Quantification of phase-based magnified motion using image enhancement and optical flow techniques

Phase-based motion magnification (PMM) has been widely implemented in the field of vibration and structural health monitoring for its non-invasive nature to reveal hidden system dynamics. The approach has shown success in magnifying subtle structural oscillatory motions for system identification and observation of operating shapes. Although this method has been implemented and is becoming increasingly popular, the amount of physical motion associated with the degree of magnification has yet to be quantified. Within this work, a synthetic simulation containing an oscillating geometry is presented to quantify its magnified pixel displacement. Computer vision techniques including centroid detection and edge-feature tracking via optical flow are adopted to quantify the relation between amplification and true motion. The quantification techniques are also tested and verified on an experimental structure with the use of a high-speed optical sensing system. Motion artifacts distort the integrity of the magnified motion, which can pose problems for accurate quantification. Image enhancement techniques such as the two-dimensional Wiener filter and Total Variation Denoising (TVD) are used to smooth the high-frequency content that is observed following magnification. Associative error concerning a discrete shift of the Gabor wavelet is analytically derived to show the justification of spatial aliasing. An adjusted bound on magnification is presented to display the limitations of the technique, while providing insight into associated error. The results of this work will help to enhance PMM from a qualitative evaluation tool to a quantitative measurement tool of magnified displacements.