Multi-label Depth Estimation for Graph Cuts Stereo Problems

We describe here a method to compute the depth of a scene from a set of at least two images taken at known view-points. Our approach is based on an energy formulation of the 3D reconstruction problem which we minimize using a graph-cut approach that computes a local minimum whose energy is comparable (modulo a multiple constant) with the energy of the absolute minimum. As usually done, we treat the input images symmetrically, match pixels using photoconsistency, treat occlusion and visibility problems and consider a spatial regularization term which preserves discontinuities. The details of the graph construction as well as the proof of the correctness of the method are given. Moreover we introduce a multi-label refinement algorithm in order to increase the number of depth labels without significantly increasing the computational complexity. Finally we compared our algorithm with the results available in the Middlebury database.