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

TL;DR

This paper introduces a Riemannian geometry-based model for analyzing cyclic body actions, enabling assessment of execution quality and consistency across repetitions, demonstrated on gym videos.

Contribution

It presents a novel approach using manifold geometry to model and analyze cyclic activities, improving accuracy in pose comparison and cycle segmentation.

Findings

Effective in detecting cycle boundaries and alignment.

Accurately estimates mean and variance of poses.

Demonstrated on real-world gym videos.

Abstract

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.