三维医学解剖学结构提取的变分模型和快速算法研究

基于PDE的变分模型给图像处理带来了前所未有的数学理论基础，原来无法解决的图像问题用非线性数学中的微分方程能得以解决。三维医学解剖学结构的提取是医学图像处理中的一个重要的难题。本项目旨在促进基于PDE的图像分割方法在三维医学解剖学结构提取中的应用，深入研究迎合临床医学诊断的图像分割的变分模型，并构造快速有效地数值计算方法和正则参数选择方法。与已有的基于区域的变分能量图像分割模型的研究工作相比，我们将注重单个医学解剖学结构的提取，对图像和解剖学结构的几何特征以及医生提供的先验信息如标记点等开展比较具体的分析和研究，建立一些衡量局部统计特征的匹配性的新的能量模型，我们还将提出新的精度高，实现简单且快速有效的模型的求解方法。本课题的研究是一项具有重要理论意义和实际应用价值的工作，有利于医学图像处理的发展。

PDE-based variational models have brought unprecedented mathematical theory to image processing, the hard image problems can be solved by using PDE-base methods of the nonlinear mathematical theory. The extraction of 3D medical anatomical structures is a hard problem in medical image processing. This project is to promote the application of PDE-based image segmentation methods in the extraction of three dimensional medical anatomical structures, the work will focus on studying image segmentation variational models in clinical diagnosis, and constructing fast and effective numerical methods and selection methods of regularization parameter. Compare with the exist works of region-based image segmentation models, we should mainly study the extraction of a single medical anatomical structure, analyze the geometric characteristics of the medical anatomical structures and a priori information provided by the doctor, establish the new energy model matching local statistical feature, we should also propose a new high precision, fast and effective numerical methods solving the model. The work is of great both theoretical and practical significance, is conducive to the development of medical image processing.