In this paper, the problem of automatic dance performance evaluation from human Motion Capture (MoCap) data is addressed. A novel framework is presented, using data captured by Kinect-based human skeleton tracking, where the evaluation of user's performance is achieved against a gold-standard performance of a teacher. The framework addresses several technical challenges, including global and local temporal synchronization, spatial alignment and comparison of two “dance motion signals.” Towards the solution of these technical challenges, a set of appropriate quaternionic vector-signal processing methodologies is proposed, where the 4D (spatiotemporal) human motion data are represented as sequences of pure quaternions. Such a quaternionic representation offers several advantages, including the facts that joint angles and rotations are inherently encoded in the phase of quaternions and the three coordinates variables ( X,Y,Z) are treated jointly, with their intra-correlations being taken into account. Based on the theory of quaternions, a number of advantageous algorithms are formulated. Initially, global temporal synchronization of dance MoCap data is achieved by the use of quaternionic cross-correlations, which are invariant to rigid spatial transformations between the users. Secondly, a quaternions-based algorithm is proposed for the fast spatial alignment of dance MoCap data. Thirdly, the MoCap data can be temporally synchronized in a local fashion, using Dynamic Time Warping techniques adapted to the specific problem. Finally, a set of quaternionic correlation-based measures (scores) are proposed for evaluating and ranking the performance of a dancer. These quaternions-based scores are invariant to rigid transformations, as proved and demonstrated. A total score metric, through a weighted combination of three different metrics is proposed, where the weights are optimized using Particle Swarm Optimization (PSO). The presented experimental results using the Huawei/3DLife/EMC 2 dataset are promising and verify the effectiveness of the proposed methods.
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