Gauge invariant framework for trajectories analysis

Hassen Drira, Barbara Tumpach and Mohamed Daoudi

Abstract

Analysis of trajectories are very important in many areas, e.g. medical imaging, computer vision etc. In this paper, we have provided a gauge invariant framework for comparing trajectories while being invariant to time-warping. Specifically, we have defined a proper Riemannian metric directly on the quotient (shape) space, rather than inheriting it from pre-shape space. We have used it to formulate a path energy that measures only the normal components of velocities along the path. The geodesic computation is based on a path-straightening technique that iteratively corrects paths between curves until geodesics are achieved. Both theoretical proofs and experimental results on trajectories from human action are provided to validate this framework.

Session

Workshop: 1st International Workshop on DIFFerential Geometry in Computer Vision for Analysis of Shapes, Images and Trajectories (DIFF-CV)

Files

Paper (PDF, 1093K)

DOI

10.5244/C.29.DIFFCV.6
https://dx.doi.org/10.5244/C.29.DIFFCV.6

Citation

Bibtex

@inproceedings{DIFFCV2015_6,
	title={Gauge invariant framework for trajectories analysis},
	author={Hassen Drira and Barbara Tumpach and Mohamed Daoudi},
	year={2015},
	month={September},
	pages={6.1-6.11},
	articleno={6},
	numpages={11},
	booktitle={Proceedings of the 1st International Workshop on DIFFerential Geometry in Computer Vision for Analysis of Shapes, Images and Trajectories (DIFF-CV 2015)},
	publisher={BMVA Press},
	editor={H. Drira, S. Kurtek, and P. Turaga},
	doi={10.5244/C.29.DIFFCV.6},
	isbn={1-901725-56-1},
	url={https://dx.doi.org/10.5244/C.29.DIFFCV.6}
}