Mumford-Shah Model Based on Weighted Total Generalized Variation
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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
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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