Binocular stereopsis depends on the small differences between images from two slightly different viewpoints. When these differences are too great, fusion fails, although over a somewhat larger range stereo depth judgements are still possible. Burt and Julesz (1980) have shown that the gradient of disparity imposes a limit on achieving fusion. For stereopsis, such a limit could reduce the number of possible matches. Alternatively, slope and possibly curvature bounds could enter as explicit constraints on later processes such as those related to surface perception. Both have been features of computational models of stereopsis. To begin to address this issue we asked if derivative bounds affect the ability to make relative depth judgements. Subjects viewed three horizontal rows of static zero disparity black and white random dots on a gray background. During each trial the rows were briefly (150 ms) replaced by rows forming either a tilted plane or `V'-shaped depth profile, and observers reported the sense of tilt or convexity. Row separation and disparity were varied independently over a wide range. Subjects found the tilted plane task significantly more difficult and thresholds were correspondingly poorer. For the `V' configuration, thresholds are not simply determined by an absolute disparity limit. Although the separation of the flanking lines has an effect on thresholds, there is neither a fixed disparity gradient nor disparity curvature value that limits our ability to make relative depth judgements.
D.G. Jones, A.Dobbins