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SRGB Color Space
sRGB (standard RGB) is a colorspace, for use on monitors, printers, and the World Wide Web. It was initially proposed by HP and Microsoft in 1996 and became an official standard of the International Electrotechnical Commission (IEC) as IEC 61966-2-1:1999. It is the current standard colorspace for the web, and it is usually the assumed colorspace for images that do not have an embedded color profile. The sRGB standard uses the same color primaries and white point as the ITU-R BT.709 standard for HDTV, but a different transfer function (or gamma) compatible with the era's CRT displays, and assumes a viewing environment closer to typical home and office viewing conditions. Matching the behavior of PC video cards and CRT displays greatly aided sRGB's popularity. History By the 1970s, most computers translated 8-bit digital data fairly linearly to a signal that was sent to a video monitor. However video monitors and TVs produced a brightness that was not linear with the input ...
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CIE 1931 Color Space
In 1931, the International Commission on Illumination (CIE) published the CIE 1931 color spaces which define the relationship between the visible spectrum and human color vision. The CIE color spaces are mathematical models that comprise a "standard observer", which is a static idealization of the color vision of a normal human. A useful application of the CIEXYZ colorspace is that a mixture of two colors in some proportion lies on the straight line between those two colors. One disadvantage is that it is not perceptually uniform. This disadvantage is remedied in subsequent color models such as CIELUV and CIELAB, but these and modern color models still use the CIE 1931 color spaces as a foundation. The CIE (from the French name " Commission Internationale de l'éclairage" - International Commission on Illumination) developed and maintains many of the standards in use today relating to colorimetry. The CIE color spaces were created using data from a series of experiments, where ...
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Trichromacy
Trichromacy or trichromatism is the possession of three independent channels for conveying color information, derived from the three different types of cone cells in the eye. Organisms with trichromacy are called trichromats. The normal explanation of trichromacy is that the organism's retina contains three types of color receptors (called cone cells in vertebrates) with different absorption spectra. In actuality, the number of such receptor types may be greater than three, since different types may be active at different light intensities. In vertebrates with three types of cone cells, at low light intensities the rod cells may contribute to color vision. Humans and other animals that are trichromats Humans and some other mammals have evolved trichromacy based partly on pigments inherited from early vertebrates. In fish and birds, for example, four pigments are used for vision. These extra cone receptor visual pigments detect energy of other wavelengths, sometimes includi ...
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Color Triangle
A color triangle is an arrangement of colors within a triangle, based on the additive or subtractive combination of three primary colors at its corners. An additive color space defined by three primary colors has a chromaticity gamut that is a color triangle, when the amounts of the primaries are constrained to be nonnegative. Before the theory of additive color was proposed by Thomas Young and further developed by James Clerk Maxwell and Hermann von Helmholtz, triangles were also used to organize colors, for example around a system of red, yellow, and blue primary colors. After the development of the CIE system, color triangles were used as chromaticity diagrams, including briefly with the trilinear coordinates representing the chromaticity values. Since the sum of the three chromaticity values has a fixed value, it suffices to depict only two of the three values, using Cartesian co-ordinates. In the modern ''x,y'' diagram, the large triangle bounded by the imaginary p ...
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Gamut
In color reproduction and colorimetry, a gamut, or color gamut , is a convex set containing the colors that can be accurately represented, i.e. reproduced by an output device (e.g. printer or display) or measured by an input device (e.g. camera or visual system). Devices with a larger gamut can represent more colors. Similarly, gamut may also refer to the colors within a defined color space, which is not linked to a specific device. A trichromatic gamut is often visualized as a color triangle. A less common usage defines gamut as the subset of colors contained within an image, scene or video. Introduction The term ''gamut'' was adopted from the field of music, where the medieval Latin expression "gamma ut" meant the lowest tone of the G scale and, in time, came to imply the entire range of musical notes of which musical melodies are composed. William Shakespeare, Shakespeare's use of the term in ''The Taming of the Shrew'' is sometimes attributed to the author / musician Thom ...
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Primary Color
Primary colors are colorants or colored lights that can be mixed in varying amounts to produce a gamut of colors. This is the essential method used to create the perception of a broad range of colors in, e.g., electronic displays, color printing, and paintings. Perceptions associated with a given combination of primary colors can be predicted by an appropriate mixing model (e.g., additive, subtractive) that uses the physics of how light interacts with physical media, and ultimately the retina to be able to accurately display the intended colors. The most common color mixing models are the additive primary colors (red, green, blue) and the subtractive primary colors (cyan, magenta, yellow). Red, yellow and blue are also commonly taught as primary colors (usually in the context of subtractive color mixing as opposed to additive color mixing), despite some criticism due to its lack of scientific basis. Primary colors can also be conceptual (not necessarily real), either as ...
