Active contour methods are popular in obtaining unsupervised object segmentations in digital images. Multiphase active contours segment a given image into multiple regions corresponding to certain regional properties. Active contour without edges, is a variant which gained immense popularity in various application domains, and traditionally implemented with level set methods. Recently, there has been great interest in obtaining convex approximations of traditional level set driven multiphase active contours. Many of these formulations involve utilizing different contributions of the total variation (TV) of soft functions used as regularization within energy minimization formulation. In this work, we propose a new multiphase segmentation that better approximates the boundary regions by utilizing coupling gradient constraints of relaxed membership functions. This extends geometrical regularization capabilities of the TV, and enables our method to obtain improved segmentation results. Our method is based on minimizing an initialization independent convex energy functional on a specific space with the penalization of the gradient of phases using L2 differences. Detailed theoretical analysis of the coupled multiphase active contour (CMAC) method is presented and the existence of minimizer is proved using direct methods of calculus of variations. We apply our multiphase active contours to segment natural images. Extensive comparisons with other related variational based multiphase active contours is undertaken on the Berkeley segmentation dataset. Results show that our method is able to obtain better segmentations with respect to various standard segmentation error metrics, when compared with the gold standard ground truth segmentations. Moreover, theoretical analysis provides a solid foundation using an efficient split Bregman based implementation, which makes our proposed CMAC very attractive for image segmentation.
Related projects: VTV-Vectorial TV Denoising