By Eric Dubois, Alan C. Bovik

This lecture describes the author's method of the illustration of colour areas and their use for colour photo processing. The lecture starts off with an actual formula of the distance of actual stimuli (light). The version contains either non-stop spectra and monochromatic spectra within the type of Dirac deltas. The spectral densities are thought of to be capabilities of a continuing wavelength variable. This leads into the formula of colour area as a three-d vector area, with the entire linked constitution. The method is to begin with the axioms of colour matching for regular human audience, referred to as Grassmann's legislation, and constructing the ensuing vector house formula. in spite of the fact that, as soon as the fundamental defining portion of this vector area is pointed out, it may be prolonged to different colour areas, possibly for various creatures and units, and dimensions except 3. The CIE areas are provided as major examples of colour areas. Many homes of the colour house are tested. as soon as the vector area formula is tested, quite a few worthy decompositions of the distance could be proven. the 1st such decomposition relies on luminance, a degree of the relative brightness of a colour. This ends up in a direct-sum decomposition of colour area the place a two-dimensional subspace identifies the chromatic characteristic, and a 3rd coordinate offers the luminance. a special decomposition concerning a projective house of chromaticity sessions is then provided. eventually, it's proven how the 3 kinds of colour deficiencies found in a few teams of people ends up in a direct-sum decomposition of 3 one-dimensional subspaces which are linked to the 3 kinds of cone photoreceptors within the human retina. subsequent, a number of particular linear and nonlinear colour representations are awarded. the colour areas of 2 electronic cameras also are defined. Then the problem of differences among \emph{different} colour areas is addressed.

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Additional info for The Structure and Properties of Color Spaces and the Representation of Color Images (Synthesis Lectures on Image, Video, and Multimedia Processing)

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The set of equivalence classes of = on the vector space A forms a real vector space that we call the color vector space C = {[C(λ)] = | C(λ) ∈ A}. 8 Proof. 4, addition and multiplication by a real scalar are well-defined operations on the set of equivalence classes of = . The neutral element is [0] = , and the negative of any element is −[C(λ)] = = [−C(λ)] = . The other requisite properties of a vector space (see Appendix C) follow simply from the properties of real numbers. ✷ In the following sections, we will always assume that the equivalence relation is = and write simply [·] without the subscript to denote an element of C.

Since −C(λ) ∈ P, there must be some non-zero K(λ) ∈ K such that C1 (λ) = C(λ) + K(λ) ∈ P. 16. Thus, if [C] ∈ CR , then −[C] ∈ CR , and there must be a plane through the origin so that [C] ∈ CR lies entirely on one side of it. (ii) The statement that all monochromatic lights lie on the boundary of CR is, in fact, an empirical result of the form of the color matching functions for human vision. Fig. 7 illustrates two views of the tristimulus values of the set of monochromatic lights, on the axes determined by the CIE1931 XYZ primaries.

In practice, the p¯ i are continuous and these limits are well behaved. A more informal proof starts by defining the color matching functions directly from Eq. 16). 18) which can be seen as the superposition of an infinite number of Dirac deltas with infinitesmal weights Cc (μ)dμ. If we directly apply the linearity of color matching to this expression, the same result follows. Fig. 4 shows the color matching functions that correspond to the Sony CRT RGB primaries mentioned above. We will see how these are obtained shortly.

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