| 基于加权总广义变差的Mumford-Shah模型 |
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| 引用本文： | 张文娟,冯象初,王旭东.基于加权总广义变差的Mumford-Shah模型[J].自动化学报,2012,38(12):1913-1922. |
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| 作者姓名： | 张文娟 冯象初 王旭东 |
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| 作者单位： | 1.西安电子科技大学理学院应用数学系 西安 710071; |
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| 基金项目： | 国家自然科学基金(60872138,61271294,61105011,11101292)~~ |
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| 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 (Fast iterative 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.
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| 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 |
| 收稿时间： | 2012-05-15 |
Mumford-Shah Model Based on Weighted Total Generalized Variation |
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| ZHANG Wen-Juan,FENG Xiang-Chu,WANG Xu-Dong.Mumford-Shah Model Based on Weighted Total Generalized Variation[J].Acta Automatica Sinica,2012,38(12):1913-1922. |
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| Authors: | ZHANG Wen-Juan FENG Xiang-Chu WANG Xu-Dong |
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| Affiliation: | 1.Department of Applied Mathematics, School of Science, Xidian University, Xi'an 710071;2.School of Science, Xi'an Technological University, Xi'an 710021 |
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| Abstract: | 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 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. |
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| Keywords: | Mumford-Shah model denoising edge detection level set method weighted total generalized variation (TGV) |
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