaces whose distributions of orientation or corrugation frequency have negligible overlap and very different means. If segregation were governed by selective processing of a small number of image features then this dependence on the statistical make-up of the images would not be expected, because individual features of the image should still be readily discriminable. In several cases the functions of the present experiment show no tendency towards 100% even at 1200 msec. This supports the idea that the limiting factor in performance is the statistical nature of the texture; either the system resolves the two textures or it does not. Anecdotally, it was found that with very prolonged inspection of those stimuli employed in the experiment which could not be segregated at short presentation times, the task could eventually be solved by serial scanning of the bumps and hollows, in a manner similar to that of figure 6.1c in the luminance domain.

It cannot be argued that the statistical variation alters performance because it makes individual features somehow more difficult to locate or process, because if this were the case, performance should be much worse in Experiment 11, as a whole, compared with Experiment 10. If anything, performance is better in Experiment 11, especially for observer DK. The most likely conclusion therefore is that performance in this experiment is the result of a statistical characterization acting on a parallel representation of orientation or size. Applying the type of explanation employed for luminance textures in the disparity domain, changing the standard deviation of the distribution of orientation or corrugation frequency will affect the ability o f the second- stage mechanism to resolve the outputs of sets o f cyclopean spatial filters tuned to corrugation frequency and orientation.