Double Expansion for Multilabel Segmentation with Shape Prior

We propose a new class of energies for segmentation of multiple foreground objects with a common shape prior. Our energy involves infinity constraints. For such energies standard expansion algorithm has no optimality guarantees and in practice gets stuck in bad local minima. Therefore, we develop a new move making algorithm, we call double expansion. In contrast to expansion, the new move allows each pixel to choose a label from a pair of new labels or keep the old label. This results in an algorithm with optimality guarantees and robust performance in practice. We experiment with several types of shape prior such as star-shape, compactness and a novel symmetry prior, and empirically demonstrate the advantage of the double expansion.