| 基于混合梯度最小化Mumford-Shah模型的高维滤波算法 |
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| 引用本文： | 李波,苏卓,冷成财,王胜法,罗笑南.基于混合梯度最小化Mumford-Shah模型的高维滤波算法[J].自动化学报,2014,40(12):2926-2935. |
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| 作者姓名： | 李波 苏卓 冷成财 王胜法 罗笑南 |
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| 作者单位： | 1.南昌航空大学数学与信息科学学院 南昌 330063; |
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| 基金项目： | 国家自然科学基金(61262050,61300083,61363049),广东省科技计划(2012B010900009),广州市科技计划(2013J4300059)资助 |
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| 摘 要： | 为解决高维滤波中存在的边缘特征模糊和细节保持问题, 创新性提出了一种基于混合梯度最小化Mumford-Shah模型的平滑算法. 通过最小化包含梯度的L0、L1范数的正则化函数, 实现边缘保持和局部光滑的滤波分解效果. 从二维图像来看, 梯度的L0范数刻画了图像中非光滑像素的个数, 最小化梯度的L0范数可以实现图像分片同质的效果, 即可对应Mumford-Shah模型中要求的边缘内部尽量均匀; 梯度的L1范数, 即全变差项, 刻画了图像中所有水平集的长度, 最小化梯度的L1范数可以实现控制图像边缘锐利度的目的, 即Mumford-Shah模型中关于图像边缘保持的约束. 由于Mumford-Shah模型具有鲁棒的信号平滑和边缘特征描述能力, 因此在进行高维信号分解等处理时,可以取得良好分离效果. 实验结果表明, 混合梯度Mumford-Shah模型在滤波过程中可以实现边缘保持和纹理平滑相统一的特性, 获得优异的图像结构纹理分解效果, 对多个图像应用的处理效果有显著的提升, 在三维网格数据上也获得良好的去噪性能.
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| 关 键 词： | 边缘保持 纹理平滑 梯度最小化 Mumford-Shah模型 |
| 收稿时间： | 2013-10-16 |
Gradient Minimized Mumford-Shah Model for High-dimensional Filtering |
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| LI Bo,SU Zhuo,LENG Cheng-Cai,WANG Sheng-Fa,LUO Xiao-Nan.Gradient Minimized Mumford-Shah Model for High-dimensional Filtering[J].Acta Automatica Sinica,2014,40(12):2926-2935. |
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| Authors: | LI Bo SU Zhuo LENG Cheng-Cai WANG Sheng-Fa LUO Xiao-Nan |
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| Affiliation: | 1.School of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063;2.The National Engineering Research Center of Digital Life, State-Province Joint Laboratory of Digital Home Interactive Applications, School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006;3.Institute of Dongguan Sun Yat-sen University, Dongguan 523808;4.School of Software Technology, Dalian University of Technology, Dalian 116024 |
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| Abstract: | To address the problems of edge blurring and detail preservation in filtering, a novel high-dimensional filtering using gradient minimized Mumford-Shah model is proposed, which uses the minimization of L0 and L1 regularization terms to achieve edge-preserving and texture-smoothing. For 2D images, the L0 norm describes the number of non-smooth pixels in the image, which is minimized to obtain the local flat region, that is, to make the filtered output as smooth as possible in the Mumford-Shah model. The L1 norm (total variation term) describes the length of all level-sets in the image, which is minimized to control the sharpness of the edges, that is, the length constraint in the Mumford-Shah model. Due to the robustness of the Mumford-Shah model to edge-preserving and texture-smoothing, a sound component separation can be obtained in high-dimensional signal decomposition. In the experiments, it is demonstrated that the proposed high-dimensional filter can achieve both edge-preserving and texture-smoothing. The characteristic is helpful for obtaining a perfect structure-texture separation and optimizing the result in some specific visual applications. |
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| Keywords: | Edge-preserving texture-smoothing gradient minimization Mumford-Shah model |
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