三维图像多相分割的变分水平集方法  

A Variational Level Set Method of Multiphase Segmentation for 3D Images

作　　者：潘振宽[1] 李华[1] 魏伟波[1] 郭振波[1] 张春芬[2] 

机构地区：[1]青岛大学信息工程学院,山东青岛266071 [2]江苏大学计算机科学与通信工程学院,江苏镇江212013

出　　处：《计算机学报》2009年第12期2464-2474,共11页Chinese Journal of Computers

基　　金：教育部新世纪优秀人才支持计划( NCET-05-0601)资助

摘　　要：变分水平集方法是图像分割等领域出现的新的建模方法,借助多个水平集函数可有效地实现图像多相分割.但在区域/相的通用表达、不同区域内图像模型的表达、通用的能量泛函的设计、高维图像分割中的拓展研究等方面仍是图像处理的变分方法、水平集方法、偏微分方程方法等研究的热点问题.文中以三维图像为研究对象,系统地建立了一种新的三维图像多相分割的变分水平集方法.该方法用n-1个水平集函数划分n个区域,并基于Heaviside函数设计出区域划分的通用的特征函数;其能量泛函包括通用的区域模型、边缘检测模型和水平集函数为符号距离函数的约束项3部分;最后,针对所得到的曲面演化方程,采用半隐式差分格式进行离散,并对多种类型三维图像进行分割验证了所提出模型的通用性和有效性.The variational level set method is a new modeling method for image segmentation which has been extended to multiphase segmentation of images successfully. But the generic expressions of region/phase partitioning, image models in every region, energy functional, and their extensions to applications in segmentation of high dimensional images are current research focuses in image processing based on variational method, level set method and methods using PDEs（Partial Differential Equations）. The purpose of this paper is to develop a novel variational level set method for 3D image multiphase segmentation. For this goal, a generic characteristic function for region partitioning based on n-1 level set functions for n regions and their Heaviside functions is designed, and a generic energy functional includes region-based model, edge-based model and constraint term enforcing the level set functions as signed distance functions are suggested also. The corresponding PDEs of evolution of level set functions are discretized using finite difference method and semi-implicit iterations and used to multiphase segmentation for 3D images finally.

关 键 词：三维重建 多相图像分割 变分方法 水平集方法 差分方法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]