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Structures in Spaces of RGB Histograms
Linköping University, Department of Science and Technology, Digital Media.ORCID iD: 0000-0001-7557-4904
2008 (English)Conference paper, Published paper (Refereed)
Abstract [en]

We introduce the theory of group representations as a tool to investigate the structure of spaces related to RGB vectors. Our basic assumption is that for many sources of RGB vectors we can assume that the three channels R, G and B are interchangeable. This means that vectors (RGB) and their permutations such as (GRB) appear approximately with the same probability. We introduce the wide-sense-stationary processes as processes whose matrix of second-order moments commute with the permutations of the channels. For such processes the theory of group representations provides the tools to construct a coordinate transformation that block-diagonalizes the corresponding matrices of second-order moments. This coordinate transformation defines therefore a partial principal component analysis. We implemented the transform and investigated its properties with the help of two large databases together containing over one million images. We also introduce a new parametrization of the coefficient space and show that this parametrization can be used to provide information about the internal structure of the RGB histogram space. We also sketch a generalization taking into account the effect of the reducing the number of bins used.

Place, publisher, year, edition, pages
Aachen: Shaker Verlag , 2008. , 13-22 p.13-22 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-43080Local ID: 71439ISBN: 978-3-8322-7578-5 (print)OAI: oai:DiVA.org:liu-43080DiVA: diva2:263937
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2016-08-31

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http://www.shaker.de/Online-Gesamtkatalog/Details.asp?ISBN=978-3-8322-7578-5

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Lenz, Reiner

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  • apa
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Language
  • de-DE
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
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  • text
  • asciidoc
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