论文标题
各向异性的陈族分割
Anisotropic Chan-Vese segmentation
论文作者
论文摘要
在本文中，我们研究了与直线各向异性的变体到陈族图像分割模型。我们显示了在$ 2 $ ploses案中的最小化器以及与（各向异性）rudin-osher-osher-fatemi denoising模型（ROF）的关系。我们的分析表明，在矩形图像上的分段常数（简称PCR函数）的自然情况下，存在Chan-Vese函数的最小化器，该功能的最小化器在矩形上也在矩形上分散了与原始图像所定义的网格相同的网格。在多相情况下，我们表明，在初始图像是PCR函数的情况下，Chan-Vese多相功能的最小化也共享此属性。我们还研究了截短的ROF算法的多相和各向同性版本，并将该算法给出的解决方案与多相偏激型Chan-Vese功能的最小化器进行了比较。
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.
