Since the introduction of phase-based motion magnification (PMM) technology, PMM has been used in several studies as a preprocessing technique prior to vision-based measurement processes. It effectively reduces the uncertainty of measurement techniques that track objects. However, while PMM uses a complex steerable pyramid (CSP) to represent local motion, the fixed wavelet envelope of the CSP has drawbacks that increase uncertainty in the measurement. First, there is a discrepancy between the actual magnification shift and the designated magnification factor. As the magnified displacement deviates from the envelope, image degradation in blurring and artifacts becomes apparent. In this study, we mathematically analyze the characteristics of the CSP-like Gabor filter and propose a method to shift the envelope in a Eulerian method while maintaining the local characteristics of the CSP. Through the implementation of the proposed method, it becomes possible to mitigate image blurring and artifacts while also narrowing the gap between the actual magnification and the designated magnification factor, consequently reducing the uncertainty associated with displacement measurement. In the noisy simulation, the root mean squared error (RMSE) of the proposed method was 36.4% of the original PMM and 10.1% of the original video. Through a cantilever beam experiment, we compared displacement measurement performance at eight locations by referencing an accelerometer. The results demonstrated that the proposed method had better measurement performance than the existing PMM, regardless of the position and magnification factor.

中文翻译：

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利用包络线位移增强视频运动放大率进行基于视觉的振动测量

自从引入基于相位的运动放大 (PMM) 技术以来，PMM 已在多项研究中用作基于视觉的测量过程之前的预处理技术。它有效地降低了跟踪物体的测量技术的不确定性。然而，虽然 PMM 使用复杂的可操纵金字塔 (CSP) 来表示局部运动，但 CSP 的固定小波包络具有增加测量不确定性的缺点。首先，实际的放大倍率变化与指定的放大倍数之间存在差异。当放大的位移偏离包络线时，模糊和伪像的图像质量下降变得明显。在本研究中，我们对类 CSP Gabor 滤波器的特性进行了数学分析，并提出了一种在保持 CSP 局部特​​性的同时以欧拉方法移动包络的方法。通过实施所提出的方法，可以减轻图像模糊和伪影，同时缩小实际放大倍率和指定放大倍数之间的差距，从而减少与位移测量相关的不确定性。在噪声模拟中，该方法的均方根误差（RMSE）为原始PMM的36.4%和原始视频的10.1%。通过悬臂梁实验，我们参考加速度计比较了八个位置的位移测量性能。结果表明，无论位置和放大系数如何，所提出的方法都比现有 PMM 具有更好的测量性能。