Nonlocal Active Contours

This article introduces a novel class of active contour models for image segmentation. It makes use of nonlocal comparisons between pairs of patches within each region to be segmented. The corresponding variational segmentation problem is implemented using a level set formulation that can handle an arbitrary number of regions. The pairwise interaction of features constrains only the local homogeneity of image features, which is crucial in capturing regions with smoothly spatially varying features. This segmentation method is generic and can be adapted to various segmentation problems by designing an appropriate metric between patches. We instantiate this framework using several classes of features and metrics. Piecewise smooth grayscale and color images are handled using $L^2$ distance between image patches. We show examples of efficient segmentation of natural color images. Locally oriented textures are segmented using the $L^2$ distance between patches of Gabor coefficients. We use a Wasserstein distance between local empirical distributions for locally homogeneous random textures. A correlation metric between local motion signatures is able to segment piecewise smooth optical flows