Texture Segmentation via Non-local Non-parametric Active Contours

This article introduces a novel active contour model that makes use of non-parametric estimators over patches for the segmentation of textured images. It is based on an energy that enforces the homogeneity of these statistics. This smoothness is measured using Wasserstein distances among discretized probability distributions that can handle features in arbitrary dimension. It is thus usable for the segmentation of color images or other high dimensional features. The Wasserstein distance is more robust than traditional pointwise statistical metrics (such as the Kullback-Leibler divergence) because it takes into account the relative distances between modes in the distributions. This makes the corresponding energy robust and does not require any smoothing of the statistical estimators. To speed-up the computational time, we propose an alternative metric that retains the main qualities of the Wasserstein distance, while being faster to compute. It aggregates 1-D Wasserstein distances over a set of directions, and thus benefits from the simplicity of 1-D statistical metrics while being able to discriminate high dimensional features. We show numerical results that instantiate this novel framework using grayscale and color values distributions. This allows us to segment regions with smoothly varying intensities or colors as well as complicated textures.