A novel marker for robust and accurate phase-based 2D motion estimation from noisy image data

Markers with high-contrast patterns are commonly used to improve the accuracy of image intensity-based motion estimation techniques. It has been proven that the phase, which can be extracted by using quadrature pair filters, is more robust to light condition changes than the intensity of the image. However, the marker design for utilizing and stabilizing the phases using phase-based motion estimation has rarely been studied, and errors from the nonlinear phase and sub-pixel motion due to the unique phase extraction process still need to be considered. Herein, we introduce a robust and accurate phase-based 2D motion estimation technique using a novel marker comprising an array of evenly spaced white squares and two complex Gabor filters. The causes of the nonlinear phase error and the sub-pixel motion error and their effects on motion estimation were established. With the novel marker design, the nonlinear phase error can be attenuated by using appropriate filter parameters while the sub-pixel motion error can be controlled by adjusting the marker orientations. The pattern of evenly spaced squares in an array also maximizes the filter response to improve the robustness of phase-based motion estimation against image noise. Experimental demonstrations of the two types of errors were carried out on a building structure by comparing the results from the proposed technique and laser Doppler velocimetry. The anti-noise performances were compared to the other markers, the Kernel-Based Optical Sensor, and the image intensity-based optical flow technique at various noise levels. The proposed technique was also applied to a real gas booster in low-light conditions with a maximum vibrating amplitude of 0.05 mm, which further demonstrated its accuracy and robustness.