Digital image correlation method based on Taylor series interpolation

Abstract Digital image correlation methods are used to obtain the deformation parameters by matching the target image with the reference image. The analysis accuracy of the deformation parameters is affected by several factors, among which the reconstruction algorithm of the target image is one of the main influencing factors. In this study, a target image reconstruction algorithm based on Taylor series interpolation is proposed to improve the calculation accuracy of deformation parameters. According to the theory of Fourier transform, the general relationship between the image gray value gradient and the image Fourier transform is deduced, which lays the foundation for Taylor series interpolation to be applied to the reconstruction of target image. Since the global derivatives of the image are pre-calculated based on the fast Fourier transform algorithm, and the derivatives used for Hessian matrix and Taylor series interpolation of the image sub-regions can be read directly from the overall derivatives in the subsequent iterations, this algorithm is characterized by high computational efficiency. Considering the computational accuracy and efficiency, this paper adopts the fourth-order Taylor series expansion as the interpolation algorithm for target image reconstruction. In order to evaluate the displacement analysis accuracy of the proposed algorithm in this paper, the displacement analysis results of the Taylor series interpolation algorithm are compared with the computational results of the bicubic B-spline interpolation and biquintic B-spline interpolation algorithms, respectively. The analysis of the results shows that the proposed algorithm is superior to the above two algorithms in terms of displacement analysis accuracy and computational efficiency. In addition, the results of the displacement field analysis of the proposed algorithm in actual tensile experiments with a hole are also shown in the paper.