We propose a novel Riemannian framework for analyzing orientation distribution functions (ODFs), or their probability density functions (PDFs), in HARDI data sets for use in comparing, interpolating, averaging, and denoising PDFs. This is accomplished by separating shape and orientation features of PDFs, and then analyzing them separately under their own Riemannian metrics. We formulate the action of the rotation group on the space of PDFs, and define the shape space as the quotient space of PDFs modulo the rotations. In other words, any two PDFs are compared in: (1) shape by rotationally aligning one PDF to another, using the Fisher-Rao distance on the aligned PDFs, and (2) orientation by comparing their rotation matrices. This idea improves upon the results from using the Fisher-Rao metric in analyzing PDFs directly, a technique that is being used increasingly, and leads to geodesic interpolations that are biologically feasible. This framework leads to definitions and efficient computations for the Karcher mean that provide tools for improved interpolation and denoising. We demonstrate these ideas, using an experimental setup involving several PDFs. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester, 2011. / August 3, 2011. / Fisher-Rao, HARDI, Interpolation, ODF, Orientation, Riemannian Framework / Includes bibliographical references. / Anuj Srivastava, Professor Directing Dissertation; Eric Klassen, University Representative; Wei Wu, Committee Member; Xufeng Niu, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_183035 |
| Contributors | Ncube, Sentibaleng, 1983- (authoraut), Srivastava, Anuj (professor directing dissertation), Klassen, Eric (university representative), Wu, Wei (committee member), Niu, Xufeng (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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