Accurate and simple digital volume correlation using pre-interpolation

Abstract

Existing incremental digital volume correlation methods can reduce the number of errors introduced by interpolation calculations in the inverse-compositional Gauss–Newton (IC-GN) algorithm 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 algorithm and the curve-fitting method. Experimental results show that the maximum mean bias error and the maximum standard deviation of the improved IC-GN algorithm are reduced by 34% and 75%, respectively. The improved curve-fitting has better accuracy and computational efficiency than the IC-GN algorithm under small strain and the curve-fitting method can achieve about 3.2 times speedup than the IC-GN algorithm.