INCIDENCIA RESPONSABILIDAD SOCIAL EMPRESARIAL Y

If s t e r e o s c o p i c v i s i o n is o r g a n i z e d s o a s to c o m p u t e t h e s l a n t a n d c u r v a t u r e o f s u r f a c e s , o n e c a n e x p e c t to fi nd h i g h s e n s i t i v i t y t o d i s p a r i t y g r a d i e n t s a n d d i s p a r i t y c u r v a t u r e . I ' h e s t e r e o s c o p i c sl ant a n i s o t r o p y p r o v i d e s an e x a m p l e o f i n s e n s i t i v i t y t o s l o w c h a n g e s in d i s p a r i t y . T h e f o l l o w i n g s e c t i o n s e x a m i n e s t u d i e s w h i c h h a v e a d v a n c e d t he h y p o t h e s i s t hat s t e r e o s c o p i c v i s i o n is s e n s i t i v e t o o n e o r bot h o f t he s p a t i a l d e r i v a t i v e s o f d i s p a r i t y .

Sensitivity to disparity gradient

It has been suggested that a disparity gradient limit operates in the process of binocular matching (Burt and Julesz, 1980; Pollard. Mayhew and Frisby, 1985). However, the use of a disparity gradient limit is logically independent o f whether the visual system employs disparity gradients for the perception of surface slant. Nevertheless, there is empirical evidence to suggest that in certain conditions the visual system is sensitive to disparity gradient.

A very simple approach is to examine the perception o f just two targets as a function of disparity and disparity gradient. Bülthoff, Fahle and Wegmann (1991) used a matching technique to measure the perceived depth between two small targets. They found that as the two targets were moved closer together with the relative disparity between them held constant, the perceived depth decreased. The effect was found when the targets were separated vertically and horizontally, so orientation disparity cannot be responsible for the result. The authors concluded that perceived depth is scaled with disparity gradient rather than relative disparity. Ryan and Gillam (1993) measured the aftereffect produced by extended free viewing of two lines of varying separation and relative disparity. The test stimulus was also a two-line stimulus of varying separation in which the observer had to alter the relative disparity in order to null the aftereffect. Adaptation was found to be to disparity gradient, rather than to the relative disparity. In some cases, the nulling disparity required in test lines at a large separation could be greater than the adapting disparity of a more narrowly separated pair. Again, the effect was found with both horizontal and vertical separations. The authors concluded that disparity gradient may plays an important role in stereopsis.

A problem with both of these two-target studies is that results obtained with reduced stimuli may not generalize to situations where many features are present. For these reasons, the results need not imply that processing of disparity gradient takes priority over processing of relative disparity. Furthermore, as regards the Ryan and Gillam (1993) study, strong effects of adaptation need not imply sensitivity. In fact, according to the logic of selective adaptation usually employed in psychophysics, strong effects of adaptation imply coarse coding of a stimulus variable, as the fatiguing of a section of coarsely tuned detectors produces greater shifts in perception. Hence, that the aftereffect due to disparity gradient swamped the effect due to relative disparity might imply relative insensitivity to disparity gradient! Another factor to consider in this experiment is that the free viewing of the adapting stimulus may have made it more likely that adaptation would be to disparity gradient. Mechanisms sensitive to disparity gradient may sum over a larger area of visual field or be less likely to be tuned to absolute disparity than mechanisms sensitive to relative disparity.

Holliday and Braddick (1991) have shown "perceptual pop-out" on the basis of stereoscopic slant. Response times to locate a target parallelogram of different slant were found to be largely independent of the number of distracting parallelograms. This result

implies that stereoscopic slant is processed in parallel across the visual field, either by extracting orientation disparity or disparity gradient.

