.. SPDX-License-Identifier: GFDL-1.1-no-invariants-or-later
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.. _colorspaces:
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Colorspaces
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'Color' is a very complex concept and depends on physics, chemistry and
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biology. Just because you have three numbers that describe the 'red',
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'green' and 'blue' components of the color of a pixel does not mean that
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you can accurately display that color. A colorspace defines what it
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actually *means* to have an RGB value of e.g. (255, 0, 0). That is,
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which color should be reproduced on the screen in a perfectly calibrated
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environment.
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In order to do that we first need to have a good definition of color,
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i.e. some way to uniquely and unambiguously define a color so that
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someone else can reproduce it. Human color vision is trichromatic since
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the human eye has color receptors that are sensitive to three different
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wavelengths of light. Hence the need to use three numbers to describe
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color. Be glad you are not a mantis shrimp as those are sensitive to 12
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different wavelengths, so instead of RGB we would be using the
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ABCDEFGHIJKL colorspace...
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Color exists only in the eye and brain and is the result of how strongly
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color receptors are stimulated. This is based on the Spectral Power
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Distribution (SPD) which is a graph showing the intensity (radiant
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power) of the light at wavelengths covering the visible spectrum as it
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enters the eye. The science of colorimetry is about the relationship
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between the SPD and color as perceived by the human brain.
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Since the human eye has only three color receptors it is perfectly
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possible that different SPDs will result in the same stimulation of
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those receptors and are perceived as the same color, even though the SPD
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of the light is different.
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In the 1920s experiments were devised to determine the relationship
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between SPDs and the perceived color and that resulted in the CIE 1931
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standard that defines spectral weighting functions that model the
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perception of color. Specifically that standard defines functions that
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can take an SPD and calculate the stimulus for each color receptor.
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After some further mathematical transforms these stimuli are known as
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the *CIE XYZ tristimulus* values and these X, Y and Z values describe a
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color as perceived by a human unambiguously. These X, Y and Z values are
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all in the range [0…1].
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The Y value in the CIE XYZ colorspace corresponds to luminance. Often
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the CIE XYZ colorspace is transformed to the normalized CIE xyY
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colorspace:
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x = X / (X + Y + Z)
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y = Y / (X + Y + Z)
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The x and y values are the chromaticity coordinates and can be used to
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define a color without the luminance component Y. It is very confusing
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to have such similar names for these colorspaces. Just be aware that if
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colors are specified with lower case 'x' and 'y', then the CIE xyY
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colorspace is used. Upper case 'X' and 'Y' refer to the CIE XYZ
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colorspace. Also, y has nothing to do with luminance. Together x and y
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specify a color, and Y the luminance. That is really all you need to
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remember from a practical point of view. At the end of this section you
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will find reading resources that go into much more detail if you are
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interested.
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A monitor or TV will reproduce colors by emitting light at three
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different wavelengths, the combination of which will stimulate the color
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receptors in the eye and thus cause the perception of color.
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Historically these wavelengths were defined by the red, green and blue
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phosphors used in the displays. These *color primaries* are part of what
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defines a colorspace.
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Different display devices will have different primaries and some
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primaries are more suitable for some display technologies than others.
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This has resulted in a variety of colorspaces that are used for
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different display technologies or uses. To define a colorspace you need
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to define the three color primaries (these are typically defined as x, y
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chromaticity coordinates from the CIE xyY colorspace) but also the white
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reference: that is the color obtained when all three primaries are at
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maximum power. This determines the relative power or energy of the
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primaries. This is usually chosen to be close to daylight which has been
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defined as the CIE D65 Illuminant.
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To recapitulate: the CIE XYZ colorspace uniquely identifies colors.
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Other colorspaces are defined by three chromaticity coordinates defined
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in the CIE xyY colorspace. Based on those a 3x3 matrix can be
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constructed that transforms CIE XYZ colors to colors in the new
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colorspace.
