Exact Principal Geodesic Analysis for Data on SO(3)

Salem Said (1) , Nicolas Courty (2) , Nicolas Le Bihan (1) , Stephen J. Sangwine (3)

1 GIPSA-SIGMAPHY - GIPSA - Signal Images Physique
2 VALORIA - Laboratoire de Recherche en Informatique et ses Applications de Vannes et Lorient
3 departement of Electronic Systems and Engineering

PGA, or Principal Geodesic Analysis, is an extension of the classical PCA (Principal Component Analysis) to the case of data taking values on a Riemannian manifold. In this paper a new and original algorithm, for the exact computation of the PGA of data on the rotation group SO(3), is presented. Some properties of this algorithm are illustrated, with tests on simulated and real data, and its possible applications are finally discussed.

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]

Salem Said, Nicolas Courty, Nicolas Le Bihan, Stephen J. Sangwine. Exact Principal Geodesic Analysis for Data on SO(3). EUSIPCO 2007 - 15th European Signal Processing Conference, Sep 2007, Poznan, Poland. pp.1700-1705. ⟨hal-00494170⟩