The optimal scale level of complex steerable pyramid for phase-based motion estimation under different motion ranges and target sizes

• The scale level of the complex steerable pyramid (CSP) is found to significantly affect the measurement performance of phase-based motion estimation. Furthermore, there exists an optimal CSP scale level for the displacement estimation of a certain motion video, and the reason for its existence is also explained. • The optimal scale level of CSP is found to be positively correlated with the motion region, interpreted as the motion range and target size in motion video. Based on the relationships, a 2D contour map of the optimal scale level in relation to motion range ratio and target size ratio is proposed. • A new measurement strategy is proposed to optimize the measurement performance of phase-based method based on the inherent properties of the motion video (target size and motion range) without the need for ground-truth motion. In recent years, the phase-based motion estimation method has received significant attention in the field of vision-based motion estimation due to its robustness under illumination variation and high subpixel accuracy. The complex steerable pyramid (CSP) is widely adopted to generate phase of frames for motion estimation. The scale level of CSP is a significant influential parameter that affects the displacement measurement performance. However, systematic study regarding the optimal scale level of CSP in relation to motion video’s properties (motion range and target size) has not been carried out. Understanding this relationship could be helpful to identify the optimal scale level based on these properties, rather than simply comparing measurement results with the ground truth. In our work, a series of numerical motion videos with different properties are employed to find the optimal scale levels of CSP for motion estimation. Based on the phase-based motion estimation results, we found that the optimal scale level has clearly positive relationships with both the motion range and target size of motion video. Leveraging these relationships, a measurement strategy is proposed to automatically select the optimal scale level without the need to know ground truth of motion. The proposed strategy is further verified through a series of laboratory experiments, including shaker tests on a column and impact tests on a four-floor frame structure, using phased-based method alongside conventional sensors such as laser displacement sensor and accelerometers.