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The physics of how colored light is reflected from surfaces is based on spectral distributions, but a practical imaging system, including the human vision system, works with a small number of samples from the distribution of wavelengths The infinite-dimensional vector space of spectral distributions is reduced to a finite-dimensional vector space of samples (Equation 102) For any finite set of spectral response functions {Rk (\), k = 1,, p}, there is an infinite number of spectral distributions that are filtered to the same set
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of response values {Pk, k = 1, ,p} For example, the spectral distribution at wavelengths where Rk(>") = a can be varied arbitrarily without affecting the value of the response For color imagery, the perceptually meaningful differences in spectral distributions are captured by the quantities of hue, saturation, and brightness (luminance) Hue is determined by the dominant wavelength in the spectral distribution of light wavelengths The spectral hues are single wavelengths in the visible spectrum For example, the primary colors (red, green, and blue) are located at specific positions in the visible spectrum Nonspectral hues are mixtures of wavelengths; for example; purple is a mixture of red and blue Saturation is the magnitude of the hue relative to the other wavelengths:
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(103)
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where 81 is the amount of light at the dominant wavelength and 82 is the amount of light at all wavelengths For example, a deep red color has saturation close to 1; but as other wavelengths are added, the color approaches the distribution of white light, the proportion of red and hence the saturation is reduced, and the color is desaturated to a shade of pink The brightness is a measure of the overall amount of light that passes through all of the spectral response functions You can think of the brightness as a scale factor that is applied to the entire spectral distribution The hue is the location of the peak in the spectral distribution (or the location and relative magnitudes of two peaks in the case of nonspectral hues such as purple) The saturation is the height of the peak relative to the entire spectral distribution The location and shape of the peak in the spectral distribution (hue and saturation) determine the characteristics of light that are normally thought of as color
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The CIE (Commission Internationale de l'Eclairage--the International Commission on Illumination) color system is based on three spectral curves for the CIE primaries Colors are specified by the relative amounts of the CIE primaries X, Y, and Z that match a given color The Y value is luminance, a measure of the amount of light at all wavelengths that corresponds
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to perceived brightness The chromaticity values depend on the dominant wavelength and saturation, independent of the luminance:1
x y z
X X+y+Z y X+y+Z Z X+y+Z'
(lOA) (105) (106)
Since x + y + z = 1, only two chromaticity values are needed Colors are conveniently represented by the x and y chromaticities and luminance Y The x and y chromaticities represent the components of color independent of luminance Two colors, such as dark green and light green, may appear different but may actually have the same relative distribution of wavelengths If the spectral distribution is scaled by a constant, the color may appear lighter or darker, but the shape of the spectral distribution is not changed and the hue (dominant wavelength) and saturation (relative amount of the dominant wavelength) are not changed The perceptually significant chromaticities lie inside the arch-shaped region in Figure 101 White light is at the center ofthe chromaticity diagram Draw a line from white at position W, through a particular color P, to a position H along the outer boundary of the chromaticity diagram The hue is H, and the saturation S is the length of W P relative to W H You can think of a color as an additive mixture of white light and pure spectral hue, p
= S H + (1 - S) W,
(107)
where the saturation S controls the relative proportions of white tint and hue Hue, saturation, and luminance are encoded in the RGB color values in a way that makes it hard to use hue and saturation in vision algorithms For example, it may be easy to identify objects with different hues by setting thresholds on the range of hues (spectral wavelengths) that bracket the objects But where are these thresholds in the RGB cube, what is the shape of
ITechnically, the chromaticities are calculated from luminance and the other CIE values, but the chromaticities are normalized and used in a way that describes color independent of, or at least conceptually separate from, luminance [81]
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