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How many points are needed to determine a geometric surface?

Miha Polanc (2016) How many points are needed to determine a geometric surface?. EngD thesis.

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    A geometric surface can be approximately described using a finite point-sample. The main question of this thesis is the following: how many points, depending on the sampling model and surface genus, are needed to confidently reconstruct the original geometric surface. First we present different sampling models of surface points — the uniform and the random sample. We use topological methods, in particular persistent homology, to process our data. Using Javaplex software package we construct a filtration with Vietoris-Rips simplicial complexes and consider the bar-code diagram of its Betti numbers. Finally we present our computational results for both the sphere and the geometric torus with respect to the two sampling models , and several options for further improvements.

    Item Type: Thesis (EngD thesis)
    Keywords: Vietoris-Rips complex, Betti numbers, Javaplex, persistent homology, sphere, torus.
    Number of Pages: 40
    Language of Content: Slovenian
    Mentor / Comentors:
    Name and SurnameIDFunction
    Izr. prof. dr. Gašper Fijavž246Mentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=51012&select=(ID=1537149123)
    Institution: University of Ljubljana
    Department: Faculty of Computer and Information Science
    Item ID: 3565
    Date Deposited: 12 Sep 2016 14:12
    Last Modified: 28 Sep 2016 13:23
    URI: http://eprints.fri.uni-lj.si/id/eprint/3565

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