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Robust statistics over Riemannian manifolds for computer vision
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Robust statistics over Riemannian manifolds for computer vision
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Subbarao
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Raghav
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Raghav Subbarao
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Peter
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Advisory Committee
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Peter Meer
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Dana
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Kristin
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Kristin Dana
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Orfanidis
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Sophocles
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Advisory Committee
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Sophocles Orfanidis
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Wade
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Advisory Committee
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Wade Trappe
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Genc
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Yakup
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Advisory Committee
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Yakup Genc
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Rutgers University
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Graduate School - New Brunswick
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theses
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2008
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2008-05
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English
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electronic
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xiv, 146 pages
Abstract
The nonlinear nature of many compute vision tasks involves analysis over curved nonlinear spaces embedded in higher dimensional Euclidean spaces. Such spaces are known as manifolds and can be studied using the theory of differential geometry. In this thesis we develop two algorithms which can be applied over manifolds.
The nonlinear mean shift algorithm is a generalization of the original mean shift, a popular 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 scale, the level of noise corrupting the inliers. We build on the connections between kernel density estimation and robust M-estimators and 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.
A new sensor fusion method which can handle heteroscedastic data and incomplete estimates of parameters is also discussed. The method is used to combine image based pose estimates with inertial sensors.
The nonlinear mean shift algorithm is a generalization of the original mean shift, a popular 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 scale, the level of noise corrupting the inliers. We build on the connections between kernel density estimation and robust M-estimators and 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.
A new sensor fusion method which can handle heteroscedastic data and incomplete estimates of parameters is also discussed. The method is used to combine image based pose estimates with inertial sensors.
Note
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Ph.D.
Note
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Includes bibliographical references (p. 137-144).
Subject
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Topic
Electrical and Computer Engineering
Subject
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Topic
Robust statistics
Subject
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Topic
Riemannian manifolds
Subject
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Topic
Computer vision
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Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.17398
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ETD_764
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doi:10.7282/T3736R88
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ETD doctoral
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Copyright protected
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Open
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Name
Raghav Subbarao
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Affiliation
Rutgers University. Graduate School - New Brunswick
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Non-exclusive ETD license
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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