Quaternionic wavelet transform for colour images

Philippe Carré; Patrice Denis

doi:10.1117/12.685942

12 October 2006 Quaternionic wavelet transform for colour images

Philippe Carré, Patrice Denis

Proceedings Volume 6383, Wavelet Applications in Industrial Processing IV; 638301 (2006) https://doi.org/10.1117/12.685942
Event: Optics East 2006, 2006, Boston, Massachusetts, United States

Abstract

Quaternionic Wavelet Transform (QWT) already exist but it dealt with greyscale images. In this paper we propose a quaternionic wavelet transform aimed to colour image processing. To encode colour information in our new transformation, a pixel in the spatial domain is represented by a quaternion as described by Sangwine. First, we propose to use the discrete quaternionic Fourier transform to study the spectral information of the colour image. It is well known that the frequency space of a real signal is a complex hermitian signal, we then studied the digital spectral domain of the quaternionic Fourier transform in order to analyze symmetry properties. This study gives us one characterization of the colour Fourier domain. Second we use the quaternion formalism to define a wavelet transform for colour images. We propose to generalize the filter bank construction to quaternionic formalism. Especially, we describe conditions on quaternionic filters to obtain a perfect reconstruction. We build a first colour quaternionic filter bank: the colour Shannon Wavelet. This family of functions are based on a windowing process in the quaternionic Fourier space.

Citation Download Citation

Philippe Carré and Patrice Denis "Quaternionic wavelet transform for colour images", Proc. SPIE 6383, Wavelet Applications in Industrial Processing IV, 638301 (12 October 2006); https://doi.org/10.1117/12.685942

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