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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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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