Discrete Morse Theory & Persistent Homotopy
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Description
In this thesis, we present new theoretical tools in topological data analysis with applications in image analysis. We draw on a number of tools from Discrete Morse theory, presenting the relevant concepts from [7], [15] and [16] in Chapter 2. We prove an original result in Chapter 3 concerning the attaching maps of CW complex comprised of the critical cells of a discrete Morse function. We introduce the concept of a homotopy merge tree in Chapter 4 as an algebraic tool to summarise homotopical...[Show more]
Collections | Open Access Theses |
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Date published: | 2018 |
Type: | Thesis (Honours) |
URI: | http://hdl.handle.net/1885/173636 |
DOI: | 10.25911/5d9efb87e2964 |
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File | Description | Size | Format | Image |
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Kelly_Maggs.pdf | 4.4 MB | Adobe PDF |
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