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 − 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. 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. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of
Doctor of Philosophy. / Summer Semester, 2010. / May 3, 2010. / Extrinsic Mean, Statistics on Manifolds, Nonparametric Bootstrap, Image Analysis / Includes bibliographical references. / Victor Patrangenaru, Professor Directing Dissertation; Xiuwen Liu, University Representative; Fred W. Huffer, Committee Member; Debajyoti Sinha, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_254353 |
| Contributors | Crane, Michael (authoraut), 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) |
| Publisher | Florida State University, Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource, computer, application/pdf |
| Rights | This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them. |
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