多相图像分割变分模型的标签函数提升方法  

Label function lifting method for variational model of multiphase image segmentation

作　　者：董璐璐 宋金涛 魏伟波 潘振宽 DONG Lulu;SONG Jintao;WEI Weibo;PAN Zhenkuan(College of Computer Science and Technology,Qingdao University,Qingdao 266071,Shandong,China)

机构地区：[1]青岛大学计算机科学技术学院,山东青岛266071

出　　处：《山东大学学报（工学版）》2022年第4期54-68,共15页Journal of Shandong University（Engineering Science）

基　　金：国家自然科学基金资助项目(61772294,11472144);山东省联合基金资助项目(ZR2019LZH002)。

摘　　要：针对多相图像分割变分模型的局部极值问题,采用函数提升方法实现模型的全局优化。基于笛卡尔流思想和校准理论,将离散的标签函数提升为二值超水平集函数。利用二值标签函数凸松弛技术,设计标签函数子问题的凸优化方法,通过原-对偶算法和投影算法简化计算以提高计算效率。对多幅多相灰度图像和彩色图像进行分割试验,结果表明:所提模型的能量极小值较原模型直接计算结果小得多,与最小值的误差仅为0、0.426%、0.040%等。改进后的方法几乎不依赖初始水平集的设置和试验参数的选择,可以得到全局最小值;所提算法的迭代次数大大减少,计算效率显著提高。Aiming at the local extremum problem of variational model used for multiphase image segmentation,functional lifting method was used to realize global optimization.Based on the idea of Cartesian flow and calibration theory,discrete label function was promoted to a binary super level set function.Using convex relaxation technique of binary label function,convex optimization method of label function subproblem was designed,and the calculation was simplified by primal dual algorithm and projection algorithm to improve calculation efficiency.Segmentation experiments of multiple multiphase gray and color images were carried out,and the results showed that the energy minimum of proposed model was much smaller than the direct calculation result of original model,and the error with the minimum value was only 0,0.426%,0.040%,etc.The improved method hardly depended on settings of initial level set and selection of experimental parameters;the iterations of the proposed algorithm were greatly reduced,and the computational efficiency was significantly improved.

关 键 词：多相图像分割 标签函数 凸优化 函数提升 原-对偶算法 投影算法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]