A Riemannian Framework for Annotated Curves Analysis

• Other Authors: Liu, Wei, 1979 March 11- (authoraut)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Statistics
• Online Access: http://purl.flvc.org/fsu/fd/FSU_migr_etd-4997

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. === 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 15, 2011. === Annotated curve, Riemannian, Shape analysis === Includes bibliographical references. === Anuj Srivastava, Professor Directing Dissertation; Jinfeng Zhang, Professor Co-Directing Dissertation; Eric P. Klassen, University Representative; Fred Huffer, Committee Member.