Dissertation/Thesis Abstract

A Riemannian framework for annotated curves analysis
by Liu, Wei, Ph.D., The Florida State University, 2011, 89; 3502862
Abstract (Summary)

We propose a Riemannian framework for shape analysis of annotated curves, curves that have certain attributes defined along them, in addition to their geometries.These attributes may be in form of vector-valued functions, discrete landmarks, or symbolic labels, and provide auxiliary information along the curves. The resulting shape analysis, that is comparing, matching, and deforming, is naturally influenced by the auxiliary functions. Our idea is to construct curves in higher dimensions using both geometric and auxiliary coordinates, and analyze shapes of these curves. The difficulty comes from the need for removing different groups from different components: the shape is invariant to rigid-motion, global scale and re-parameterization while the auxiliary component is usually invariant only to the re-parameterization. Thus, the removal of some transformations (rigid motion and global scale) is restricted only to the geometric coordinates, while the re-parameterization group is removed for all coordinates. We demonstrate this framework using a number of experiments.

Indexing (document details)
Advisor: Srivastava, Anuj, Zhang, Jinfeng
Commitee: Huffer, Fred, Klassen, Eric
School: The Florida State University
Department: Statistics
School Location: United States -- Florida
Source: DAI-B 73/08(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Statistics, Computer science
Keywords: Annotated curves, Auxiliary functions, Riemannian framework, Shapes
Publication Number: 3502862
ISBN: 9781267262356
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