Background: Digital Image Correlation (DIC) is based on the matching, between reference and deformed state images, of features contained in patterns that are deposited on test sample surfaces. These features are often suitable for a single scale, and there is a current lack of multiscale patterns capable of providing reliable displacement measurements over a wide range of scales. Objective: Here, we aim to demonstrate that a pattern based on a fractal (self-affine) surface would make a suitable pattern for multiscale DIC. Methods: A method to numerically generate patterns directly from a desired auto-correlation function is introduced. It is then enhanced by a Mean Intensity Gradient (MIG) improvement process based on grey level redistribution. Numerical experiments at multiple scales are performed for two different imposed displacement fields and results for one of the patterns generated are compared with those obtained for a random pattern and a Perlin noise one. Results: The proposed pattern is shown to lead to DIC errors comparable to those found with the two others for the first scales, but has much greater robustness. More importantly, the pattern generated here exhibits stable errors and robustness with respect to the scale whereas these two outputs become significantly degraded for the other two patterns as the scale increases. Conclusions: As a result, scale invariance properties of the pattern based on fractal surfaces correspond to scale invariance in DIC errors as well. This is of great interest regarding the use of such patterns in multiscale DIC.

中文翻译：

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多尺度数字图像相关的分形模式

背景：数字图像相关 (DIC) 基于参考图像和变形状态图像之间的匹配，这些特征包含在测试样品表面上沉积的图案中。这些特征通常适用于单一尺度，目前缺乏能够在广泛尺度范围内提供可靠位移测量的多尺度模式。目标：在这里，我们旨在证明基于分形（自仿射）表面的图案可以为多尺度 DIC 制作合适的图案。方法：介绍了一种直接从所需的自相关函数以数字方式生成模式的方法。然后通过基于灰度级重新分布的平均强度梯度 (MIG) 改进过程对其进行增强。对两个不同的强加位移场进行了多尺度的数值实验，并将生成的模式之一的结果与随机模式和柏林噪声模式的结果进行比较。结果：所提出的模式被证明会导致 DIC 错误，与其他两个在第一个尺度中发现的错误相当，但具有更大的鲁棒性。更重要的是，这里生成的模式在规模方面表现出稳定的误差和鲁棒性，而随着规模的增加，这两个输出对于其他两个模式变得显着退化。结论：因此，基于分形表面的图案的尺度不变性也对应于 DIC 误差中的尺度不变性。这对于在多尺度 DIC 中使用此类模式非常感兴趣。