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Equal Noise Resistance of Two Mainstream Iterative Sub-pixel Registration Algorithms in Digital Image Correlation

机译：数字图像相关中的两个主流迭代子像素配准算法的平等抗噪声

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摘要

The inverse compositional Gauss-Newton (IC-GN) algorithm and the forward additive Newton-Raphson (FA-NR) algorithm are two mainstream iterative sub-pixel registration algorithms in digital image correlation. This study compares the accuracy and convergence ability of the two algorithms by theoretical analysis and numerical experiments in the speckle images that have been contaminated with artificial Gaussian noise. Based on the derived error model, the systematic errors of the two algorithms are dominated by interpolation-induced error and are insensitive to noise. The random errors are proportional to the noise level. The noise also reduces the convergence radius and rate in the two algorithms. The two algorithms demonstrate equal noise resistance due to their mathematical equivalence. These conclusions are well supported by the experimental study. The recently reported vulnerability of the FA-NR algorithm to noise is not associated with the inherent flaw of the algorithm but with its implementation. If an inappropriate method is employed to estimate the gradients at sub-pixel locations in the FA-NR algorithm, abnormally large errors may be induced. This problem can be eliminated using the method that is proposed in this study, which has an insignificant extra-computation cost.
机译：逆成分高斯 - 牛顿（IC-GN）算法和前向添加剂牛顿-Raphson（FA-NR）算法是数字图像相关中的两个主流迭代子像素配准算法。该研究比较了两种算法的准确性和收敛能力，通过人工高斯噪声被污染的斑点图像中的理论分析和数值实验进行了理论分析和数值实验。基于派生错误模型，两种算法的系统误差由插值引起的误差主导，对噪声不敏感。随机误差与噪声水平成比例。噪声还降低了两种算法中的收敛半径和速率。由于它们的数学等效性，这两个算法表现出相同的抗噪声电阻。这些结论得到了实验研究得到了很好的支持。最近报告了FA-NR算法对噪声的漏洞与算法的固有漏洞无关，而是通过实现。如果采用不适当的方法来估计FA-NR算法中子像素位置处的梯度，则可以诱导异常大的误差。可以使用本研究中提出的方法来消除此问题，这具有微不足道的额外计算成本。

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