Statistical analysis on Stiefel and Grassmann manifolds with applications in computer vision

Many applications in computer vision and pattern recognition involve drawing inferences on certain manifoldvalued parameters. In order to develop accurate inference algorithms on these manifolds we need to a) understand the geometric structure of these manifolds b) derive appropriate distance measures and c) develop probability distribution functions (pdf) and estimation techniques that are consistent with the geometric structure of these manifolds. In this paper, we consider two related manifolds - the Stiefel manifold and the Grassmann manifold, which arise naturally in several vision applications such as spatio-temporal modeling, affine invariant shape analysis, image matching and learning theory. We show how accurate statistical characterization that reflects the geometry of these manifolds allows us to design efficient algorithms that compare favorably to the state of the art in these very different applications. In particular, we describe appropriate distance measures and parame...

• Type: Conference
• Year: 2008
• Where: CVPR
• Authors: Pavan K. Turaga, Ashok Veeraraghavan, Rama Chellappa
• Keywords: Accurate Inference Algorithms, Affine Invariant Shape, Appropriate Distance Measures, Computer Vision, CVPR 2008, Derive Appropriate Distance, Related Manifolds