The role of disparity gradient in stereo vision

Burt and Julesz experimentally demonstrated that, in addition to Panum's fusional area, a quantity defined by them and named disparity gradient also plays a crucial part in deciding whether the human visual system would be able to fuse the images seen by the left and right eyes. The physical meaning of this quantity remains obscure despite attempts to interpret it in terms of depth gradient. Nevertheless, it has been found to be an effective selector of matches in stereo correspondence algorithms. A proof is provided that a disparity gradient limit of less than 2 implies that the matches between the two images preserve the topology of the images. The result, which is invariant under rotations and under relative as well as overall magnifications, holds for pairs of points separated in any direction, not just along epipolar lines. This in turn can be shown to prevent correspondences being established between points which would have to be located in three dimensions on a surface invisible to one eye, assuming opaque surfaces.