Nonlocal linear image regularization and supervised segmentation
Nonlocal linear image regularization and supervised segmentation
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DOI：
10.1137/060669358
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发表时间：
2007-01-01
影响因子：
1.6
通讯作者：
Osher, Stanley
中科院分区：
文献类型：
--
作者：
Gilboa, Guy;Osher, Stanley
加权di的非局部二次泛函。对推理进行了检验。权重是基于图像特征的，表示图像与图像之间的相关性。图像中的事件像素。通过处方di。事件公式的权重，可以推广许多局部和非局部线性去噪算法，包括非局部均值。信和双边。lte。在这个框架下，可以很容易地证明连续迭代的普遍化。服从一定的全局特征，收敛于一个常数解。与泛函的欧拉-拉格朗日方程相关的线性算子与图拉普拉斯算子密切相关。因此，我们可以将最小化泛函的最陡下降解释为非局部di。usion过程。这个公式为非局部变分最小化提供了一个方便的框架，包括变分去噪、布雷格曼迭代和最近提出的逆尺度空间。它还演示了如何最陡的下降。Ow可用于分割。继机器学习中基于核的方法之后，广义di。使用融合过程将零星的初始用户信息传播到整个图像。与经典的变分分割方法不同，该方法不是明确地基于曲线长度能量，因此可以很好地处理高度非凸的形状和角落。仍然达到了合理的噪声鲁棒性。
A nonlocal quadratic functional of weighted di. erences is examined. The weights are based on image features and represent the a. nity between di. erent pixels in the image. By prescribing di. erent formulas for the weights, one can generalize many local and nonlocal linear denoising algorithms, including the nonlocal means. lter and the bilateral. lter. In this framework one can easily show that continuous iterations of the generalized. lter obey certain global characteristics and converge to a constant solution. The linear operator associated with the Euler-Lagrange equation of the functional is closely related to the graph Laplacian. We can thus interpret the steepest descent for minimizing the functional as a nonlocal di. usion process. This formulation allows a convenient framework for nonlocal variational minimizations, including variational denoising, Bregman iterations, and the recently proposed inverse scale space. It is also demonstrated how the steepest descent. ow can be used for segmentation. Following kernel based methods in machine learning, the generalized di. usion process is used to propagate sporadic initial user's information to the entire image. Unlike classical variational segmentation methods, the process is not explicitly based on a curve length energy and thus can cope well with highly nonconvex shapes and corners. Reasonable robustness to noise is still achieved.