Exact and Approximate Inference in Associative Hierarchical Networks using Graph Cuts

Markov Networks are widely used through out computer vision and machine learning. An important subclass are the Associative Markov Networks which are used in a wide variety of applications. For these networks a good approximate minimum cost solution can be found efficiently using graph cut based move making algorithms such as alpha-expansion. Recently a related model has been proposed, the associative hierarchical network, which provides a natural generalisation of the Associative Markov Network for higher order cliques (i.e. clique size greater than two). This method provides a good model for object class segmentation problem in computer vision. Within this paper we briefly describe the associative hierarchical network and provide a computationally efficient method for approximate inference based on graph cuts. Our method performs well for networks containing hundreds of thousand of variables, and higher order potentials are defined over cliques containing tens of thousands of variables. Due to the size of these problems standard linear programming techniques are inapplicable. We show that our method has a bound of 4 for the solution of general associative hierarchical network with arbitrary clique size noting that few results on bounds exist for the solution of labelling of Markov Networks with higher order cliques.

Within this paper we briefly describe the associative hierarchical network and provide a computationally efficient method for approximate inference based on graph cuts. Our method performs well for networks containing hundreds of thousand of variables, and higher order potentials are defined over cliques containing tens of thousands of variables. Due to the size of these problems standard linear programming techniques are inapplicable. We show that our method has a bound of 4 for the solution of general associative hierarchical network with arbitrary clique size noting that few results on bounds exist for the solution of labelling of Markov Networks with higher order cliques.