SIAM Journal on Imaging Sciences, Volume 13, Issue 3, Page 1692-1715, January 2020.
In this paper, we propose a new three-stage segmentation framework based on a convex variant of the Mumford--Shah model and the intensity inhomogeneity information of an image. The first stage in our framework is to perform a dimension lifting method. An intensity inhomogeneity image is added as an additional channel, which results in a vector-valued image. In the second stage, a convex variant of the Mumford--Shah model is applied to each channel of the vector-valued image to obtain a smooth approximation. We use the semi--proximal alternating direction method of multipliers (sPADMM) to solve this model and prove that the sPADMM for solving this convex model has Q-linear convergence rate. In the last stage, we apply a thresholding method to the smoothed vector-valued image to get the final segmentation. Experiments demonstrate clearly that the proposed methods can provide more accurate segmentation results in comparison with five state-of-the-art methods including a deep learning approach.

中文翻译：

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结合强度不均匀信息的三阶段变分图像分割框架

SIAM影像科学杂志，第13卷，第3期，第1692-1715页，2020年1月。
在本文中，我们基于Mumford-Shah模型的凸变体和图像的强度不均匀性信息，提出了一个新的三阶段分割框架。我们框架的第一步是执行尺寸提升方法。添加强度不均匀性图像作为附加通道，从而生成矢量值图像。在第二阶段，将Mumford-Shah模型的凸变体应用于矢量值图像的每个通道，以获得平滑逼近。我们使用乘数的半近似交替方向方法（sPADMM）来求解该模型，并证明用于求解该凸模型的sPADMM具有Q线性收敛速度。在最后阶段，我们将阈值化方法应用于平滑的矢量值图像以获得最终分割。