Sensitivity to disparity curvature

Stevens and Brookes (1988) required observers to judge the relative depths of pairs of dots superimposed on stereograms made from grid patterns. The perspective information in the grid was found to strongly dominate and sometimes to completely veto the stereoscopic information for slanting planar surfaces, but not for surfaces whose profiles were Gaussian ridges or edges. The authors argued that stereoscopic vision was hence primarily sensitive to stimuli with non-zero second spatial derivatives and relatively insensitive to disparity gradient. One problem with this study is that in order to introduce the patterns of disparity the lines in the monocular images of the curved stereograms were changed from straight to curved. Viewing the demonstrations provided by Stevens and Brookes one can see large differences in the monocularly available perspective information in the curved surfaces. The increase in strength of the stereoscopic cue may thus have resulted from a decrease in the strength of the monocular perspective cue, which was not independently controlled for.

Front v ie w

Plan v ie w

(a) (b)

F ig ure 1.18. Stereoacuity m easured with pattern (a) is an o rd er o f m agn itu de g rea ter than w hen m e a su re d w ith pattern (b). From M itchison and W estheim er (1984).

Detection and discrimination studies

All of the studies reviewed in this section so far imply that there exist mechanisms which process stereoscopic slant and curvature. Yet none of them genuinely isolate and measure the sensitivity of mechanisms tuned to disparity gradient or disparity curvature.

Measuring the detection and discrimination of slant and curvature is the best way to gauge how accurate perceptions of surface orientation and shape resulting from stereoscopic vision really are.

Mitchison and Westheimer (1984) found stereoacuity to be an order of magnitude higher for seeing rotation about the vertical in a grid pattern o f dots (figure 1.18a) compared with deciding which of the two lines of dots is closest in a two-line pattern (figure 1.18b), despite the fomier figure containing six replicates of the latter. Similarly, Fahle and Westheimer (1988) showed that! threshold for two points rises monotonically with the number of intervening points. Clearly, sensitivity to disparity gradient does not govern performance in these studies. Mitchison (1993) argues that these results require that the visual system is sensitive to the second derivative of disparity. Furthermore, in contrast to Brookes and Stevens, Mitchison argues that they are best accounted for by Cyclopean spatial filters with a centre-surround structure.

Using surfaces much larger (10 x 10 deg) than the dot-arrays employed by Mitchison and Westheimer (1984), Cagenello and Rogers (1993) report thresholds for detecting the direction of slant from the fronto-parallel (ground plane vs. sky plane) to be as low as 1 deg at a viewing distance of 57 cm. Although this is impressive sensitivity to surface slant, Rogers and Cagenello (1989) report greater sensitivity to surface curvature. The detection thresholds for curvature in parabolic surfaces, measured by requiring observers to discriminate convex from concave, was found to be such that the difference in slant between the extremes of the parabola was smaller than the slant detection threshold over the same spatial extent. They also reported that discrimination of disparity curvature gives a Weber fraction of just 4 - 6%^^ across a range of reference curvatures. Johnston (1991) measured disparity curvature Weber fractions of approximately 7% for 84% frequency-of-seeing, requiring observers to discriminate the curvature of elliptical cylinders; surfaces which unlike those employed by Rogers and Cagenello (1989) also have a non-zero third spatial derivative. All of these studies varied disparity only in one direction. That is, they provide estimates of curvature and slant sensitivity which take no account of the second free parameter which is necessary to represent the orientation of a planar surface, namely tilt (Marr, 1982). The present author is unaware of any study which has assessed tilt judgements for stereo.scopic surfaces. Furthermore, the curvature studies only examined sensitivity to surfaces curving in a single direction. Recently, De Vries, Kappers and Koenderink (1994) have measured observers' ability to discriminate the shape index of surfaces curving in more than one direction. They observed results consistent with the notion that the visual system extracts curvature with a sensitivity similar to that found by Rogers and Cagenello (1989) and Johnston (1991), then combines curvature estimates into a representation of shape index.

w a s u n f o r u i n a i e l y n o t s i a i c d w h e t h e r t h i s t h r e s h o l d w a s l o r 7 5 % , 8 4 % o r s o m e o t h e r f r e q u e n c y - o f - s e e i n g .