Anisotropic Chan-Vese segmentation

In this paper we study a variant to Chan-Vese (CV) segmentation model with rectilinear anisotropy. We show existence of minimizers in the 2-phases case and how they are related to the (anisotropic) Rudin-Osher-Fatemi (ROF) denoising model. Our analysis shows that in the natural case of a piecewise constant on rectangles image (PCR function in short), there exists a minimizer of the CV functional which is also piecewise constant on rectangles over the same grid that the one defined by the original image. In the multiphase case, we show that minimizers of the CV multiphase functional also share this property in the case that the initial image is a PCR function. We also investigate a multiphase and anisotropic version of the Truncated ROF algorithm, and we compare the solutions given by this algorithm with minimizers of the multiphase anisotropic CV functional. & COPY; 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).