Structures in Spaces of RGB Histograms
2008 (English)Conference paper (Refereed)
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.
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-43080Local ID: 71439ISBN: 978-3-8322-7578-5OAI: oai:DiVA.org:liu-43080DiVA: diva2:263937