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Shape classification via Optimal Transport and Persistent Homology

Abstract Details

2019, Master of Mathematical Sciences, Ohio State University, Mathematical Sciences.
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.
Facundo Mémoli (Advisor)
Tom Needham (Advisor)
Janet Best (Committee Member)
76 p.

Recommended Citations

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)