  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.
