Anisotropic Chan-Vese segmentation

TL;DR

This paper introduces a rectilinear anisotropic variant of the Chan-Vese image segmentation model, establishing existence of minimizers, their relation to anisotropic denoising, and properties for piecewise constant images, along with algorithmic comparisons.

Contribution

It develops a new anisotropic Chan-Vese model, proves existence of minimizers, and connects these to anisotropic denoising and piecewise constant image properties.

Findings

Existence of minimizers for the anisotropic Chan-Vese model.

Minimizers are piecewise constant on rectangles for PCR images.

Comparison of anisotropic Chan-Vese solutions with a multiphase Truncated ROF algorithm.

Abstract

In this paper we study a variant to Chan-Vese image 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 denoising model (ROF). 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 Chan-Vese 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 Chan-Vese 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 Chan-Vese functional.