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Chromaticity
Chromaticity is an objective specification of the quality of a color regardless of its luminance. Chromaticity consists of two independent parameters, often specified as '' hue'' (''h'') and ''colorfulness'' (''s''), where the latter is alternatively called ''saturation'', ''chroma'', ''intensity'', or '' excitation purity''. This number of parameters follows from trichromacy of vision of most humans, which is assumed by most models in color science. Quantitative description In color science, the white point of an illuminant or of a display is a neutral reference characterized by a chromaticity; all other chromaticities may be defined in relation to this reference using polar coordinates. The ''hue'' is the angular component, and the ''purity'' is the radial component, normalized by the maximum radius for that hue. ''Purity'' is roughly equivalent to the term '' saturation'' in the HSV color model. The property '' hue'' is as used in general color theory and in specific c ...
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Smooth Function
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives (''differentiability class)'' it has over its domain. A function of class C^k is a function of smoothness at least ; that is, a function of class C^k is a function that has a th derivative that is continuous in its domain. A function of class C^\infty or C^\infty-function (pronounced C-infinity function) is an infinitely differentiable function, that is, a function that has derivatives of all orders (this implies that all these derivatives are continuous). Generally, the term smooth function refers to a C^-function. However, it may also mean "sufficiently differentiable" for the problem under consideration. Differentiability classes Differentiability class is a classification of functions according to the properties of their derivatives. It is a measure of the highest order of derivative that exists and is continuous for a function. Consider an ...
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Continuous Function
In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies there are no abrupt changes in value, known as '' discontinuities''. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is . Until the 19th century, mathematicians largely relied on intuitive notions of continuity and considered only continuous functions. The epsilon–delta definition of a limit was introduced to formalize the definition of continuity. Continuity is one of the core concepts of calculus and mathematical analysis, where arguments and values of functions are real and complex numbers. The concept has been generalized to functions between metric spaces and between topological spaces. The latter are the most general continuous functions, and their d ...
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Power Law
In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, relative change in one quantity results in a relative change in the other quantity proportional to the change raised to a constant exponent: one quantity varies as a power of another. The change is independent of the initial size of those quantities. For instance, the area of a square has a power law relationship with the length of its side, since if the length is doubled, the area is multiplied by 2, while if the length is tripled, the area is multiplied by 3, and so on. Empirical examples The distributions of a wide variety of physical, biological, and human-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, cloud sizes, the foraging pattern of various species, the sizes of activity patterns of neuronal populations, the frequencies of words ...
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Linear Function
In mathematics, the term linear function refers to two distinct but related notions: * In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. For distinguishing such a linear function from the other concept, the term ''affine function'' is often used. * In linear algebra, mathematical analysis, and functional analysis, a linear function is a linear map. As a polynomial function In calculus, analytic geometry and related areas, a linear function is a polynomial of degree one or less, including the zero polynomial (the latter not being considered to have degree zero). When the function is of only one variable, it is of the form :f(x)=ax+b, where and are constants, often real numbers. The graph of such a function of one variable is a nonvertical line. is frequently referred to as the slope of the line, and as the intercept. If ''a > 0'' then the gradient is positive an ...
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SRGB Gamma
sRGB (standard RGB) is a colorspace, for use on monitors, printers, and the World Wide Web. It was initially proposed by HP and Microsoft in 1996 and became an official standard of the International Electrotechnical Commission (IEC) as IEC 61966-2-1:1999. It is the current standard colorspace for the web, and it is usually the assumed colorspace for images that do not have an embedded color profile. The sRGB standard uses the same color primaries and white point as the ITU-R BT.709 standard for HDTV, but a different transfer function (or gamma) compatible with the era's CRT displays, and assumes a viewing environment closer to typical home and office viewing conditions. Matching the behavior of PC video cards and CRT displays greatly aided sRGB's popularity. History By the 1970s, most computers translated 8-bit digital data fairly linearly to a signal that was sent to a video monitor. However video monitors and TVs produced a brightness that was not linear with the input s ...
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