Phased-based motion estimation through short-distance Hilbert transform

Digital video cameras enable the collection of high -density spatial information remotely. Among these methods, the Hilbert transform enhanced phase -based motion estimation (HPME) has received greater attention due to the advantages of no surface preprocessing and insensitivity to illumination changes. HPME considers the linear relationship between motion and phase variations to estimate structural motion via Hilbert transform. However, the Hilbert transform is defined over the whole signal/spectrum of the signal and has the characteristics of global transformation. Changes in localisation are subject to the characteristics of Hilbert's global transformation. This increases the uncertainty reduce the accuracy of HPME algorithm when recognition the structural motion. To solve this issue, phase -based motion estimation through short -distance Hilbert transform (SHPME) is proposed in this paper. A novel short -distance Hilbert transform is defined, which improves the accuracy drop due to the characteristics of global transformation for Hilbert transform. The relationship between phase and motion in windowed short -distance Hilbert transform is theoretically derived. The proposed SHPME algorithm is validated using both numerical simulation and experimental testing. The results demonstrate that, compared to the original HPME algorithm, the proposed SHPME algorithm reduces the mean absolute error (MAE) and standard deviation (STD) by 72.3 % and 37.5 %, respectively. A 3.87 m wind turbine tower model is adopted and the proposed SHPME algorithm is conducted to estimate structural motion from the captured images. The frequencies and mode shapes are extracted using the SHPME and HPME for comparative analysis, demonstrating the advantage of the proposed SHPME algorithm in recognition the structural motion and modal extraction.