On the preservation of coarse properties over products and on persistence curves
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- Austin Lawson (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
- Advisor
- Gregory Bell
Abstract: We explore two facets of topology, coarse and computational, that share a similar philosophy: “The perceived shape of a space depends on the scale at which that space is viewed”. In coarse topology, we analyze the preservation of properties of coarse spaces over direct products. We define a free product of a coarse space and prove these properties are preserved under this operation. On the computational side, we present a new class of topological descriptors called Persistence Curves. We prove the stability of these descriptors, we show that they generalize another popular descriptor called Persistence Landscapes, and finally we use these persistence curves to perform texture classification with great results on four popular texture databases: Outex, UIUCTex, KTH-TIPS, and FMD.
On the preservation of coarse properties over products and on persistence curves
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Created on 5/1/2019
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Additional Information
- Publication
- Dissertation
- Language: English
- Date: 2019
- Keywords
- Coarse, Data, Homology, Persistent, Texture, Topology
- Subjects
- Topology
- Homology theory
- Materials $x Texture