TY - GEN
T1 - Statistical analysis on stiefel and grassmann manifolds with applications in computer vision
AU - Turaga, Pavan
AU - Veeraraghavan, Ashok
AU - Chellappa, Rama
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008
Y1 - 2008
N2 - Many applications in computer vision and pattern recognition involve drawing inferences on certain manifold-valued 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 parametric and non-parametric density estimators on these manifolds. These methods are then used to learn class conditional densities for applications such as activity recognition, video based face recognition and shape classification.
AB - Many applications in computer vision and pattern recognition involve drawing inferences on certain manifold-valued 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 parametric and non-parametric density estimators on these manifolds. These methods are then used to learn class conditional densities for applications such as activity recognition, video based face recognition and shape classification.
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U2 - 10.1109/CVPR.2008.4587733
DO - 10.1109/CVPR.2008.4587733
M3 - Conference contribution
AN - SCOPUS:51949097477
SN - 9781424422432
T3 - 26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR
BT - 26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR
T2 - 26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR
Y2 - 23 June 2008 through 28 June 2008
ER -