A homography transform based higher-order MRF model for stereo matching

Stereo matching is one of the most important and fundamental topics in computer vision. It is usually solved by minimizing an energy function, which includes a data term and a smoothness term. The data term consists of the matching cost, and the smoothness term encodes the prior assumption that the surfaces are piecewise smooth. In contrast to the traditional methods, in which the smoothness term is modeled by the pairwise interactions, the smoothness term is modeled with a higher-order model in this paper. With the prior assumption that a tiny piece of a smooth surface is approximately planar, a higher-order potential function based on the homography transformations is presented. Then the energy function defined on a factor graph is proposed, in which the coefficients of the factors depend on the color information of the input images so that the discontinuous edges are preserved. The belief propagation (BP) algorithm is adopted to minimize the energy function, and the experimental results tested on the Middlebury data set show the potential of the proposed method.