Algorithm and Marker Development for 6D Motion Measurement Using a Single Camera

Abstract

This study developed a novel composite marker system and an associated six-dimensional (6D) motion measurement algorithm for complex motions using a single camera. The composite marker, consisting of three spherical markers arranged in an equilateral triangle, provided a stable reference to achieve sub-pixel accuracy in motion measurement. The proposed three-dimensional (3D) measurement algorithm enabled the determination of the 3D coordinates of the composite marker from a single image, thereby reducing the complexity and cost compared to traditional multi-camera systems. This study also introduced an automated intensity distribution fitting method to precisely determine the visual center of each marker, enabling accurate evaluation of the deviation between the optical and physical centers for each individual marker within the composite marker. These measurements support accurate camera extrinsic calibration based on the markers. The proposed method achieved a static resolution between 0.05 and 0.2 mm, depending on the direction of movement, with further improvements possible through low-pass filtering. Motion measurement involved both circular trajectory tracking and complex 6D motion measurement of the composite marker. The circular trajectory motion included depth changes relative to the camera, with deviation in the circular trajectory of less than 0.23 mm. For complex 6D motion, the positional accuracy deviation was less than 1.5 mm, and the estimated normal vector compared to the actual normal vector had an offset of 4°. Experimental results confirmed the effectiveness of the method for capturing 6D motion, showing reliable performance in tracking both depth and tangential movements.