Auxiliary Variables for Markov Random Fields with Higher Order Interactions

Abstract. Markov Random Fields are widely used in many image processing applications. Recently the shortcomings of some of the simpler forms of these models have become apparent, and models based on larger neighbourhoods have been developed. When single-site updating methods are used with these models, a large number of iterations are required for convergence. The Swendsen-Wang algorithm and Partial Decoupling have been shown to give potentially enormous speed-up to computation with the simple Ising and Potts models. In this paper we show how the same ideas can be used with binary Markov Random Fields with essentially any support to construct auxiliary variable algorithms. However, because of the complexity and certain characteristics of the models, the computational gains are limited.