Robust Statistics Over Riemannian Manifolds: Applications in Computer Vision - Couverture souple

Subbarao, Raghav; Meer, Peter

 
9783843388085: Robust Statistics Over Riemannian Manifolds: Applications in Computer Vision
Couverture souple
ISBN 10 : 3843388083 ISBN 13 : 9783843388085
Editeur : LAP LAMBERT Academic Publishing, 2011

Synopsis

The nonlinear nature of many vision tasks involves analysis over nonlinear spaces embedded in higher dimensional Euclidean spaces. Such manifolds can be studied using the theory of differential geometry. Here we develop two algorithms which can be applied over manifolds. The nonlinear mean shift algorithm is a generalization of the popular mean shift, a feature space analysis method for vector spaces. Nonlinear mean shift can be applied to any Riemannian manifold and is provably convergent to the local maxima of an appropriate kernel density. This algorithm is used for motion segmentation with different motion models and for the filtering of complex image data. The projection based M-estimator is a robust regression algorithm which does not require a user supplied estimate of the level of noise corrupting the inliers. We build on the connections between kernel density estimation and M-estimators to develop data driven rules for scale estimation. The method can be generalized to handle heteroscedastic data and subspace estimation. The results of using pbM for affine motion estimation, fundamental matrix estimation and multibody factorization are presented.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

The nonlinear nature of many vision tasks involves analysis over nonlinear spaces embedded in higher dimensional Euclidean spaces. Such manifolds can be studied using the theory of differential geometry. Here we develop two algorithms which can be applied over manifolds. The nonlinear mean shift algorithm is a generalization of the popular mean shift, a feature space analysis method for vector spaces. Nonlinear mean shift can be applied to any Riemannian manifold and is provably convergent to the local maxima of an appropriate kernel density. This algorithm is used for motion segmentation with different motion models and for the filtering of complex image data. The projection based M-estimator is a robust regression algorithm which does not require a user supplied estimate of the level of noise corrupting the inliers. We build on the connections between kernel density estimation and M-estimators to develop data driven rules for scale estimation. The method can be generalized to handle heteroscedastic data and subspace estimation. The results of using pbM for affine motion estimation, fundamental matrix estimation and multibody factorization are presented.

Biographie de l'auteur

Dr.Subbarao has a B.Tech degree from the Indian Institute of Technology, Delhi in Electrical engineering and a PhD from Rutgers University in Computer Engineering. Peter Meer is currently a professor of Electrical and Computer Engineering at Rutgers University.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2011
Langue
anglais
ISBN 10 
3843388083
ISBN 13 
9783843388085
Reliure
Broché
Nombre de pages
132
Coordonnées du fabricant
non disponible
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