An Image Segmentation Model with Transformed Total Variation

TL;DR

This paper introduces a novel image segmentation model using transformed total variation (TTV) regularization, which improves robustness and effectiveness over traditional TV methods, validated through numerical experiments.

Contribution

The paper proposes a TTV-regularized Mumford--Shah model with fuzzy membership and an ADMM algorithm for efficient optimization, advancing image segmentation techniques.

Findings

TTV outperforms classical TV and other nonconvex TV variants in segmentation tasks.

The proposed method achieves more robust image recovery.

Numerical experiments confirm the effectiveness of TTV in segmentation.

Abstract

Based on transformed $\ell_1$ regularization, transformed total variation (TTV) has robust image recovery that is competitive with other nonconvex total variation (TV) regularizers, such as TV$^p$, $0<p<1$. Inspired by its performance, we propose a TTV-regularized Mumford--Shah model with fuzzy membership function for image segmentation. To solve it, we design an alternating direction method of multipliers (ADMM) algorithm that utilizes the transformed $\ell_1$ proximal operator. Numerical experiments demonstrate that using TTV is more effective than classical TV and other nonconvex TV variants in image segmentation.