Multiway cut for stereo and motion with slanted surfaces

Slanted surfaces pose a problem for correspondence algorithms utilizing search because of the greatly increased number of possibilities, when compared with fronto-parallel surfaces. In this paper we propose an algorithm to compute correspondence between stereo images or between frames of a motion sequence by minimizing an energy functional that accounts for slanted surfaces. The energy is minimized in a greedy strategy that alternates between segmenting the image into a number of non-overlapping regions (using the multiway-cut algorithm of Boykov, Veksler, and Zabih) and finding the affine parameters describing the displacement function of each region. A follow-up step enables the algorithm to escape local minima due to oversegmentation. Experiments on real images show the algorithm's ability to find an accurate segmentation and displacement map, as well as discontinuities and creases, from a wide variety of stereo and motion imagery.