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.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_182980 |
| Contributors | Liu, Wei, 1979 March 11- (authoraut), Srivastava, Anuj (professor directing dissertation), Zhang, Jinfeng (professor co-directing dissertation), Klassen, Eric P. (university representative), Huffer, Fred (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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