Texture Segmentation via Non-local Non-parametric Active Contours

Abstract

Abstract. 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.

Local regularity for texture segmentation: Combining wavelet leaders and proximal minimization

“…Comparisons against alternative segmentation features, such as local entropy, will be conducted. Comparisons of the robust convex optimization based segmentation achieved here against recent classification techniques, such as the one proposed in [28,3] will also be made. Moreover, extensions of the procedure to the class of piecewise smooth local regularity images are currently under study.…”

“…Texture characterization and segmentation constitutes a challenging task in image processing (see e.g., [1,2,3,4,5] and references therein). In a variety of applications of possibly very different natures, the relevant information characterizing textures, and thus conveying the information to be analyzed, consists of the fluctuations across space of their local regularity.…”

“…Also, a proximal solution in a context of disparity estimation was proposed in [27]. Alternatively, recent techniques are framed into variational principles, making use of comparisons between pairs of neighboring patches [28,3]. Notably, in [28], a convex relaxation of the original problem was envisaged so as to ensure to find the global minimizer, while in [3] a more general but non-convex framework was proposed, which yields good results at the price of a well-chosen initialization.…”

Convex Color Image Segmentation with Optimal Transport Distances

“…Its successful application in various image processing tasks has demonstrated its practical interest (see e.g. [10,11,13,7,8]). Some limitations have been also shown and partially addressed, such as time complexity, regularity and relaxation [3,6].…”

“…In this work, we are interested in the use of the optimal transport framework for Image segmentation. This has been first investigated in [10] for 1D features, then extended to multi-dimensional features using approximations of the optimal transport cost [7,12], and adapted to region-based active contour in [12], relying on a non-convex formulation. In [14], a convex formulation is proposed, making use of sub-iterations to compute the proximity operator of the Wasserstein distance, which use is restricted to low dimensions.…”