基于Lagrange插值的数字图像相关亚像素位移测量算法  

A Sub-pixel Displacement Measurement Algorithm Based onLagrange Interpolation in Digital Image Correlation

作　　者：刘小勇[1] 郑晓林 李荣丽[1] 黄远泽[2] 徐哲 李凯凯 裴晓日 张晓伟 LIU Xiaoyong;ZHENG Xiaolin;LI Rongli;HUANG Yuanze;XU Zhe;LI Kaikai;PEI Xiaori;ZHANG Xiaowei(School of Mechatronic Engineering,Changchun University of Technology,Changchun 130012,Jilin,P.R.China;China Water Resources Dongbei Investigation,Design&Research Co.,Ltd,Changchun 130021,Jilin,P.R.China)

机构地区：[1]长春工业大学机电工程学院,吉林长春130012 [2]中水东北勘测设计研究有限责任公司,吉林长春130021

出　　处：《影像科学与光化学》2024年第5期407-415,共9页Imaging Science and Photochemistry

基　　金：吉林省科技厅发展计划项目中央引导地方科技发展资金(YDZJ202201ZYTS604);吉林省教育厅“十三五”科学技术研究项目(JJKH20210719KJ);吉林大学数控装备可靠性教育部重点实验室开放基金项目(202103)。

摘　　要：本文旨在通过改进经典Newton-Raphson算法中的插值方法来优化数字图像相关(DIC)亚像素位移测量的计算效率。针对经典Newton-Raphson算法在数字图像相关亚像素位移测量中应用的双三次样条插值算法,特别是在需要计算边界点灰度梯度(即灰度值的一阶导数)时,存在计算量大的问题,本文提出一种基于Lagrange插值的改进算法作为解决方案。Lagrange插值算法在未增加计算节点数的情况下,成功避免了边界点灰度梯度的计算,使插值效率可提高近1/3。应用数值模拟实验和真实刚体平移实验对本文算法的性能进行验证。结果表明,本文算法在保持求解精度的同时,计算测量效率较传统Newton-Raphson算法有了明显提升。单点插值效率平均提升近30%;单点测量效率平均提升近20%。本文首次将Lagrange插值算法应用于数字图像相关的亚像素位移测量中,解决了双三次样条插值算法计算量大的问题,为相关领域提供了一种更为优化的变形测量方法。该研究为DIC亚像素位移测量技术的进一步发展和应用提供了新的思路和参考,有望在实际工程中得到广泛应用,促进相关领域的进步与发展。It aims to optimize the computational efficiency of sub-pixel displacement measurement in digital image correlation by improving the interpolation method in the classic Newton-Raphson algorithm in this paper.The bicubic spline interpolation algorithm is used in the classic Newton-Raphson algorithm,which increases computational complexity,especially when calculating the grayscale gradient of boundary points(i.e.the first derivative of grayscale values).Therefore,an improved algorithm based on Lagrange interpolation is proposed.The Lagrange interpolation algorithm successfully avoids the calculation of grayscale gradients at boundary points without increasing the number of calculation nodes,resulting in an interpolation efficiency improvement of nearly 1/3.The performance of the algorithm proposed in this paper is verified through numerical simulation experiments and real rigid body translation experiments.The results show that the algorithm proposed in this paper has significantly improved measurement efficiency compared to the traditional Newton-Raphson algorithm while maintaining solution accuracy.The average efficiency of single point interpolation has increased by nearly 30%.The average measurement efficiency of single point has increased by nearly 20%.The Lagrange interpolation algorithm is used in sub-pixel displacement measurement of digital image correlation(DIC)for the first time,solving the problem of high computational complexity in the bicubic spline interpolation algorithm.It provides a more optimized deformation measurement method for related fields.This study provides new ideas and references for the further development and application of sub-pixel displacement measurement technology of DIC,and is expected to be widely applied in practical engineering,promoting progress and development in related fields.

关 键 词：数字图像相关 LAGRANGE插值 Newton-Raphson算法 亚像素位移测量 

分 类 号：O348[理学—固体力学]