Solving multilabel graph cut problems with multilabel swap

Approximate solutions to labelling problems can be found using binary graph cuts and either the α-expansion or α - β swap algorithms. In some specific cases, an exact solution can be computed by constructing a multilabel graph. However, in many practical applications the multilabel graph construction is infeasible due to its excessively large memory requirements. In this work, we expand the concept of α - β swap to consider larger sets of labels at each iteration, and demonstrate how this approach is able to produce good approximate solutions to problems which can be solved using multilabel graph cuts. Furthermore, we show how α-expansion is a special case of multilabel swap, and from this new formulation, illustrate how α-expansion is now able to handle binary energy functions which do not satisfy the triangle inequality. Compared to α-β swap, multilabel swap is able to produce an approximate solution in a shorter amount of time. We demonstrate the merits of our approach by considering the denoising and stereo problems. We illustrate how multilabel swap can be used in a recursive fashion to produce a good solution quickly and without requiring excessive amounts of memory.