Multiphase image segmentation via equally distanced multiple well potential

Variational models for image segmentation, e.g. Mumford-Shah variational model [47] and Chan-Vese model [21,59], generally involve a regularization term that penalizes the length of the boundaries of the segmentation. In practice often the length term is replaced by a weighted length, i.e., some portions of the set of boundaries are penalized more than other portions, thus unbalancing the geometric term of the segmentation functional. In the present paper we consider a class of variational models in the framework of ?-convergence theory. We propose a family of functionals defined on vector valued functions that involve a multiple well potential of the type arising in diffuse-interface models of phase transitions. A potential with equally distanced wells makes it possible to retrieve the penalization of the true (i.e., not weighted) length of the boundaries as the ?-convergence parameter tends to zero. We explore the differences and the similarities of behavior of models in the proposed class, followed by some numerical experiments. © 2014 Elsevier Inc. All rights reserved.