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1 | .. -*- coding: utf-8; mode: rst -*- |
2 | ||
3 | .. _colorspaces: | |
4 | ||
5 | *********** | |
6 | Colorspaces | |
7 | *********** | |
8 | ||
9 | 'Color' is a very complex concept and depends on physics, chemistry and | |
10 | biology. Just because you have three numbers that describe the 'red', | |
11 | 'green' and 'blue' components of the color of a pixel does not mean that | |
12 | you can accurately display that color. A colorspace defines what it | |
13 | actually *means* to have an RGB value of e.g. (255, 0, 0). That is, | |
14 | which color should be reproduced on the screen in a perfectly calibrated | |
15 | environment. | |
16 | ||
17 | In order to do that we first need to have a good definition of color, | |
18 | i.e. some way to uniquely and unambiguously define a color so that | |
19 | someone else can reproduce it. Human color vision is trichromatic since | |
20 | the human eye has color receptors that are sensitive to three different | |
21 | wavelengths of light. Hence the need to use three numbers to describe | |
22 | color. Be glad you are not a mantis shrimp as those are sensitive to 12 | |
23 | different wavelengths, so instead of RGB we would be using the | |
24 | ABCDEFGHIJKL colorspace... | |
25 | ||
26 | Color exists only in the eye and brain and is the result of how strongly | |
27 | color receptors are stimulated. This is based on the Spectral Power | |
28 | Distribution (SPD) which is a graph showing the intensity (radiant | |
29 | power) of the light at wavelengths covering the visible spectrum as it | |
30 | enters the eye. The science of colorimetry is about the relationship | |
31 | between the SPD and color as perceived by the human brain. | |
32 | ||
33 | Since the human eye has only three color receptors it is perfectly | |
34 | possible that different SPDs will result in the same stimulation of | |
35 | those receptors and are perceived as the same color, even though the SPD | |
36 | of the light is different. | |
37 | ||
38 | In the 1920s experiments were devised to determine the relationship | |
39 | between SPDs and the perceived color and that resulted in the CIE 1931 | |
40 | standard that defines spectral weighting functions that model the | |
41 | perception of color. Specifically that standard defines functions that | |
42 | can take an SPD and calculate the stimulus for each color receptor. | |
43 | After some further mathematical transforms these stimuli are known as | |
44 | the *CIE XYZ tristimulus* values and these X, Y and Z values describe a | |
45 | color as perceived by a human unambiguously. These X, Y and Z values are | |
46 | all in the range [0…1]. | |
47 | ||
48 | The Y value in the CIE XYZ colorspace corresponds to luminance. Often | |
49 | the CIE XYZ colorspace is transformed to the normalized CIE xyY | |
50 | colorspace: | |
51 | ||
52 | x = X / (X + Y + Z) | |
53 | ||
54 | y = Y / (X + Y + Z) | |
55 | ||
56 | The x and y values are the chromaticity coordinates and can be used to | |
57 | define a color without the luminance component Y. It is very confusing | |
58 | to have such similar names for these colorspaces. Just be aware that if | |
59 | colors are specified with lower case 'x' and 'y', then the CIE xyY | |
60 | colorspace is used. Upper case 'X' and 'Y' refer to the CIE XYZ | |
61 | colorspace. Also, y has nothing to do with luminance. Together x and y | |
62 | specify a color, and Y the luminance. That is really all you need to | |
63 | remember from a practical point of view. At the end of this section you | |
64 | will find reading resources that go into much more detail if you are | |
65 | interested. | |
66 | ||
67 | A monitor or TV will reproduce colors by emitting light at three | |
68 | different wavelengths, the combination of which will stimulate the color | |
69 | receptors in the eye and thus cause the perception of color. | |
70 | Historically these wavelengths were defined by the red, green and blue | |
71 | phosphors used in the displays. These *color primaries* are part of what | |
72 | defines a colorspace. | |
73 | ||
74 | Different display devices will have different primaries and some | |
75 | primaries are more suitable for some display technologies than others. | |
76 | This has resulted in a variety of colorspaces that are used for | |
77 | different display technologies or uses. To define a colorspace you need | |
78 | to define the three color primaries (these are typically defined as x, y | |
79 | chromaticity coordinates from the CIE xyY colorspace) but also the white | |
80 | reference: that is the color obtained when all three primaries are at | |
81 | maximum power. This determines the relative power or energy of the | |
82 | primaries. This is usually chosen to be close to daylight which has been | |
83 | defined as the CIE D65 Illuminant. | |
84 | ||
85 | To recapitulate: the CIE XYZ colorspace uniquely identifies colors. | |
