The Effect of Low-pass Pre-filtering on Subvoxel Registration Algorithms in Digital Volume Correlation: A revisited study

In digital volume correlation (DVC), random image noise in volumetric images leads to increased systematic error and random error in the displacements measured by subvoxel registration algorithms. Previous studies in DIC have shown that adopting low-pass pre-filtering to the images prior to the correlation analysis can effectively mitigate the systematic error associated with the classical forward additive Newton-Raphson (FA-NR) algorithm. However, the effect of low-pass pre-filtering on the state-of-the-art inverse compositional Gauss-Newton (ICGN) algorithm has not been investigated so far. In this work, we focus on the effect of low-pass pre-filtering on two mainstream subvoxel registration algorithms (i.e., 3D FA-NR algorithm and 3D IC-GN algorithm) used in DVC. Basic principles and theoretical error analyses of the two algorithms are described first. Then, based on numerical experiments with precisely controlled subvoxel displacements and noise levels, the influences of image noise on the displacements measured by two subvoxel algorithms are examined. Further, the effects of low-pass pre-filtering on these two subvoxel algorithms are examined for simulated image sets with different noise levels and deformation modes. The results show that the low-pass pre-filtering can effectively suppress the systematic errors for the 3D FA-NR algorithm, which is consistent with the previously drawn conclusion in DIC. On the contrary, different form the 3D FA-NR algorithm, the 3D IC-GN algorithm itself can reduce the influence of image noise, and the effect of low-pass pre-filtering on it is not so obvious as on 3D FA-NR algorithm.