Truncated convex models (TCM) are special cases of pairwise random fields that have been widely used in computer vision. However, by restricting the order of the potentials to be at most two, they fail to capture useful image statistics. We propose a natural generalization of TCM to high-order random fields, which we call truncated max-of-convex models (TMCM). The energy function of TMCM consists of two types of potentials: (i) unary potentials, which have no restriction on their form; and (ii) high-order potentials, which are the sum of the truncation of the m largest convex distances over disjoint pairs of random variables in an arbitrary size clique. The use of a convex distance function encourages smoothness, while truncation allows for discontinuities in the labeling. By using m > 1, TMCM provides robustness towards errors in the clique definition. In order to minimize the energy function of a TMCM over all possible labelings, we design an efficient st-mincut based range expansion algorithm. We prove the accuracy of our algorithm by establishing strong multiplicative bounds for several special cases of interest.
View on arXiv