# Fitting, Comparison, and Alignment of Trajectories on Positive Semi-Definite Matrices with Application to Action Recognition

## TL;DR

This paper introduces a novel approach for action recognition using trajectories on the manifold of positive semi-definite matrices, employing new metrics and algorithms, and demonstrates competitive results on multiple datasets.

## Contribution

The work proposes a new metric and algorithms for curve fitting and alignment on the manifold of fixed-rank positive semi-definite matrices for action recognition.

## Key findings

- Competitive accuracy on UTKinect-Action3D, KTH-Action, and UAV-Gesture datasets.
- Method relies solely on body skeleton data, avoiding complex feature extraction.
- Outperforms or matches state-of-the-art methods in action recognition tasks.

## Abstract

In this paper, we tackle the problem of action recognition using body skeletons extracted from video sequences. Our approach lies in the continuity of recent works representing video frames by Gramian matrices that describe a trajectory on the Riemannian manifold of positive-semidefinite matrices of fixed rank. In comparison with previous works, the manifold of fixed-rank positive-semidefinite matrices is here endowed with a different metric, and we resort to different algorithms for the curve fitting and temporal alignment steps. We evaluated our approach on three publicly available datasets (UTKinect-Action3D, KTH-Action and UAV-Gesture). The results of the proposed approach are competitive with respect to state-of-the-art methods, while only involving body skeletons.