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

Ettore Maria Celozzi (1) , Luca Ciabini (1) , Luca Cultrera (1) , Pietro Pala (1) , Stefano Berretti (1) , Mohamed Daoudi (2) , Alberto Del Bimbo (1)

1 UniFI - Università degli Studi di Firenze = University of Florence = Université de Florence
2 IMT Lille Douai - Ecole nationale supérieure Mines-Télécom Lille Douai

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 cross-sectional mean and variance of poses across different cycles. The proposed model is demonstrated using gym videos taken from the Internet.

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]

Ettore Maria Celozzi, Luca Ciabini, Luca Cultrera, Pietro Pala, Stefano Berretti, et al.. Modelling the Statistics of Cyclic Activities by Trajectory Analysis on the Manifold of Positive-Semi-Definite Matrices. 15th IEEE International Conference on Automatic Face and Gesture Recognition, Nov 2020, Buenos Aires, Argentina. ⟨hal-02863164⟩