Efficient Shape Matching Via Graph Cuts

Meaningful notions of distance between planar shapes typically involve the computation of a correspondence between points on one shape and points on the other. To determine an optimal correspondence is a computationally challenging combinatorial problem. Traditionally it has been formulated as a shortest path problem which can be solved efficiently by Dynamic Time Warping. In this paper, we show that shape matching can be cast as a problem of finding a minimum cut through a graph which can be solved efficiently by computing the maximum network flow. In particular, we show the equivalence of the minimum cut formulation and the shortest path formulation, i.e. we show that there exists a one-to-one correspondence of a shortest path and a graph cut and that the length of the path is identical to the cost of the cut. In addition, we provide and analyze some examples for which the proposed algorithm is faster resp. slower than the shortest path method.