Modelling the Statistics of Cyclic Activities by Trajectory Analysis on the Manifold of Positive-Semi-Definite Matrices

In this paper, a model is presented to extract statistical summaries to characterize the repetition of a cyclic body action, for instance a gym exercise, for the purpose of checking the compliance of the observed action to a template one and highlighting the parts of the action that are not correctly executed (if any). The proposed system relies on a Riemannian metric to compute the distance between two poses in such a way that the geometry of the manifold where the pose descriptors lie is preserved; a model to detect the begin and end of each cycle; a model to temporally align the poses of different cycles so as to accurately estimate the \emph{cross-sectional} mean and variance of poses across different cycles. The proposed model is demonstrated using gym videos taken from the Internet.