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

arXiv: https://arxiv.org/abs/1908.00646 · HTML: https://mlsanity.com/paper/1908.00646/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Aug 2019.

## Built on by (most cited first, 1 of 1)

- [Automatic Estimation of Self-Reported Pain by Trajectory Analysis in the Manifold of Fixed Rank Positive Semi-Definite Matrices](https://mlsanity.com/paper/2209.01813/) (2022)

## Abstract (arXiv)

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.