Abstract 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.

中文翻译：

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低通预滤波对数字体积相关中亚体素配准算法的影响：一项重新审视的研究

摘要 在数字体积相关（DVC）中，体积图像中的随机图像噪声导致亚体素配准算法测量的位移的系统误差和随机误差增加。DIC 之前的研究表明，在相关分析之前对图像采用低通预滤波可以有效地减轻与经典前向加性牛顿拉夫森 (FA-NR) 算法相关的系统误差。然而，到目前为止，还没有研究低通预滤波对最先进的逆合成高斯牛顿 (ICGN) 算法的影响。在这项工作中，我们重点研究了低通预滤波对 DVC 中使用的两种主流亚体素配准算法（即 3D FA-NR 算法和 3D IC-GN 算法）的影响。首先介绍两种算法的基本原理和理论误差分析。然后，基于精确控制亚体素位移和噪声水平的数值实验，研究了图像噪声对两种亚体素算法测量位移的影响。此外，针对具有不同噪声水平和变形模式的模拟图像集，检查了低通预滤波对这两种亚体素算法的影响。结果表明，低通预滤波可以有效抑制3D FA-NR算法的系统误差，这与之前DIC中得出的结论是一致的。相反，与 3D FA-NR 算法不同，3D IC-GN 算法本身可以减少图像噪声的影响，