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Topological analysis of images

Matjaž Cerar (2015) Topological analysis of images. EngD thesis.

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    In this thesis we present an implementation of a topological approach to 2-dimensional digital images. First, we present two methods for simplifying and preparing the image, without loss of information, for further algorithms. We represent the image as a topological structure called a cubical complex. On the cubical complex, a discrete vector field encoding the directions of descent of grey scale values is constructed, together with the corresponding list of critical cells. From these, the Morse complex, which captures the vital information about the image, is built. Using Betti numbers, important features in the image are described. We present two approaches to computing Betti numbers. The thesis concludes with a presentation of how the implemented algorithms can be used for counting bright objects on specific examples of images.

    Item Type: Thesis (EngD thesis)
    Keywords: discrete Morse theory, topological data analysis, cubical complex, Morse complex, Betti number
    Number of Pages: 48
    Language of Content: Slovenian
    Mentor / Comentors:
    Name and SurnameIDFunction
    prof. dr. Neža Mramor Kosta242Mentor
    doc. dr. Žiga VirkComentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=51012&select=(ID=1536401091)
    Institution: University of Ljubljana
    Department: Faculty of Computer and Information Science
    Item ID: 3010
    Date Deposited: 08 Jul 2015 14:58
    Last Modified: 13 Aug 2015 10:07
    URI: http://eprints.fri.uni-lj.si/id/eprint/3010

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