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MORSE THEORY APPLIED TO SURFACE TOPOLOGY SENSING
by
Vanessa D. Carson
A Thesis Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
MASTER OF ARTS
(PURE MATHEMATICS)
August 2007
Copyright 2007 Vanessa D. Carson
Object Description
| Title | Morse theory applied to surface topology sensing |
| Author | Carson, Vanessa D. |
| Author email | vdj@usc.edu |
| Degree | Master of Arts |
| Document type | Thesis |
| Degree program | Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2007-06-20 |
| Date submitted | 2007 |
| Restricted until | Unrestricted |
| Date published | 2007-07-17 |
| Advisor (committee chair) |
Jonckheere, Edmond Guralnick, Robert |
| Advisor (committee member) | Lanski, Charles |
| Abstract | Techniques in computational geometry such as Morse theory, Reeb graphs and Voronoi tessellations have been used in robotics applications to solve problems such as motion planning, sensor coverage and visualization. This paper begins by discussing the theoretical background relating to the Morse decomposition of a compact manifold and its discrete counterpart, the Reeb graph. Then, current applications of Morse theory in surface topology sensing are presented and discussed for single robot configurations. Finally, ideas for theoretical advancements in Reeb graph representations motivated by surface topology sensing in a distributed network are discussed informally. |
| Keyword | Morse; Reeb graph; sensing; topology; robotics; homology |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Type | texts |
| Legacy record ID | usctheses-m619 |
| Rights | Carson, Vanessa D. |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Carson-20070717 |
| Archival file | uscthesesreloadpub_Volume44/etd-Carson-20070717.pdf |
Description
| Title | Page 1 |
| Full text | MORSE THEORY APPLIED TO SURFACE TOPOLOGY SENSING by Vanessa D. Carson A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful llment of the Requirements for the Degree MASTER OF ARTS (PURE MATHEMATICS) August 2007 Copyright 2007 Vanessa D. Carson |
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