基于共轭梯度法的离散L_(2)模型曲面重建  

Surface Reconstruction of Discrete L_(2)Model Based on Conjugate Gradient Method

作　　者：付飞凡 杨奋林[1] 刘广英 安耿 FU Feifan;YANG Fenlin;LIU Guangying;AN Geng(School of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China)

机构地区：[1]吉首大学数学与统计学院,湖南吉首416000

出　　处：《吉首大学学报(自然科学版)》2025年第1期25-31,共7页Journal of Jishou University(Natural Sciences Edition)

基　　金：吉首大学校级科研项目(JDY22012)。

摘　　要：利用微积分求解最优化问题泛函时,会产生带有Neumann边界的欧拉-拉格朗日方程.针对此问题,运用最大似然估计来离散L_(2)模型,得到能够处理自由边界的离散L_(2)模型,并对其最优线性条件采用共轭梯度法进行求解,得到重建曲面.数值实验结果表明,相较于快速傅里叶变换方法和Horn-Brook's方法,共轭梯度法得到的图像边界更平滑且鲁棒性更优.Euler Lagrange equations with Neumann boundary are generated when the functional of optimization problem is solved by calculus.To solve this problem,the L_(2)model is discretized by using maximum likelihood estimation,and a discrete L_(2)model that can handle free boundaries is obtained.The optimal linear conditions are solved by conjugate gradient method,and the surface to be reconstructed is obtained.The numerical results show that compared with the fast Fourier transform method and Horn-Brook's method,the image boundary obtained by the conjugate gradient method is smoother and more robust.

关 键 词：共轭梯度法 梯度重建 三角测量 L_(2)模型 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]