Hypercomplex Fourier transforms of color images

Hypercomplex Fourier transforms based on quaternions have been proposed by several groups for use in image processing, particularly of color images. So far, however, there has not been a coherent explanation of what the spectral domain coefficients produced by a hypercomplex Fourier transform repres...

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Bibliographic Details
Published in2001 International Conference on Image Processing Vol. 1; pp. 137 - 140 vol.1
Main Authors Sangwine, S.J., Ell, T.A.
Format Conference Proceeding
LanguageEnglish
Published IEEE 2001
Subjects
Color
Discrete transforms
Fourier transforms
Frequency domain analysis
Image processing
Nonlinear filters
Pixel
Quaternions
Signal processing
Systems engineering and theory
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ISBN0780367251
9780780367258
DOI10.1109/ICIP.2001.958972

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Summary:Hypercomplex Fourier transforms based on quaternions have been proposed by several groups for use in image processing, particularly of color images. So far, however, there has not been a coherent explanation of what the spectral domain coefficients produced by a hypercomplex Fourier transform represent and this paper attempts to present such an explanation for the first time making use of the polar form of a quaternion and a separation of a quaternion spectral coefficient into components parallel and perpendicular to the hypercomplex exponentials in the transform (the basis functions).
ISBN:0780367251
9780780367258
DOI:10.1109/ICIP.2001.958972