Gradient Minimized Mumford-Shah Model for High-dimensional Filtering
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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
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.-
Key words:
- Edge-preserving /
- texture-smoothing /
- gradient minimization /
- Mumford-Shah model
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