Abstract

Here we provide a method for comparing geometric objects. Two objects of interest are embedded into an infinite dimensional Hilbert space using their Laplacian eigenvalues and eigenfunctions, truncated to a finite dimensional Euclidean space, where correspondences between the objects are searched for and voted on. To simplify correspondence finding, we propose using several geometric invariants to reduce the necessary computations. This method improves on voting methods by identifying isometric regions including shapes of genus greater than 0 and dimension greater than 3, as well as almost retaining isometry.

Advisor

Ke Zhu

Committee Member

Wook Kim

Committee Member

Brandon Rowekamp

Date of Degree

2020

Language

english

Document Type

Thesis

Degree

Master of Arts (MA)

Department

Mathematics and Statistics

College

Science, Engineering and Technology

Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License

Rights Statements

http://rightsstatements.org/vocab/InC/1.0/

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