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Ying_master_thesis (1).pdf (5.59 MB)
ETD Abstract Container
Abstract Header
Shape classification via Optimal Transport and Persistent Homology
Author Info
Yin, Ying
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu155525117003685
Abstract Details
Year and Degree
2019, Master of Mathematical Sciences, Ohio State University, Mathematical Sciences.
Abstract
Quantifying similarity between shapes is an important task in many disciplines, such as architecture, anatomy, security, and manufacturing. My research project is motivated by taxonomic studies in Biology. Taxonomy is the classification of biological organisms based on shared characteristics. In this thesis, we will explore two approaches, based on optimal transport and persistent homology, to discriminating shapes through defining a meaningful distance that reflects geometric or topological features of the shapes under study. By approximating lower bounds to the Gromov-Wasserstein distance and the Gromov-Hausdorff distance, we automate the process of taxon classification by comparing geometric or topological features of anatomical surfaces. We test our implementations on a data set containing surfaces of crowns of teeth that are from primates and non-primates close relatives.
Committee
Facundo Mémoli (Advisor)
Tom Needham (Advisor)
Janet Best (Committee Member)
Pages
76 p.
Subject Headings
Mathematics
Keywords
shape analysis
;
optimal transport
;
persistent homology
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Citations
Yin, Y. (2019).
Shape classification via Optimal Transport and Persistent Homology
[Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu155525117003685
APA Style (7th edition)
Yin, Ying.
Shape classification via Optimal Transport and Persistent Homology.
2019. Ohio State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu155525117003685.
MLA Style (8th edition)
Yin, Ying. "Shape classification via Optimal Transport and Persistent Homology." Master's thesis, Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu155525117003685
Chicago Manual of Style (17th edition)
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Document number:
osu155525117003685
Download Count:
731
Copyright Info
© 2019, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.