Mumford-Shah型图像分割问题研究

项目名称： Mumford-Shah型图像分割问题研究

项目编号： No.U1304610

项目类型： 联合基金项目

立项/批准年度： 2014

项目学科： 无线电电子学、电信技术

项目作者： 庞志峰

作者单位： 河南大学

项目金额： 30万元

中文摘要： 随着信息科学和图像处理技术的发展，基于Mumford-Shah(MS)模型的分割问题研究已成为分割领域内的一个重要研究课题。本项目针对MS型分割模型中存在的缺陷和数值困难，利用图像的区域信息、边缘信息、统计特征和先验信息，结合分块常数区域内的梯度信息、适当的光滑逼近函数和聚类分析方法，提出有效的分块常数区域和分块光滑(非齐次)区域分割模型，并综合利用数值优化和偏微分方程数值解理论，改进水平集方法和图割方法；通过建立适当的约束空间和预处理技术，改进凸松弛方法和极大流/极小割方法，并对提出的算法进行稳定性和收敛性分析。本项目的完成将为MS型分割模型的课题研究提供更有效的分割模型和数值算法，为图像分割问题的实际应用提供更坚实的理论保障和技术支撑。

中文关键词： 图像分割；图像复原；交替方向乘子法；分裂Bregman方法；Mumford-Shah模型

英文摘要： With the development of information science and image processing technology, the segmentation problem based on the Mumford-Shah(MS) model becomes one of the most important research topics in this field. However, many challenging issues on mathematical understanding and numerical implementations are still well worthy of deep investigation. This project aims to surmount some of the obstacles for Mumford-Shah-type models. More precisely, we extract some information of regions and edges, statistic structures and a priori information of the image, and integrate the gradient information in the piecewise regions with the clustering techniques to develop efficient segmentation models for piecewise constant images and piecewise smooth (inhomogeneous) image segmentation. We search for new level set method and the graph cut method by using the related theory of numerical solution of partial differential equation and numerical optimization methods. We improve the convex relaxation method and max-flow/min-cut method based on proposing some suitable constrained spaces and preconditioning methods. We also attempt to analyze the stability and the convergence of proposed algorithms. The success of the project will lead to novel effective segmentation models and numerical methods. It will also provide more theoretical and technic

英文关键词： Image Segmentation；Image Restoration；Alternating Direction Method of Multipliers；Splitting Bregman Method；Mumford-Shah Model