Low-rank completion for motion capture data recovery: Approaches, constraints, and algorithms

Motion capture (MoCap) systems are indispensable tools across fields such as biomechanics, computer animation, human-robot interaction, and clinical gait analysis, owing to their ability to accurately record and analyze human movement in 3D space. Marker-based systems use reflective markers attached to subjects and video recordings to track human movement. The tracking requires markers to be detected in the video, which is not always possible due to occlusions, sensor failures, and limited camera coverage. These issues create gaps in recorded trajectories, compromising data integrity and making the motion difficult to utilize in practical applications. Therefore, a wide range of MoCap data completion techniques has been proposed to reconstruct missing trajectories while preserving the realism and dynamics of human movement. Human motion data exhibits a low-rank property due to the inherent repetitive nature of human movement as well as the correlations between joints and markers, enforced by the skeletal structure and biomechanical constraints. Low-rank completion techniques exploit this property to reconstruct missing marker positions. This paper reviews state-of-the-art low-rank completion methods for MoCap data completion, focusing specifically on optimization-based low-rank methods. These optimization approaches directly address the missing data completion problem through optimization formulations. We examine two main aspects: kinematic priors, which embed anatomical constraints, joint dependencies, and motion smoothness, and low-rank priors, which exploit inter-marker correlations through matrix and tensor formulations. We further evaluate optimization algorithms for solving these completion problems, such as alternating minimization, proximal algorithms, ADMM, and hybrid schemes, as well as the datasets and tools commonly used in the literature.