On a Variational and Convex Model of the Blake–Zisserman Type for Segmentation of Low-Contrast and Piecewise Smooth Images

Abstract

This paper proposes a new variational model for segmentation of low-contrast and piecewise smooth images. The model is motivated by the two-stage image segmentation work of Cai–Chan–Zeng (2013) for the Mumford–Shah model. To deal with low-contrast images more effectively, especially in treating higher-order discontinuities, we follow the idea of the Blake–Zisserman model instead of the Mumford–Shah. Two practical ideas are introduced here: first, a convex relaxation idea is used to derive an implementable formulation, and second, a game reformulation is proposed to reduce the strong dependence of coupling parameters. The proposed model is then analysed for existence and further solved by an ADMM solver. Numerical experiments can show that the new model outperforms the current state-of-the-art models for some challenging and low-contrast images.