Cost aggregation table: A theoretic derivation on the Markov random field and its relation to message passing

The cost aggregation table (CAT) algorithm is a cost aggregation method for stereo matching that combines the ideas of the summed area table and semi-global matching (SGM). For the same computational complexity, this method generates more accurate disparity results than SGM, which was the most efficient stereo matching method for a decade. However, it has not been explained theoretically why CAT generates more accurate disparity results than SGM even though they have the same computational complexity. In this paper, we address the theoretic derivation of CAT based on Markov random fields (MRFs). The reason that CAT gives better disparity results than SGM is proven to be an aspect of energy minimization on the factor graph. In addition, we show that the origin of CAT is in message passing-based algorithms by showing that SGM, CAT, and belief propagation are all related to each other on different graph structures. We hope that this work will be the start of the generalization of CAT as a solution to labeling problems.