SIAM Journal on Imaging Sciences, Volume 14, Issue 3, Page 1078-1113, January 2021.
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.

中文翻译：

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松弛芒福德的各向异性和各向同性总变差的加权差--Shah颜色和多相图像分割

SIAM 成像科学杂志，第 14 卷，第 3 期，第 1078-1113 页，2021 年 1 月。
在一类分段常数图像分割模型中，我们建议结合各向异性和各向同性总变差 (AITV) 的加权差异来正则化图像中的分区边界。特别是，我们用所提出的 AITV 替换了 Chan-Vese 分割模型和模糊区域竞争模型中的总变异正则化。为了处理 AITV 的非凸性质，我们应用了凸差算法 (DCA)，其中子问题可以通过线性搜索的原始对偶混合梯度方法最小化。分析了DCA方案的收敛性。此外，还讨论了对彩色图像分割的概括。在数值实验中，