Abstract :
We examine the implications of shape on the process of finding dense correspondence and halfocclusions
for a stereo pair of images. The desired property of the disparity map is that it should be a piecewise
continuous function which is consistent with the images and which has the minimum number of discontinuities.
To zeroth order, piecewise continuity becomes piecewise constancy. Using this approximation, we
first discuss an approach for dealing with such a fronto-parallel shapeless world, and the problems involved
therein. We then introduce horizontal and vertical slant to create a first order approximation to piecewise
continuity. In particular, we emphasize the following geometric fact: a horizontally slanted surface (i.e., having
depth variation in the direction of the separation of the two cameras) will appear horizontally stretched
in one image as compared to the other image. Thus, while corresponding two images, N pixels on a scanline
in one image may correspond to a different number of pixels M in the other image. This leads to three
important modifications to existing stereo algorithms: (a) due to unequal sampling, existing intensity matching
metrics must be modified, (b) unequal numbers of pixels in the two images must be allowed to correspond
to each other, and (c) the uniqueness constraint, which is often used for detecting occlusions, must be
changed to an interval uniqueness constraint. We also discuss the asymmetry between vertical and horizontal
slant, and the central role of non-horizontal edges in the context of vertical slant. Using experiments, we discuss
cases where existing algorithms fail, and how the incorporation of these new constraints provides correct
results.
