Spatially Adaptive Regularization in Image Segmentation

面向含间接与不完整测量数据的逆问题的加权非齐次正则化

Weighted inhomogeneous regularization for inverse problems with indirect and incomplete measurement data

针对含不完整测量数据的逆问题，提出融合新型指数设计与空间变化权重的加权非齐次正则化方法，缓解特征邻近误分类与小尺度区域恢复难题，经合成图像与海冰数据实验验证有效。

在图像分割中的Ambrosio-Tortorelli近似中正则化参数的选择

Selection of the Regularization Parameter in the Ambrosio-Tortorelli Approximation of the Mumford-Shah Functional for Image Segmentation

本文研究了Ambrosio-Tortorelli函数在图像分割中的正则化参数选择问题，通过渐近分析揭示了正则化参数对分割行为的影响，并提出了一种参数选择策略和解的缩放方法，以提高分割效果。

关于分布依赖的Mumford-Shah模型的$\varepsilon$-正则化在高光谱图像分割中的重要性

On the importance of the $\varepsilon$-regularization of the distribution-dependent Mumford-Shah model for hyperspectral image segmentation

本文研究了高光谱图像分割中分布依赖的Mumford-Shah模型的理论性质，证明了泛函极小值的存在性及其$Γ$-收敛性，揭示了特征值正则化对保证极小值存在不可或缺的重要作用。

Spatially Adapted First and Second Order Regularization for Image Reconstruction: From an Image Surface Perspective

In this paper, we propose a new variational model for image reconstruction by minimizing the $L^1$ norm of the \emph{Weingarten map} of image surface $(x,y,f(x,y))$ for a given image $f:{\mathrmΩ}\rightarrow \mathbb R$. We analytically prove that the Weingarten map minimization model can not only keep the greyscale intensity contrasts of images, but also preserve edges and corners of objects. The alternating direction method of multiplier (ADMM) based algorithm is developed, where one subproblem needs to be solved by gradient descent. In what follows, we derive a hybrid nonlinear first and sec…

基于剪切波正则化的凸多类分割

Convex Multiclass Segmentation with Shearlet Regularization

本文提出一种基于离散剪切波变换的正则化项，用于凸多类图像分割模型，通过交替方向乘子法求解，相比全变分正则化能更好地分割弯曲纹理。

自适应特征空间分割

Adaptive Eigenspace Segmentation

本文提出了一种基于自适应特征空间的通用框架，用于解决图像分割中的正则化问题，无需参数调优即可实现鲁棒且准确的分割结果。