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Both the CIE XYZ and the RGB colorspace that are derived from the
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specific chromaticity primaries are linear colorspaces. But neither the
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eye, nor display technology is linear. Doubling the values of all
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components in the linear colorspace will not be perceived as twice the
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intensity of the color. So each colorspace also defines a transfer
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function that takes a linear color component value and transforms it to
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the non-linear component value, which is a closer match to the
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non-linear performance of both the eye and displays. Linear component
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values are denoted RGB, non-linear are denoted as R'G'B'. In general
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colors used in graphics are all R'G'B', except in openGL which uses
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linear RGB. Special care should be taken when dealing with openGL to
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provide linear RGB colors or to use the built-in openGL support to apply
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the inverse transfer function.
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The final piece that defines a colorspace is a function that transforms
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non-linear R'G'B' to non-linear Y'CbCr. This function is determined by
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the so-called luma coefficients. There may be multiple possible Y'CbCr
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encodings allowed for the same colorspace. Many encodings of color
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prefer to use luma (Y') and chroma (CbCr) instead of R'G'B'. Since the
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human eye is more sensitive to differences in luminance than in color
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this encoding allows one to reduce the amount of color information
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compared to the luma data. Note that the luma (Y') is unrelated to the Y
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in the CIE XYZ colorspace. Also note that Y'CbCr is often called YCbCr
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or YUV even though these are strictly speaking wrong.
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Sometimes people confuse Y'CbCr as being a colorspace. This is not
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correct, it is just an encoding of an R'G'B' color into luma and chroma
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values. The underlying colorspace that is associated with the R'G'B'
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color is also associated with the Y'CbCr color.
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The final step is how the RGB, R'G'B' or Y'CbCr values are quantized.
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The CIE XYZ colorspace where X, Y and Z are in the range [0…1] describes
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all colors that humans can perceive, but the transform to another
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colorspace will produce colors that are outside the [0…1] range. Once
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clamped to the [0…1] range those colors can no longer be reproduced in
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that colorspace. This clamping is what reduces the extent or gamut of
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the colorspace. How the range of [0…1] is translated to integer values
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in the range of [0…255] (or higher, depending on the color depth) is
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called the quantization. This is *not* part of the colorspace
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definition. In practice RGB or R'G'B' values are full range, i.e. they
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use the full [0…255] range. Y'CbCr values on the other hand are limited
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range with Y' using [16…235] and Cb and Cr using [16…240].
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Unfortunately, in some cases limited range RGB is also used where the
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components use the range [16…235]. And full range Y'CbCr also exists
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using the [0…255] range.
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In order to correctly interpret a color you need to know the
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quantization range, whether it is R'G'B' or Y'CbCr, the used Y'CbCr
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encoding and the colorspace. From that information you can calculate the
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corresponding CIE XYZ color and map that again to whatever colorspace
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your display device uses.
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The colorspace definition itself consists of the three chromaticity
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primaries, the white reference chromaticity, a transfer function and the
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luma coefficients needed to transform R'G'B' to Y'CbCr. While some
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colorspace standards correctly define all four, quite often the
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colorspace standard only defines some, and you have to rely on other
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standards for the missing pieces. The fact that colorspaces are often a
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mix of different standards also led to very confusing naming conventions
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where the name of a standard was used to name a colorspace when in fact
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that standard was part of various other colorspaces as well.
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If you want to read more about colors and colorspaces, then the
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following resources are useful: :ref:`poynton` is a good practical
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book for video engineers, :ref:`colimg` has a much broader scope and
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describes many more aspects of color (physics, chemistry, biology,
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etc.). The
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`http://www.brucelindbloom.com <http://www.brucelindbloom.com>`__
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website is an excellent resource, especially with respect to the
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mathematics behind colorspace conversions. The wikipedia
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`CIE 1931 colorspace <http://en.wikipedia.org/wiki/CIE_1931_color_space#CIE_xy_chromaticity_diagram_and_the_CIE_xyY_color_space>`__
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article is also very useful.
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