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Nonparametric Estimation of Three Dimensional Projective Shapes with Applications in Medical Imaging and in Pattern Recognition

Title: Nonparametric Estimation of Three Dimensional Projective Shapes with Applications in Medical Imaging and in Pattern Recognition.
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Name(s): Crane, Michael, author
Patrangenaru, Victor, professor directing dissertation
Liu, Xiuwen, university representative
Huffer, Fred W., committee member
Sinha, Debajyoti, committee member
Department of Statistics, degree granting department
Florida State University, degree granting institution
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2010
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: This dissertation is on analysis of invariants of a 3D configuration from its 2D images in pictures of this configuration, without requiring any restriction on the camera positioning relative to the scene pictured. We briefly review some of the main results found in the literature. The methodology used is nonparametric, manifold based combined with standard computer vision re- construction techniques. More specifically, we use asymptotic results for the extrinsic sample mean and the extrinsic sample covariance to construct boot- strap confidence regions for mean projective shapes of 3D configurations. Chapters 4, 5 and 6 contain new results. In chapter 4, we develop tests for coplanarity. In chapter 5, is on reconstruction of 3D polyhedral scenes, including texture from arbitrary partial views. In chapter 6, we develop a nonparametric methodology for estimating the mean change for matched samples on a Lie group. We then notice that for k '' 4, a manifold of projective shapes of k-ads in general position in 3D has a structure of 3k and #8722; 15 dimensional Lie group (P-Quaternions) that is equivariantly embedded in an Euclidean space, therefore testing for mean 3D projective shape change amounts to a one sample test for extrinsic mean PQuaternion Objects. The Lie group technique leads to a large sample and nonparametric bootstrap test for one population extrinsic mean on a projective shape space, as recently developed by Patrangenaru, Liu and Sughatadasa [1]. On the other hand, in absence of occlusions, the 3D projective shape of a spatial configuration can be recovered from a stereo pair of images, thus allowing to test for mean glaucomatous 3D projective shape change detection from standard stereo pairs of eye images.
Identifier: FSU_migr_etd-7118 (IID)
Submitted Note: A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Summer Semester, 2010.
Date of Defense: May 3, 2010.
Bibliography Note: Includes bibliographical references.
Advisory Committee: Victor Patrangenaru, Professor Directing Dissertation; Xiuwen Liu, University Representative; Fred W. Huffer, Committee Member; Debajyoti Sinha, Committee Member.
Subject(s): Statistics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_migr_etd-7118
Owner Institution: FSU

Choose the citation style.
Crane, M. (2010). Nonparametric Estimation of Three Dimensional Projective Shapes with Applications in Medical Imaging and in Pattern Recognition. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_etd-7118