Two-dimensional motion estimation using phase-based image processing with Riesz transform

As a kind of photogrammetry technique, phase-based motion estimation (PME) has proven to be a powerful image/video processing algorithm in the extraction of structural dynamics, due to its full-filed resolution and no requirement of surface preparation, compared to conventional structural testing. Although images and videos employed in PME are two-dimensional arrays, PME only extracts phase information in a single direction at a time. Therefore, extracting two -directional motions at the same time is needed to avoid two times of PME implementation. To address this issue, Riesz-transform is integrated to the phase-based motion estimation algorithm, and Riesz transform PME (RPME) is proposed in this work. The concept of plane phase is extended to spatial phase using Riesz transform to process images, because Riesz transform is able to extract phase information in two directions simultaneously. Then quaternion is utilized to derive the theoretical relationship between spatial phase and structure motions. In order to obtain the mono -component image sequence required in Riesz transform, an ideal narrow bandpass filter is con-structed based on the set of Butterworth low-pass filters. Due to the capability of recognizing two -directional motions simultaneously using the proposed RPME, a much-improved efficiency of structural dynamics identification is observed. In addition, Riesz transform extracts instantaneous phase, thus the motion recognition accuracy is improved as well. To validate the benefit of RPME, both numerical simulation and laboratory-scale experiments are conducted, and motions in x and y directions are extracted simultaneously, with a drastically increased accuracy in both the simulation and experimental validations.