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Function Spaces Vs. Scaling Functions: Tools for Image Classification

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Mathematical Image Processing

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 5))

Abstract

We investigate the properties of several classes of new parameters issued from multifractal analysis and used in image analysis and classification. They share the following common characteristics: They are derived from local quantities based on wavelet coefficients; at each scale, l p averages of these local quantities are performed and exponents are deduced form a regression through the scales on a log–log plot. This yields scaling functions, which depend on the parameter p, and are used for model selection and classification. We expose possible variants, and their pros and cons. We relate the values taken by these scaling functions with the determination of the regularity of the image in some classes of function spaces, and we show that looking for richer criteria naturally leads to the introduction of new classes of function spaces. We will show which type of additional information this information yields for the initial image.

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Authors and Affiliations

  1. Laboratoire d’Analyse et de Mathématiques Appliquées, UMR 8050 du CNRS, Université Paris Est Créteil Val de Marne, 61 Avenue du Général de Gaulle, 94010, Créteil Cedex, France

    Stéphane Jaffard

  2. CNRS UMR 5672 Laboratoire de Physique, ENS de Lyon, 46, allée d’Italie, F-69364, Lyon cedex, France

    Patrice Abry & Stéphane Roux

Authors
  1. Stéphane Jaffard
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  2. Patrice Abry
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  3. Stéphane Roux
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Correspondence to Stéphane Jaffard .

Editor information

Editors and Affiliations

  1. , UMR 6628-MAPMO, Université d'Orléans, Orléans Cedex 2, 45067, France

    Maïtine Bergounioux

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Jaffard, S., Abry, P., Roux, S. (2011). Function Spaces Vs. Scaling Functions: Tools for Image Classification. In: Bergounioux, M. (eds) Mathematical Image Processing. Springer Proceedings in Mathematics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19604-1_1

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