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Framework for Comparing Shape Distributions

Title: A Framework for Comparing Shape Distributions.
Name(s): Henning, Wade, author
Srivastava, Anuj, 1968-, professor directing dissertation
Alamo, Rufina G., university representative
Huffer, Fred W. (Fred William), committee member
Wu, Wei, committee member
Florida State University, degree granting institution
College of Arts and Sciences, degree granting college
Department of Statistics, degree granting department
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2014
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource (109 pages)
Language(s): English
Abstract/Description: The problem of comparisons of shape populations is present in many branches of science, including nano-manufacturing, medical imaging, particle analysis, fisheries, seed science, and computer vision. Researchers in these fields have traditionally characterized the profiles in these sets using combinations of scalar valued descriptor features, like aspect ratio or roughness, whose distributions are easy to compare using classical statistics. However, there is a desire in this community for a single comprehensive feature that uniquely defines these profiles. The shape of the profile itself is such a feature. Shape features have traditionally been studied as individuals, and comparing distributions underlying sets of shapes is challenging. Since the data comes in the form of samples from shape populations, we use kernel methods to estimate underlying shape densities. We then take a metric approach to define a proper distance, termed the Fisher-Rao distance, to quantify differences between any two densities. This distance can be used for clustering, classification and other types of statistical modeling; however, this dissertation focuses on comparing shape populations as a classical two-sample hypothesis test with populations characterized by respective probability densities on shape space. Since we are interested in the shapes of planar closed curves and the space of such curves is infinite dimensional, there are some theoretical issues in defining and estimating densities on this space. We therefore use a spherical multidimensional scaling algorithm to project shape distributions to the unit two-sphere, and this allows us to use a von Mises-Fisher kernel for density estimation. The estimated densities are then compared using the Fisher-Rao distance, which, in turn, is estimated using Monte Carlo methods. This distance estimate is used as a test statistic for the two-sample hypothesis test mentioned above. We use a bootstrap approach to perform the test and to evaluate population classification performance. We demonstrate these ideas using applications from industrial and chemical engineering.
Identifier: FSU_migr_etd-9185 (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, 2014.
Date of Defense: July 21, 2014.
Keywords: bootstrap hypothesis testing, elastic shape analysis, Fisher-Rao distance estimation, kernel density estimation, synthetic polymer shape analysis, von Mises-Fisher density estimation
Bibliography Note: Includes bibliographical references.
Advisory Committee: Anuj Srivastava, Professor Directing Dissertation; Rufina Alamo, University Representative; Fred Huffer, Committee Member; Wei Wu, Committee Member.
Subject(s): Statistics
Chemical engineering
Electrical engineering
Persistent Link to This Record:
Owner Institution: FSU

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Henning, W. (2014). A Framework for Comparing Shape Distributions. Retrieved from