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

Authors: Benjamin Szczapa, Mohamed Daoudi, Stefano Berretti, Alberto Del Bimbo, Pietro Pala, Estelle Massart

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. Compared to previous work, the
manifold of fixed-rank positive-semidefinite matrices is 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 UAVGesture). The results of the proposed approach are competitive
with respect to state-of-the-art methods, while only involving body skeletons.

Preprint available from arxiv: [Preprint]

Errata from the published version:
- Missing square root in the expression of the distance, in the Theorem on p.4 (and associated proof, in the Appendix).
- Misleading notation: the distance \delta in eq. 2 is equal to the distance d in the Thm. on p. 4