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Anisotropic Chan-Vese segmentation

Salvador MollVicent Pallard\'o
Oct 2022
摘要
In this paper we study a variant to Chan-Vese image segmentation model withrectilinear anisotropy. We show existence of minimizers in the $2$-phases caseand how they are related to the (anisotropic) Rudin-Osher-Fatemi denoisingmodel (ROF). Our analysis shows that in the natural case of a piecewiseconstant on rectangles image (PCR function in short), there exists a minimizerof the Chan-Vese functional which is also piecewise constant on rectangles overthe same grid that the one defined by the original image. In the multiphasecase, we show that minimizers of the Chan-Vese multiphase functional also sharethis property in the case that the initial image is a PCR function. We alsoinvestigate a multiphase and anisotropic version of the Truncated ROFalgorithm, and we compare the solutions given by this algorithm with minimizersof the multiphase anisotropic Chan-Vese functional.
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