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

In a class of piecewise-constant image segmentation models, we propose to incorporate weighted difference anisotropic and isotropic total variation (AITV) regularize the partition boundaries in an image. particular, replace regularization Chan--Vese model fuzzy region competition by proposed AITV. To deal with nonconvex nature AITV, apply difference-of-convex algorithm (DCA), which subproblems can be minimized primal-dual hybrid gradient method linesearch. The convergence DCA scheme is analyzed. addition, generalization color discussed. numerical experiments, compare models classic convex approaches two-stage methods (smoothing then thresholding) on various images, showing that our are effective robust respect impulsive noises.