各向异性Chan-Vese分割
Anisotropic Chan-Vese segmentation
摘要：
在本文中，我们研究了一个变种的Chan-Vese图像分割模型与直线各向异性。我们显示存在极小的$2$阶段的情况下，他们是如何相关的（各向异性）的Rudin-Osher-Fatemi去噪模型（ROF）。我们的分析表明，在自然的情况下，分段常数的矩形图像（PCR函数在短），存在一个极小的Chan-Vese功能，这也是分段常数的矩形在同一个网格，由原始图像定义。在多相的情况下，我们表明，最小化的Chan-Vese多相功能的情况下，初始图像是一个PCR功能也共享此属性。我们还研究了多相和各向异性版本的截断ROF算法，我们比较了该算法的多相各向异性Chan-Vese功能的极小值的解决方案。
英文摘要：
In this paper we study a variant to Chan-Vese image segmentation model with rectilinear anisotropy. We show existence of minimizers in the $2$-phases case and how they are related to the (anisotropic) Rudin-Osher-Fatemi denoising model (ROF). Our analysis shows that in the natural case of a piecewise constant on rectangles image (PCR function in short), there exists a minimizer of the Chan-Vese functional which is also piecewise constant on rectangles over the same grid that the one defined by the original image. In the multiphase case, we show that minimizers of the Chan-Vese multiphase functional also share this property in the case that the initial image is a PCR function. We also investigate a multiphase and anisotropic version of the Truncated ROF algorithm, and we compare the solutions given by this algorithm with minimizers of the multiphase anisotropic Chan-Vese functional.
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