Mumford-Shah Model Based on Weighted Total Generalized Variation

Abstract

The weighted total generalized variation (TGV) is deflned and the Mumford-Shah model based on weighted TGV is proposed, in which the second-order weighted TGV semi-norm of images is used as the regularization term. Besides, the second-order weighted TGV semi-norm of the level set function is used for approximating the length of boundary. A numerical calculation model is presented for solving the unknown functions by using the alternating Split-Bregman method, Fenchel dual method, and FISTA (fast iterative shrinkage-thresholding algorithm), separately. Simulation results show that the second-order weighted TGV semi-norm of images has better denoising efiect than the common L2 norm of gradient norm and the weighted TV semi-norm. And the result of edge detection is better than the traditional TV semi-norm and weighted TV semi-norm by using the second-order weighted TGV semi-norm of the level set function to approximate the length of boundary.