Physics – Nuclear Physics
Scientific paper
Aug 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992nupha.545..409b&link_type=abstract
Nuclear Physics A, Volume 545, Issue 1-2, p. 409-418.
Physics
Nuclear Physics
Scientific paper
Extended astronomical objects are irregular structures for which models can not be easily derived from analytical functions. The fractal and multifractal sets furnish a conceptual framework to this kind of objects. Studies of fractal sets led to the use of the Wavelet Transform which allows us to analyse a function both in the spatial and in the frequential spaces. We applied this analyzing method on catalogues of galaxies, in order to get some new information on the heterogeneity of the Universe. We found that the distribution of galaxies shows hierarchical clustering along the whole range of scales. In fact, all the celestial extended objects, nebulae, planetary nebulae, galaxies, etc. show hierachized structures. The wavelet transform leads to introduce the concept of Hierarchical Statistical Models.
After a definition of the continuous wavelet transform, the algorithms which furnish the discrete transform are described. We specify their links with the concept of hierarchical models. Some applications to classical image analysis problems are given: filtering, restoration, matching, detection etc., In conclusion we discuss on how this new vision model could improve our approach of the description of astronomical sources, and especially the Universe.
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