The TV p Regularized Mumford-Shah Model for Image Labeling and Segmentation

Abstract

The Mumford-Shah model is an important tool for image labeling and segmentation, which pursues a piecewise smooth approximation of the original image and the boundaries with the shortest length. In contrast to previous efforts, which use the total variation regularization to measure the total length of the boundaries, we build up a novel piecewise smooth Mumford-Shah model by utilizing a non-convex $\ell ^{p}$ regularity term for $p\in (0,1)$ , which can well preserve sharp edges and eliminate geometric staircasing effects. We present optimization algorithms with convergence verification, where all subproblems can be solved by either the closed-form solution or fast Fourier transform (FFT). The method is compared to piecewise constant labeling algorithm and several state-of-the-art piecewise smooth Mumford-Shah models based on image decomposition approximations. Both labeling and segmentation results on synthetic and real images confirm the robustness and efficiency of the proposed method.