The Structure and Properties of Color Spaces and the Representation of Color Images

This lecture describes the author's approach to the representation of color spaces and their use for color image processing. The lecture starts with a precise formulation of the space of physical stimuli (light). The model includes both continuous spectra and monochromatic spectra in the form of Dirac deltas. The spectral densities are considered to be functions of a continuous wavelength variable. This leads into the formulation of color space as a three-dimensional vector space, with all the associated structure. The approach is to start with the axioms of color matching for normal human viewers, often called Grassmann's laws, and developing the resulting vector space formulation. However, once the essential defining element of this vector space is identified, it can be extended to other color spaces, perhaps for different creatures and devices, and dimensions other than three. The CIE spaces are presented as main examples of color spaces. Many properties of the color space are examined. Once the vector space formulation is established, various useful decompositions of the space can be established. The first such decomposition is based on luminance, a measure of the relative brightness of a color. This leads to a direct-sum decomposition of color space where a two-dimensional subspace identifies the chromatic attribute, and a third coordinate provides the luminance. A different decomposition involving a projective space of chromaticity classes is then presented. Finally, it is shown how the three types of color deficiencies present in some groups of humans leads to a direct-sum decomposition of three one-dimensional subspaces that are associated with the three types of cone photoreceptors in the human retina. Next, a few specific linear and nonlinear color representations are presented. The color spaces of two digital cameras are also described. Then the issue of transformations between different color spaces is addressed. Finally, these ideas are applied to signal and system theory for color images. This is done using a vector signal approach where a general linear system is represented by a three-by-three system matrix. The formulation is applied to both continuous and discrete space images, and specific problems in color filter array sampling and displays are presented for illustration. The book is mainly targeted to researchers and graduate students in fields of signal processing related to any aspect of color imaging.

Introduction.- Light: The Physical Color Stimulus.- The Color Vector Space.- Subspaces and Decompositions of the Human Color Space.- Various Color Spaces, Representations, and Transformations.- Signals and Systems Theory.- Concluding Remarks.

Eric Dubois received the B.Eng. (honours) degree with great distinction and the M.Eng. degree from McGill University in 1972 and 1974, and the Ph.D. from the University of Toronto in 1978, all in electrical engineering. He joined the Institut national de la recherche scientifique (University of Quebec) in 1977, where he held the position of professor in the INRS-Telecommunications centre in Montreal, Canada until 1998. Since July 1998, he has been Professor with the School of Information Technology and Engineering (SITE) at the University of Ottawa, Ottawa, Canada. He was Vice-Dean (Research) and Secretary of the Faculty of Engineering from 2001 to 2004. From January 2006 to December 2008 he was Director of SITE. His research has centered on the compression and processing of still and moving images, and in multidimensional digital signal processing theory. His current research is focused on stereoscopic and multiview imaging, image sampling theory, image-based virtual environments andcolor signal processing. The research has been carried out in collaboration with such organizations as the Communications Research Centre, the National Research Council, the RCMP, and the Learning Objects Repositories Network (LORNET). Dubois is corecipient of the 1988 Journal Award from Society of Motion Picture and Television Engineers. He is a Fellow of the IEEE, of the Canadian Academy of Engineering and of the Engineering Institute of Canada. He is a registered professional engineer in Quebec (member of the Order of Engineers of Quebec). He is a member of the Society for Information Display (SID) and the Society for Imaging Science and Technology (IS&T). He is a member of the editorial board of the EURASIP journal Signal Processing: Image Communication and was an associate editor of the IEEE Transactions on Image Processing (1994-1998). He was technical program co-chair for the IEEE 2000 International Conference on Image Processing (ICIP) and a member of the organizing committee for the IEEE 2004 International Conference on Acoustics, Speech and Signal Processing (ICASSP).