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Novel Riemannian Metric for Analyzing Spherical Functions with Applications to HARDI Data

Title: A Novel Riemannian Metric for Analyzing Spherical Functions with Applications to HARDI Data.
Name(s): Ncube, Sentibaleng, 1983-, author
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
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2011
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: 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.
Identifier: FSU_migr_etd-5064 (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: Fall Semester, 2011.
Date of Defense: August 3, 2011.
Keywords: Fisher-Rao, HARDI, Interpolation, ODF, Orientation, Riemannian Framework
Bibliography Note: Includes bibliographical references.
Advisory Committee: Anuj Srivastava, Professor Directing Dissertation; Eric Klassen, University Representative; Wei Wu, Committee Member; Xufeng Niu, Committee Member.
Subject(s): Statistics
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Owner Institution: FSU

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Ncube, S. (2011). A Novel Riemannian Metric for Analyzing Spherical Functions with Applications to HARDI Data. Retrieved from