Exact optimization for a class of second order Markov random field via graph cuts

Optimization for the maximum a posterior (MAP) estimation of a Markov random field often comes down to a large combinational optimization problem, and the general purpose optimization technology such as simulated annealing requires exponential time in theory and is very slow in practice. In recent years a new method based on graph cuts has been developed to solve this problem. But right now it is restricted to the first order MRF. In this paper we have developed an exact optimization method for a class of second order MRF, which are wildly used in many applications. We consider each term in the posterior energy function separately and then merge them together. We give a detailed construction of the graph in the paper.