摘要
【目的】研究图像分割模型中水平集发展方程的高效稳定的数值解法。【方法】用移动最小二乘近似逼近水平集函数,然后将水平集发展方程离散为常微分方程组,并用向前Euler法求解。【结果】给出了一种图像分割的移动最小二乘近似方法,分割终止标准明确,形成的系数矩阵稀疏、条件数很小。【结论】数值实验表明该方法不需要重新初始化水平集函数,克服了水平集初始轮廓对分割结果的影响,是一种具有较高分割精度和较快分割速度的图像分割方法。
[Purposes]An efficient and stable numerical method is developed for the numerical solution of the level set evolution equation arising in image segmentation.[Methods]The level set function is approximated by the moving least squares approximation,and then the level set evolution equation is discredited into ordinary differential equations that can be solved by the forward Euler’s method.[Findings]A moving least squares approximation method for image segmentation is presented.In this method,the stop criterion is explicit,and the coefficient matrix is sparse and has small condition number.[Conclusions]Numerical experimental results reveal that the method requires no re-initialization procedure and conquers the effect by the initial contour of the level set function.Therefore,the developed method is robust to segment images with high precision and fast speed.
作者
李淑玲
郭岚
LI Shuling;GUO Lan(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)
出处
《重庆师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2018年第5期102-106,共5页
Journal of Chongqing Normal University:Natural Science
基金
重庆市教委科学技术研究项目(No.KJ1600330)
重庆市基础科学与前沿技术研究项目(No.cstc2017jcyjAX0176
No.cstc2015jcyjA0309)
国家自然科学基金(No.11471063)
关键词
移动最小二乘近似
数值计算
水平集方法
图像分割
moving least squares approximation
numerical computation
level set method
image segmentation
