  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.
