Enhanced video motion magnification utilizing envelop shift for vision-based vibration measurements

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. Firstly, 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 an 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 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.