Infotech Oulu Graduate School

Riemannian geometry and covariance descriptors

Lecturer: Dr. Mikko Salo, Department of Mathematics and Statistics, University of Helsinki

Date, Time & Room

Monday, April 20, 2009, 12 - 14, FY1120
Tuesday, April 21, 12 - 14, FY1120
Wednesday, April 22, 12 - 14, GO102

Covariance matrices are basic objects in statistical methods in computer vision, and recently they have attracted attention as descriptors in recognition and classification. The set of covariance matrices, equipped with a natural distance function, is an example of a Riemannian manifold. Riemannian manifolds are curved spaces having special geometric structure. The mathematical theory of Riemannian manifolds can be used to develop and analyze computational methods involving covariance matrices and other similar quantities.

In this minicourse we will discuss Riemannian manifolds and their basic properties. The presentation is intended to be accessible to engineers. We will also consider certain recent applications of the theory to pattern recognition and computer vision.

Literature:

• W. M. Boothby, An introduction to differentiable manifolds and Riemannian geometry. Academic Press, revised 2nd edition, Amsterdam 2003.
• J. M. Lee, Riemannian manifolds: an introduction to curvature. Springer-Verlag, New York 1997.
• X. Pennec, P. Fillard, and N. Ayache, A Riemannian framework for tensor computing. Int. Journal of Computer Vision 66 (2006), no. 1, p. 41-66.
• O. Tuzel, F. Porikli, and P. Meer, Human detection via classification on Riemannian manifolds. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR 2007), p. 1-8.

More information: Janne Heikkilä