Vibration Measurement with Video Processing based on Alternating Optimization of Frequency and Phase Shifts

Vision-based measurement methods have attracted growing interests over the past years because of their non-contact sensing capability for acquiring the full-field vibrations of structure. Existing vision-based measurement techniques, such as point tracking (PT) and digital image correlation (DIC), require preparation for the surface with high-contrast markers or speckle patterns before measurement. The phase-based motion magnification, enabling to extract the vibration of the structure without surface pre-processing, is a newly developed vision-based measurement method. However, it suffers from the problems such as phase noise, phase instability, and phase unwrapping. In this paper, a novel iterative algorithm called alternating optimization of frequency and phase shifts (AOFPS) is developed to measure the vibration signals from the video instead of explicitly manipulating the phase. The method of Tikhonov regularization for estimating pixel-to-pixel sinusoid patterns and the approach of the least squares for extracting frame-to-frame random phase shifts are alternately implemented to track the motion of the object. This algorithm provides robust and accurate vibration measurements without expensive computation. Simulated and laboratory experiments analyses illustrate the effectiveness and accuracy of the proposed algorithm.