An Image Segmentation Model with Transformed Total Variation
This work addresses image segmentation, a key problem in computer vision, but it is incremental as it builds on existing nonconvex total variation methods.
The authors tackled image segmentation by proposing a transformed total variation (TTV)-regularized Mumford-Shah model with a fuzzy membership function, and numerical experiments showed that TTV is more effective than classical TV and other nonconvex TV variants in this task.
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.