A note on the gradient of a multi-image
Computer Vision, Graphics, and Image Processing - Lectures notes in computer science, Vol. 201 (G. Goos and J. Hartmanis, Eds.)
Color image processing and applications
Color image processing and applications
IEEE Transactions on Signal Processing
Color in image and video processing: most recent trends and future research directions
Journal on Image and Video Processing - Color in Image and Video Processing
Journal of Visual Communication and Image Representation
Local quaternion Fourier transform and color image texture analysis
Signal Processing
Quaternion switching filter for impulse noise reduction in color image
Signal Processing
Hypercomplex Mathematical Morphology
Journal of Mathematical Imaging and Vision
Color texture analysis based on fractal descriptors
Pattern Recognition
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Hypercomplex or quaternions numbers have been used recently for both greyscale and colour image processing. Fast, numerous hypercomplex 2D Fourier transforms were presented as a generalization of the complex 2D Fourier transform to this new hypercomplex space. Thus, the major problem was to put an interpretation of what information the Fourier coefficients could provide. In this paper, we first define the conditions on the spectrum coefficients needed to reconstruct a colour image without loss of information through the inverse quaternionic Fourier transform process. The result is used to interpret the quaternionic spectrum coefficients of this specific colour Fourier transform. Secondly, with this apprehension of the quaternion numbers and the corresponding colour spectrum space, we define spatial and frequential strategies to filter colour images.