Distribution-Aware Fractional Anisotropic Filtering for Vibration Displacement Field Measurement

Vibration displacement field measurement aims to measure the displacement of each point in the visual field simultaneously. Recently developed phase-based vibration measurement methods extract phase features from video to represent vibration using complex steerable pyramid (CSP) decomposition. The phase-based method neglects to analyze decomposition errors against vibration feature, which may result in multiple peaks disturbance for large vibration and noisy disturbance for small vibration. We proposed a distribution-aware fractional anisotropic filtering (DFAF) method, which focuses on modeling the distribution of vibration features to effectively reduce decomposition errors. First, to accurately extract large vibration, fractional anisotropy estimation based on the anisotropy distribution in multiple peaks of vibration displacement is applied to detect large and small vibration points. The frame interval selection filter is designed to reduce multiple peaks disturbance, enabling accurate measurement of large vibration. Then, to accurately extract small vibration, fractional anisotropy (FA) estimation based on the anisotropy distribution in multiple vibration orientations to detect noise and small vibration points. The fractional anisotropic filter is developed to inhibit the effect of noisy points, enabling accurate measurement of small vibration. Finally, the displacement field is smoothed by considering the similarity of neighboring points, which helps reduce the effect of noise for full-field measurement. To verify the performance of the DFAF method, we conducted extensive experiments on two exciter-based datasets and two real engine videos, each containing large and small vibrations. Results demonstrate that the DFAF method significantly outperforms state-of-the-art methods, exhibiting minimum error, the most stable performance and enhanced robustness across different vibration displacement and noise levels.