多相图像分割Vese-Chan模型连续最大流方法  

Continuous max-flow method for multiphase segmentation Vese-Chan model

作　　者：王洁 潘振宽 魏伟波 徐子森[2] Wang Jie;Pan Zhenkuan;Wei Weibo;Xu Zisen(College of Computer Science and Technology,Qingdao University,Qingdao 266071,China;The Affiliated Hospital of Qingdao University,Qingdao 266003,China)

机构地区：[1]青岛大学计算机科学技术学院,青岛266071 [2]青岛大学附属医院,青岛266003

出　　处：《中国图象图形学报》2020年第5期926-935,共10页Journal of Image and Graphics

基　　金：国家自然科学基金项目(61772294)。

摘　　要：目的 多相图像分割是图像处理与分析的重要问题,变分图像分割的Vese-Chan模型是多相图像分割的基本模型,由于该模型使用较少的标签函数构造区域划分的特征函数,具有求解规模小的优点.图割(graph cut,GC)算法可将上述能量泛函的极值问题转化为最小割/最大流问题求解,大大提高了计算效率.连续最大流(con-tinuous max-flow,CMF)方法是经典GC算法的连续化表达,不仅具备GC算法的高效性,且克服了经典GC算法由于离散导致的精度下降问题.本文提出基于凸松弛的多相图像分割Vese-Chan模型的连续最大流方法.方法 根据划分区域编号的二进制表示构造两类特征函数,将多相图像分割转化为多个交替优化的两相图像分割问题.引入对偶变量将Vese-Chan模型转化为与最小割问题相对应的连续最大流问题,并引入Lagrange乘子设计交替方向乘子方法(alternating direction method of multipliers,ADMM),将能量泛函的优化问题转化为一系列简单的子优化问题.结果 对灰度图像和彩色图像进行数值实验,从分割效果看,本文方法对于医学图像、遥感图像等复杂图像的分割效果更加精确,对分割对象和背景更好地分离;从分割效率看,本文方法减少了迭代次数和运算时间.在使用2个标签函数的分割实验中,本文方法运算时间加速比分别为6.35%、10.75%、12.39%和7.83%;在使用3个标签函数的分割实验中,运算时间加速比分别为12.32%、15.45%和14.04%;在使用4个标签函数的分割实验中,运算时间加速比分别为16.69%和20.07%.结论 本文提出的多相图像分割Vese-Chan模型的连续最大流方法优化了分割效果,减少了迭代次数,从而提高了计算效率.Objective Multiphase image segmentation,an extension of two-phase image segmentation,is designed to partition images automatically into different regions according to different image features. It is a basic problem in image processing,image analysis,and computer vision. Variational image segmentation Vese-Chan model is a basic model of multiphase image segmentation that can construct characteristic functions for different phases or regions using fewer label functions,thus producing small-scale solutions. Graph cut (GC) algorithm can transform the optimization problem of energy function into the min-cut/max-flow problem,which greatly improves computational efficiency. In the spatially discrete setting,the computational results of the min-cut method are influenced by the discrete grid,resulting in measurement errors. In recent years,the continuous max-flow (CMF) method was proposed. As a continuous expression of the classical GC algorithm,CMF can keep the high efficiency of the GC algorithm and overcome measurement errors caused by the discretization of the classical GC algorithm. On the basis of the framework of variational theory,the CMF method for multiphase image segmentation Potts model and two-phase image segmentation Chan-Vese model was proposed and studied. However,a CMF method for the Vese-Chan model has not been studied. Therefore,we propose a CMF method for multiphase image segmentation Vese-Chan model based on convex relaxation and study its computational effectiveness and efficiency. Method In this study,binary label functions are used to construct different characteristic functions for different phases according to the relationship between a natural number and a binary representation of partitioned regions. The characteristic functions are divided into two parts according to the value of binary expression,i. e.,0 or 1. The characteristic functions are different. The date term of the segmentation model is also divided into two parts. Therefore,multiphase image segmentation can be transformed into two-p

关 键 词：多相图像分割 Vese-Chan模型 凸松弛 连续最大流方法 交替方向乘子方法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]