Stereo reconstruction using high order likelihood

Under the popular Bayesian approach, a stereo problem can be formulated by defining likelihood and prior. Likelihoods are often associated with unary terms and priors are defined by pair-wise or higher order cliques in Markov random field (MRF). In this paper, we propose to use high order likelihood model in stereo. Numerous conventional patch based matching methods such as normalized cross correlation, Laplacian of Gaussian, or census filters are designed under the naive assumption that all the pixels of a patch have the same disparities. However, patch-wise cost can be formulated as higher order cliques for MRF so that the matching cost is a function of image patch's disparities. A patch obtained from the projected image by a disparity map should provide a better match without the blurring effect around disparity discontinuities. Among patch-wise high order matching costs, the census filter approach can be easily reduced to pair-wise cliques. The experimental results on census filter-based high order likelihood demonstrate the advantages of high order likelihood over independent identically distributed unary model.