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We examine the implications of shape on the process of finding dense correspondence and half-occlusions for a stereo pair of images. The desired property of the depth 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 zeroeth 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. We highlight the fact that a horizontally slanted surface (ie. having depth variation in the direction of the separation of the two cameras) appears 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, which has consequences with regard to sampling and occlusion detection. We also discuss the asymmetry between vertical and horizontal slant, and the central role of nonhorizontal edges in the context of vertical slant. Using experiments, we discuss cases where existing algorithms fail, and how the incorporation of new constraints provides correct results.