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Definition of a Discrete Color Monogenic Wavelet Transform

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Advances in Heuristic Signal Processing and Applications

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Abstract

In this chapter, we propose to review different approaches for the introduction of a color monogenic wavelet transform. Monogenic wavelets offer a geometric representation of grayscale images through an AM/FM model allowing invariance of coefficients to translations and rotations. The underlying concept of a local phase includes a fine contour analysis into a coherent unified framework. Wavelet based color image processing schemes have mostly been made by using a grayscale tool separately on color channels. In this chapter, we propose to discuss definitions that consider a color (vector) image right at the beginning of the mathematical definition. After a general description of the background of monogenic concept, we review a first approach built from the grayscale monogenic wavelets together with a color extension of the monogenic signal based on geometric algebra. Then, starting from a link with structure tensors, we discuss an alternative nontrivial extension of the monogenic framework to vector-valued signals. The crucial point is that our color monogenic wavelet transform is non-marginal and it inherits the coherent geometric analysis from the monogenic framework. Finally, we address the numerical aspect by introducing an innovative scheme that uses a discrete Radon transform based on discrete geometry.

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Authors and Affiliations

  1. XLIM Laboratory, UMR CNRS 7252 University of Poitiers, BP 30179, 86962, Futuroscope Chasseneuil Cedex, France

    Raphael Soulard, Philippe Carré & Christine Fernandez-Maloigne

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  1. Raphael Soulard
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  2. Philippe Carré
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  3. Christine Fernandez-Maloigne
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Correspondence to Raphael Soulard .

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Editors and Affiliations

  1. Electrical Engineering Department, Jadavpur University, Kolkata, 700032, West Bengal, India

    Amitava Chatterjee

  2. Dept. of Aerospace Engineering, Sharif University of Technology, Azadi Street, Tehran, Iran

    Hadi Nobahari

  3. Laboratory LiSSi, University of Paris 12, av. du Général de Gaulle 61, Créteil, 94010, France

    Patrick Siarry

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Soulard, R., Carré, P., Fernandez-Maloigne, C. (2013). Definition of a Discrete Color Monogenic Wavelet Transform. In: Chatterjee, A., Nobahari, H., Siarry, P. (eds) Advances in Heuristic Signal Processing and Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37880-5_15

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  • DOI: https://doi.org/10.1007/978-3-642-37880-5_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37879-9

  • Online ISBN: 978-3-642-37880-5

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