基于加权总广义变差的Mumford-Shah模型  

Mumford-Shah Model Based on Weighted Total Generalized Variation

作　　者：张文娟[1,2] 冯象初[1] 王旭东[1] 

机构地区：[1]西安电子科技大学理学院应用数学系,710071 [2]两安工业大学理学院,西安710021

出　　处：《自动化学报》2012年第12期1913-1922,共10页Acta Automatica Sinica

基　　金：国家自然科学基金(60872138,61271294,61105011,11101292)~~

摘　　要：给出了加权总广义变差(Total generalized variation,TGV)的定义.利用图像的2阶加权TGV半范作为正则项,利用水平集函数的2阶加权TGV半范近似边界长度,提出了基于加权TGV的Mumford-Shah模型.对未知函数分别利用交替Split-Bregman方法、Fenchel对偶方法及FISTA(Fas titerative shrinkage-thresholding algorithm)给出数值计算模型.仿真实验结果表明,利用图像的2阶加权TGV半范的去噪效果优于常用的梯度模2范数和加权TV(Total variation)半范正则化;利用水平集函数的2阶加权TGV半范近似边界长度的边缘检测效果优于传统的TV半范和加权TV半范约束.The weighted total generalized variation （TGV） is defined 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 effect 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 semiqnorm 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.

关 键 词：Mumford—Shah模型 去噪 边缘检测 水平集方法 加权总广义变差 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]