Topološka obdelava slik
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.
2015
2015-07-10 14:10:01
1060
diskretna Morsova teorija, topološka analiza podatkov, kubični kompleks, Morsov kompleks, Bettijeva števila
discrete Morse theory, topological data analysis, cubical complex, Morse complex, Betti number
m5
MATJAŽ
CERAR
70
Nežka
Mramor Kosta
991
Žiga
Virk
994
VisID
16
15681
Cerar Matjaž - Topološka obdelava slik.pdf
1029153
Predstavitvena datoteka
2015-07-10 14:10:01