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Multi-Label MRF Optimization via Least Squares s −t Cuts

By Ghassan Hamarneh


There are many applications of graph cuts in computer vision, e.g. segmentation. We present a novel method to reformulate the NP-hard, k-way graph partitioning problem as an approximate minimal s − t graph cut problem, for which a globally optimal solution is found in polynomial time. Each non-terminal vertex in the original graph is replaced by a set of ceil(log2(k)) new vertices. The original graph edges are replaced by new edges connecting the new vertices to each other and to only two, source s and sink t, terminal nodes. The weights of the new edges are obtained using a novel least squares solution approximating the constraints of the initial k-way setup. The minimal s −t cut labels each new vertex with a binary (s vs t) “Gray ” encoding, which is then decoded into a decimal label number that assigns each of the original vertices to one of k classes. We analyze the properties of the approximation and present quantitative as well as qualitative segmentation results

Topics: graph cuts, graph partition, multi-way cut, s −t cut, max-flow mincut, binary, Gray code, least squares, pseudoinverse, image segmentation
Year: 2009
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