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.
