基于Hermite插值的数字图像相关亚像素位移求解算法

A Sub-pixel Displacement Estimation Algorithm Based on Hermite Interpolation in Digital Image Correlation

在数字图像相关方法中,传统Newton-Raphson算法(简称N-R算法)通常采用三次样条插值算法获得散斑图亚像素位置的灰度值。而在插值算法中,Hermite插值算法具有更加良好的光滑程度。因此,为了提高传统N-R算法的计算精度,提出一种基于Hermite插值的亚像素位移求解算法。该算法应用Hermite插值函数构建散斑图亚像素位置灰度值,并应用Barron算子计算像素点的一阶灰度梯度;之后应用牛顿迭代算法进行亚像素位移求解。应用真实散斑图的数值变形实验对算法的有效性与计算精度进行了验证。实验结果表明:提出的算法有效提高了传统N-R算法的计算精度且计算稳定性较好。

In digital image correlation method,the gray value of sub-pixel in speckle pattern is usually obtained by cubic spline interpolation in traditional Newton-Raphson algorithm.Among interpolation algorithms,the cubic Hermite interpolation algorithm has better smoothness.Therefore,a sub-pixel displacement estimation algorithm based on Hermite interpolation was proposed to improve the computation accuracy of traditional Newton-Raphson algorithm.The Hermite interpolation was used to reconstruct the gray value of sub-pixel in this algorithm.The first-order gray gradient was calculated by using Barron operator.Then,the Newton iteration algorithm was employed to compute the sub-pixel displacement.Numerical deformation experiment of real speckle patterns was conducted to verify the effectiveness and calculation accuracy of the proposed algorithm.The results show that the proposed algorithm is used to improve the calculation accuracy of the traditional N-R algorithm effectively and has good stability.