Abstract

In this work, we address the multi-label Mumford-Shah problem, i.e., the problem of jointly estimating a partitioning of the domain of the image, and functions defifined within regions of the partition. We create algorithms that are effifi- cient, robust to undesirable local minima, and are easy-toimplement. Our algorithms are formulated by slightly modifying the underlying statistical model from which the multilabel Mumford-Shah functional is derived. The advantage of this statistical model is that the underlying variables: the labels and the functions are less coupled than in the original formulation, and the labels can be computed from the functions with more global updates. The resulting algorithms can be tuned to the desired level of locality of the solution: from fully global updates to more local updates. We demonstrate our algorithm on two applications: joint multi-label segmentation and denoising, and joint multi-label motion segmentation and flflow estimation. We compare to the stateof-the-art in multi-label Mumford-Shah problems and show that we achieve more promising results.