Accurate and simple digital volume correlation using pre-interpolation

Existing incremental digital volume correlation methods can reduce the number of errors introduced by interpolation calculations in the inverse-compositional Gauss-Newton algorithm (IC-GN) iteration. However, the accuracy of these existing methods is insufficient for some conditions as the curve-fitting method has high computational efficiency but lacks accuracy. A simple pre-interpolation method is proposed to improve the accuracy and computational efficiency of digital volume correlation. First, the pretreatment of a deformed volume image is calculated by the cubic spline interpolation method with the most often chosen interpolation step of 1/2 sub-voxel. Next, the pre-interpolation is calculated only once and the block calculation techniques solve the memory problem. Then, the reference sub-volume in the updated reference volume image is translated into the nearest half-integer voxel position instead of the integer voxel position or other sub-voxel positions. The pre-interpolation method is applied to both the IC-GN and the curve-fitting method. Experimental results show that the maximum mean bias error and the maximum standard deviation of the improved IC-GN are reduced by 34% and 75%, respectively. The improved curve-fitting has better accuracy and computational efficiency than IC-GN under small strain and the curve-fitting method can achieve about 3.2 times speedup than IC-GN.

"V0-[0.1, 0.2, 0.3] of xyz" is the volume image of the sub-voxel displacement of x, y, z, respectively,

"V1-[0.1, 0.2, 0.3] of xyz" is the reference volume image.

Both of the FreeDIC and FastDVC used the improved method.

New method to improved the accuracy and computer speed for DVC can see:  http://doi.org/10.5281/zenodo.3686765