Hypercomplex Fourier transforms of color images

• Published in: 2001 International Conference on Image Processing Vol. 1; pp. 137 - 140 vol.1
• Main Authors: Sangwine, S.J., Ell, T.A.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2001
• Subjects: Color; Discrete transforms; Fourier transforms; Frequency domain analysis; Image processing; Nonlinear filters; Pixel; Quaternions; Signal processing; Systems engineering and theory
• ISBN: 0780367251; 9780780367258
• DOI: 10.1109/ICIP.2001.958972

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).