## 4 Discussion and Conclusions  
The deviations of the structural idealized edge profile contain important variations that reflect structural vibration characteristics. Low-level variations along the idealized edge profile are difficult to acquire using the traditional motion extraction method. In this study, an acceleration video magnification algorithm was introduced to magnify low-level edge profile variations in a high-speed video file. The magnified low-level variations were extracted efficiently with an SVD-based motion extraction approach.  
The theoretical subsection presented a saw blade experiment to illustrate the deviation extraction process. A simple vignetting black circle simulation test was given to show the influence of motion magnification. Two experiments were conducted in the experimental subsection. Low-level vibrations of a light-weight cantilever beam and a noise barrier were magnified using video magnification. The deviations of the magnified idealized straight-line edge profiles were reconstructed into analysis matrices. Final vibration signals were calculated with the following SVD-based extraction algorithm. From the waveforms and their spectra, low-level high-frequency vibration signals were successfully enhanced in the magnified videos. Vibration characteristics of the test beam and the noise barrier were analyzed using signals obtained by the proposed method.  
In contrast to linear phase-based magnification, the acceleration phase-based motion magnification handled only small acceleration vibrations and was more robust to large translational motions; hence, this approach is not sensitive to large motions, such as camera or object motions. However, a large magnification factor will inevitably bring motion blurs to the magnified video and influence the deviation extraction results. Given that the proposed method works on pixel intensities, sudden illumination variations in the video may lead to unclear edge profiles and pollute the deviation of the selected edge profiles. In contrast to optical flow or image registration motion extraction algorithms, which calculate the true displacement value, signals extracted using the SVD-based method only reflect the tendency of the structure's vibration. Nevertheless, these signals remain acceptable and have a high cross-correlation relationship with true vibrations. Our future work will focus on improving the tolerance of illumination and optimizing the motion blurs under a high magnification factor.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Model A** & **Model B** & **Model C** \\ \hline
**Proposed Method** (Hz) & 10.12 & 21.07 & 45.77 \\
**Laplacian Kernel** (\(\sigma\)) & - & 1.95 & 0.90 \\
**Amplification Factor** (\(\alpha\)) & - & 6 & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Identified modal frequencies and analysis parameters in the noise barrier experiment.  
**Author Contributions:** [PERSON], [PERSON], and [PERSON] conceived of and designed the field survey; [PERSON], [PERSON], [PERSON], and [PERSON] carried out the experiments; [PERSON] and [PERSON] processed and analyzed the simulation test and experiment data; [PERSON] and [PERSON] contributed to the methodology and reviewed the submitted manuscript.  
**Funding:** This project was funded by the National Natural Science Foundation of China (No. 51805006 and No. 11802003).  
**Acknowledgments:** The authors would like to thank the anonymous reviewers for their valuable comments and suggestions.  
**Conflicts of Interest:** The authors declare no conflict of interest.