Under the popular Markov random field (MRF) model, low-level vision problems are usually formulated by prior and likelihood models. In recent years, the priors have been formulated from high-order cliques and have demonstrated their robustness in many problems. However, the likelihoods have remained zeroth-order clique potentials. This zeroth-order clique assumption causes inaccurate solution and gives rise to undesirable fattening effect especially when window-based matching costs are employed. In this paper, we investigate high-order likelihood modeling for the stereo matching problem which advocates the dissimilarity measure between the whole reference image and the warped non-reference image. If the dissimilarity measure is evaluated between filtered stereo images, the matching cost can be modeled as high-order clique potentials. When linear filters and nonparametric census filter are used, it is shown that the high-order clique potentials can be reduced to pairwise energy functions. Consequently, a global optimization is possible by employing efficient graph cuts algorithm. Experimental results show that the proposed high-order likelihood models produce significantly better results than the conventional zeroth-order models qualitatively as well as quantitatively. 
Stereo reconstruction using high-order likelihoods