Wavelet Decomposition of Measures: Application to Multifractal Analysis of Images
We show the relevance of multifractal analysis for some problems in image processing. We relate it to the standard question of the determination of correct function space settings. We show why a scale-invariant analysis, such as the one provided by wavelets, is pertinent for this purpose. Since a good setting for images is provided by spaces of measures, we give some insight into the problem of multifractal analysis of measures using wavelet techniques.
KeywordsFourier transform function spaces fractals fractional integration Hölder regularity image classification image processing measures multifractal analysis scaling function scale invariance spectrum of singularities wavelets wavelet leaders
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