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.

具有高对比度图案的标记通常用于提高基于图像强度的运动估计技术的准确性。已经证明，可以通过使用正交对滤波器提取的相位比图像强度对光照条件变化更稳健。然而，很少研究使用基于相位的运动估计来利用和稳定相位的标记设计，并且由于独特的相位提取过程而导致的非线性相位和亚像素运动的误差仍然需要考虑。在此，我们介绍了一种稳健且准确的基于相位的 2D 运动估计技术，该技术使用一种新颖的标记，该标记包括一组均匀间隔的白色方块和两个复杂的 Gabor 滤波器。建立了非线性相位误差和亚像素运动误差的成因及其对运动估计的影响。通过新颖的标记设计，可以通过使用适当的滤波器参数来衰减非线性相位误差，同时可以通过调整标记方向来控制亚像素运动误差。阵列中均匀间隔的正方形图案还可以最大化滤波器响应，以提高基于相位的运动估计对图像噪声的鲁棒性。通过比较所提出的技术和激光多普勒测速仪的结果，在建筑结构上对两种类型的误差进行了实验演示。在各种噪声水平下，将抗噪声性能与其他标记、基于内核的光学传感器和基于图像强度的光流技术进行了比较。