By Eric Dubois, Alan C. Bovik
ISBN-10: 1598292323
ISBN-13: 9781598292329
This lecture describes the author's method of the illustration of colour areas and their use for colour photo processing. The lecture begins with an actual formula of the distance of actual stimuli (light). The version comprises either non-stop spectra and monochromatic spectra within the kind of Dirac deltas. The spectral densities are thought of to be services of a continual wavelength variable. This leads into the formula of colour house as a three-d vector house, with the entire linked constitution. The method is to begin with the axioms of colour matching for regular human audience, known as Grassmann's legislation, and constructing the ensuing vector house formula. even if, as soon as the fundamental defining component to 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 confirmed, a number of helpful decompositions of the distance might be proven. the 1st such decomposition relies on luminance, a degree of the relative brightness of a colour. This results 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 unique decomposition related to a projective house of chromaticity periods is then awarded. ultimately, it's proven how the 3 different types 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 sorts of cone photoreceptors within the human retina. subsequent, a couple of particular linear and nonlinear colour representations are awarded. the colour areas of 2 electronic cameras also are defined. Then the problem of ameliorations among \emph{different} colour areas is addressed.
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Extra info for The structure and properties of color spaces and the representation of color images
Example text
This is a common way to introduce the theory of color spaces although it is often based on a finite-dimensional stimulus space (rather than A) and uses matrix theory [46]. To distinguish from the human trichromatic color space discussed so far, we will call the color space to be developed D (which has no particular signification). Let VS D be a finite-dimensional subspace of A∗C ; specifically, let dim(VS D ) = M and let {p¯ 1 (λ), . . , p¯ M (λ)} be a basis for VS D . Generally, VS D will be specified by such a basis.
Some of these classes may contain a single element of P, such as 0, while most will contain an infinite number of elements. We refer to [C] as a color. Sometimes, we write [C(λ)] to indicate the metameric equivalence class containing the specific spectral density C(λ); any element of the equivalence class can be used as a class representative. Also, if it is important to identify the relation generating the equivalence class, we write [C] = . Equality of colors is denoted with an ordinary = sign, [C1 ] = [C2 ], meaning that the equivalence classes are identical.
We first establish the following simpler results. 5 Let C1 (λ), C2 (λ) ∈ P. Then C1 (λ) − C2 (λ) Proof. 1. = 0 if and only if C1 (λ) = C2 (λ). ✷ 18 CHAPTER 3. 6 Let C1 (λ), C2 (λ) ∈ A. Then C1 (λ) = C2 (λ) if and only if C1 (λ) − C2 (λ) = 0 Proof. , C1 (λ) − C2 (λ) = 0. 6: C1 (λ) 0. Proof. C1 (λ) − C2 (λ) the result follows. = = C2 (λ) if and only if C1 (λ) = C2 (λ) + C0 (λ) where C0 (λ) = 0 means C1 (λ) − C2 (λ) ∈ [0]. 4 is now straightforward. 6 occurs if and only if C1 (λ) = C2 (λ). 4). Suppose that C1 (λ) = C1a (λ) − C1b (λ) and C2 (λ) = C2a (λ) − C2b (λ) where C1a (λ), C1b (λ), C2a (λ), C2b (λ) ∈ P.