A Weighted Difference of Anisotropic and Isotropic Total Variation for Relaxed Mumford-Shah Color and Multiphase Image Segmentation

• URL: http://arxiv.org/abs/2005.04401v6
• Date: Sun, 18 Jul 2021 02:07:57 GMT
• Title: A Weighted Difference of Anisotropic and Isotropic Total Variation for Relaxed Mumford-Shah Color and Multiphase Image Segmentation
• Authors: Kevin Bui, Fredrick Park, Yifei Lou, Jack Xin
• Abstract summary: We present a class of piecewise-constant image segmentation models that incorporate a difference of anisotropic and isotropic total variation. In addition, a generalization to color image segmentation is discussed.
• Score: 2.6381163133447836
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In a class of piecewise-constant image segmentation models, we propose to incorporate a weighted difference of anisotropic and isotropic total variation (AITV) to regularize the partition boundaries in an image. In particular, we replace the total variation regularization in the Chan-Vese segmentation model and a fuzzy region competition model by the proposed AITV. To deal with the nonconvex nature of AITV, we apply the difference-of-convex algorithm (DCA), in which the subproblems can be minimized by the primal-dual hybrid gradient method with linesearch. The convergence of the DCA scheme is analyzed. In addition, a generalization to color image segmentation is discussed. In the numerical experiments, we compare the proposed models with the classic convex approaches and the two-stage segmentation methods (smoothing and then thresholding) on various images, showing that our models are effective in image segmentation and robust with respect to impulsive noises.

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