Known as the digital speckle correlation method, the digital image correlation method is a non-contact optical measurement method. The deformation information of the region of interest is obtained by correlation calculation of two digital images before and after the specimen deformation. DIC method is mainly composed of integral pixel displacement search and sub-pixel displacement iterative calculation, among which the commonly adopted sub-pixel displacement calculation methods include surface fitting, gray gradient, Gauss-Newton (G-N) method, Newton-Raphson (N-R) method, and inverse compositional Gauss-Newton (IC-GN) method. In sub-pixel displacement search algorithms, N-R and G-N methods as second-order nonlinear optimization methods have faster convergence speed and global optimal solutions. However, in the G-N method, when the Hessian matrix is approximately non-positive definite, the error of solving the inverse matrix will increase to result in incorrect final solution results. Additionally, when the texture features of speckle images are weak and the deformation amount is large, the error of solving the inverse matrix will rise. The whole pixel displacement search algorithm can not provide accurate initial value estimation, and eventually, the calculation fails. Since the inverse compositional algorithm has higher computational efficiency than these algorithms, it is employed to calculate the displacement field of speckle deformation images by sub-pixel displacement, with several algorithms explored.

The inverse compositional diagonal approximation algorithm and the inverse compositional Dog-Leg algorithm adopting to image matching are applied to the displacement field calculation of speckle images, and the parameter update strategy of the inverse compositional Levenberg-Marquardt algorithm is simplified. By the compression deformation experiment of the memory simulation speckle image and the real speckle image, the performance of these three algorithms is explored from three aspects including convergence speed, convergence evaluation rate, and computation speed. In terms of convergence rate, the speckle image is evaluated in different displacement and Gaussian noise conditions. The convergence speed and calculation speed are evaluated by different small windows and with or without Gaussian noise. Finally, three algorithms are utilized to measure the deformation of the rubber block and compared with the open-source software Dice.

According to the speckle simulation deformation experiment, the convergence speed and final calculation accuracy of several first-order algorithms are almost the same, and in simple rigid body translation deformation, the convergence speed and final calculation accuracy of the first-order algorithm are higher than those of the second-order algorithm. Generally, the convergence speed and the final calculation accuracy of the second-order algorithms IC-LM2, IC-DogLeg2, IC-Diag2, and IC-GN2 decrease from high to low values. In terms of convergence speed, the convergence frequency of the first-order algorithm is higher than that of the second-order algorithm. When the displacement is less than five pixels, several algorithms can successfully calculate the displacement of all POI, and the convergence frequency gradually decreases with the increasing deformation. In the second-order algorithm, the convergence frequency of IC-Diag2, IC-DogLeg2, IC-LM2, and IC-GN2 algorithms decreases from high to low values. With the rising subarea window size, the convergence radius of several algorithms gradually increases, and the convergence frequency of IC-GN2, IC-DogLeg2, and IC-LM2 algorithms tends to be the same, while IC-Diag2 algorithm gradually ranks first in other algorithms. Among first-order algorithms, the convergence frequency of IC-DogLeg and IC-LM algorithms is slightly higher than that of IC-GN and IC-Diag algorithms. The calculation speed of IC-GN, IC-LM, IC-DogLeg, and IC-Diag algorithms decreases from high to low values, and with the increasing displacement, the calculation speed of several algorithms is also decreasing. Meanwhile, since with the rising size of the subarea window, the pixel number in the subarea that needs to participate in the calculation is also increasing, and its calculation speed is also slowing down. In the deformation experiment of rubber blocks, both the proposed algorithm and Dice software can successfully calculate the displacement field and strain field of the experimental deformation. In the large deformation experiment, the maximum shape variable exceeds 100 pixel, and it is difficult for the Dice software to accurately calculate the displacement field and strain field of the deformation for some regions. The three algorithms can still successfully calculate the displacement field and strain field of deformation and are more applicable under large deformation measurement scenarios.

In measuring image displacement, different sub-pixel displacement iteration algorithms deal with the different performances of displacement measurement. We adopt the inverse compositional diagonal approximation algorithm and inverse compositional Dog-Leg algorithm in the digital image correlation method for displacement measurement. Additionally, the parameter update strategy of the inverse compositional Levenberg-Marquardt algorithm is simplified, and the performance of the three algorithms is compared and evaluated by the compression deformation experiment of the simulated and real speckle images. The experimental results show that in the simulation speckle experiment, each algorithm has a different convergence speed, convergence frequency, and calculation speed. In real experiments, the accuracy of a small deformation experiment is similar to that of the inverse combined G-N method, and the convergence radius of a large deformation experiment is larger.