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In Chapter 1 it was noted that a number of hypotheses have been put forward for what constitute "stereoscopic primitives", meaning the property or properties which

stereopsis has evolved to compute. The vast majority of these hypotheses propose that extraction of a quantity or quantities relating to the spatial derivatives of disparity is fundamental. These include slant and tilt (Marr, 1982), disparity gradient (Gillam et al., 1988; Gillam and Ryan, 1993), disparity curvature (Rogers and Cagenello, 1989) and shape index (Koenderink, 1990). The results o f this chapter taken as a whole dispute these proposals, because they ignore sensitivity to relative disparity.

The 2V2D Sketch

Sensitivity to stereoscopic tilt was not evaluated in the experiments of this chapter, although it is considered in Chapter 5. Nevertheless, the results presented here have implications for the 2 ViD sketch. The results of Experiment 3 must cast serious doubt over whether one can consider the 2V2D sketch to be the goal of stereoscopic processing. It is clear that stereoscopic vision is used for estimating depth intervals and can employ this cue more effectively than it can measure the slant of a surface connecting two points, at least for non-planar surfaces. Nevertheless, W eber fractions for discriminating stereoscopic slant are less than 10%, provided the surface extends over several degrees. It remains to be seen whether stereoscopic vision is particularly sensitive to surface tilt. Also, the possibility that estimates of surface curvature are produced by comparing surface slant at different points across space cannot be ruled out on the basis of the experiments reported here.

Shape Index

The present experiments suggest that stereoscopic vision is not designed to compute shape index (Koenderink, 1990). Estimating shape index requires representation o f disparity curvature in more than one direction simultaneously and it is therefore limited by the visual system's sensitivity to disparity curvature. It appears from the present experiments that this limitation is quite considerable.

Nevertheless, de Vries, Kappers and Koenderink (1994) measured observers' ability to discriminate shape index using surfaces at a constant viewing distance. Combining the estimates of disparity curvature discrimination obtained here with the sensitivity necessary to underlie their result, it seems very unlikely that observers in that experiment were genuinely comparing shape index. The acid test o f this claim would be to perform the shape index discrimination task with jittered viewing distance or by jittering the spatial and disparity dimensions in similar fashion to Experiments 4 and 5 here.

Cyclopean .spatial filters

A more plausible account of the building-blocks of stereopsis is that they consist of the outputs of cyclopean spatial filters at a range of spatial scales, in analogous fashion

to the luminance domain. Seen in this way, perception of both disparity gradient and disparity curvature may result from combining the outputs of these filters, a process which reduces sensitivity relative to the representation of relative disparity, which is the analogue of contrast in the luminance domain. Evidence for this arises from the analogous results in cyclopean and luminance domains and the similarity of the shape of the discrimination functions for disparity curvature and disparity gradient, compared with relative disparity discrimination condition in Experiment 4. Barring some minor fluctuations, Weber fractions for all 3 discriminations improve with increasing disparity and are brought into closer register when the peak-trough disparities of the waveforms are equated, particularly for one observer, EC. It is difficult to elaborate much further than this without a concrete model of cyclopean spatial filters and the way in which they are combined. Furthermore, there is considerable variation between the two observers as regards the precise shape of the functions. However, one possibility which may well deserve further attention is that disparity gradient is detected and discriminated by combining the outputs of odd-symmetric cyclopean spatial filters of an analogous form to those which have been posited in the luminance domain (e.g. Daugman, 1980). Mechanisms for the perception of disparity curvature are doubtless more complex and certainly less sensitive.

Siimmnrv

It has been previously proposed that specialized mechanisms exist for extracting the spatial derivatives of disparity for the perception of surface shape, mechanisms which have no direct analogy in the luminance domain. In particular, studies concerning the discrimination of shape and surface orientation have been used as evidence for specialized mechanisms for perceiving slant and curvature, often involving the computation of contour disparities. It was predicted on this basis of previous estimates of disparity curvature discrimination that the disparity increment discrimination function for sinusoidal corrugations would have a different form to that found for contrast increment discrimination in the luminance domain. This prediction was not confirmed and it was apparent that performance was dominated by the relative disparity cue. Re-examination of previous shape discrimination studies revealed that cues other than disparity curvature could have been employed. An experimental design which removed these cues produced Weber fractions for disparity curvature of 15 - 30% and for disparity gradient of 6 - 20%. Stereoscopic vision is relatively insensitive to disparity curvature and more sensitive to relative disparity than to either disparity gradient or disparity curvature. These results are best understood in terms of cyclopean spatial filtering which is closely analogous to that found in the luminance domain. No evidence was found for the use o f contour disparities in the present set of experiments.