基于混合梯度最小化Mumford-Shah模型的高维滤波算法

李波; 苏卓; 冷成财; 王胜法; 罗笑南

doi:10.3724/SP.J.1004.2014.02926

基于混合梯度最小化Mumford-Shah模型的高维滤波算法

doi: 10.3724/SP.J.1004.2014.02926

李波^1,2,
苏卓^2,3,
冷成财¹,
王胜法⁴,
罗笑南²

1.
南昌航空大学数学与信息科学学院南昌 330063;
2.
中山大学信息科学与技术学院国家数字家庭工程技术研究中心数字家庭互动应用国家地方共建工程实验室广州 510006;
3.
东莞中山大学研究院东莞 523808;
4.
大连理工大学软件学院大连 116024

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

详细信息

作者简介:
李波南昌航空大学数学与信息科学学院副教授. 主要研究方向为计算机图形学及图像处理.E-mail: libo@nchu.edu.cn

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出版历程
- 收稿日期: 2013-10-16
- 修回日期: 2014-03-24
- 刊出日期: 2014-12-20

Gradient Minimized Mumford-Shah Model for High-dimensional Filtering

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

Funds:

Supported by National Natural Science Foundation of China (61262050,61300083,61363049), Science and Technology Project of Guangdong Province (2012B010900009), and Science and Technology Project of Guangzhou (2013J4300059)

摘要

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.
- 边缘保持 /
- 纹理平滑 /
- 梯度最小化 /
- Mumford-Shah模型
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.
- Edge-preserving /
- texture-smoothing /
- gradient minimization /
- Mumford-Shah model

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