86 | Other colorspaces are defined by three chromaticity coordinates defined | |
87 | in the CIE xyY colorspace. Based on those a 3x3 matrix can be | |
88 | constructed that transforms CIE XYZ colors to colors in the new | |
89 | colorspace. | |
90 | ||
91 | Both the CIE XYZ and the RGB colorspace that are derived from the | |
92 | specific chromaticity primaries are linear colorspaces. But neither the | |
93 | eye, nor display technology is linear. Doubling the values of all | |
94 | components in the linear colorspace will not be perceived as twice the | |
95 | intensity of the color. So each colorspace also defines a transfer | |
96 | function that takes a linear color component value and transforms it to | |
97 | the non-linear component value, which is a closer match to the | |
98 | non-linear performance of both the eye and displays. Linear component | |
99 | values are denoted RGB, non-linear are denoted as R'G'B'. In general | |
100 | colors used in graphics are all R'G'B', except in openGL which uses | |
101 | linear RGB. Special care should be taken when dealing with openGL to | |
102 | provide linear RGB colors or to use the built-in openGL support to apply | |
103 | the inverse transfer function. | |
104 | ||
105 | The final piece that defines a colorspace is a function that transforms | |
106 | non-linear R'G'B' to non-linear Y'CbCr. This function is determined by | |
107 | the so-called luma coefficients. There may be multiple possible Y'CbCr | |
108 | encodings allowed for the same colorspace. Many encodings of color | |
109 | prefer to use luma (Y') and chroma (CbCr) instead of R'G'B'. Since the | |
110 | human eye is more sensitive to differences in luminance than in color | |
111 | this encoding allows one to reduce the amount of color information | |
112 | compared to the luma data. Note that the luma (Y') is unrelated to the Y | |
113 | in the CIE XYZ colorspace. Also note that Y'CbCr is often called YCbCr | |
114 | or YUV even though these are strictly speaking wrong. | |
115 | ||
116 | Sometimes people confuse Y'CbCr as being a colorspace. This is not | |
117 | correct, it is just an encoding of an R'G'B' color into luma and chroma | |
118 | values. The underlying colorspace that is associated with the R'G'B' | |
119 | color is also associated with the Y'CbCr color. | |
120 | ||
121 | The final step is how the RGB, R'G'B' or Y'CbCr values are quantized. | |
122 | The CIE XYZ colorspace where X, Y and Z are in the range [0…1] describes | |
123 | all colors that humans can perceive, but the transform to another | |
124 | colorspace will produce colors that are outside the [0…1] range. Once | |
125 | clamped to the [0…1] range those colors can no longer be reproduced in | |
126 | that colorspace. This clamping is what reduces the extent or gamut of | |
127 | the colorspace. How the range of [0…1] is translated to integer values | |
128 | in the range of [0…255] (or higher, depending on the color depth) is | |
129 | called the quantization. This is *not* part of the colorspace | |
130 | definition. In practice RGB or R'G'B' values are full range, i.e. they | |
131 | use the full [0…255] range. Y'CbCr values on the other hand are limited | |
132 | range with Y' using [16…235] and Cb and Cr using [16…240]. | |
133 | ||
134 | Unfortunately, in some cases limited range RGB is also used where the | |
135 | components use the range [16…235]. And full range Y'CbCr also exists | |
136 | using the [0…255] range. | |
137 | ||
138 | In order to correctly interpret a color you need to know the | |
139 | quantization range, whether it is R'G'B' or Y'CbCr, the used Y'CbCr | |
140 | encoding and the colorspace. From that information you can calculate the | |
141 | corresponding CIE XYZ color and map that again to whatever colorspace | |
142 | your display device uses. | |
143 | ||
144 | The colorspace definition itself consists of the three chromaticity | |
145 | primaries, the white reference chromaticity, a transfer function and the | |
146 | luma coefficients needed to transform R'G'B' to Y'CbCr. While some | |
147 | colorspace standards correctly define all four, quite often the | |
148 | colorspace standard only defines some, and you have to rely on other | |
149 | standards for the missing pieces. The fact that colorspaces are often a | |
150 | mix of different standards also led to very confusing naming conventions | |
151 | where the name of a standard was used to name a colorspace when in fact | |
152 | that standard was part of various other colorspaces as well. | |
153 | ||
154 | If you want to read more about colors and colorspaces, then the | |
155 | following resources are useful: :ref:`poynton` is a good practical | |
156 | book for video engineers, :ref:`colimg` has a much broader scope and | |
157 | describes many more aspects of color (physics, chemistry, biology, | |
158 | etc.). The | |
159 | `http://www.brucelindbloom.com <http://www.brucelindbloom.com>`__ | |
160 | website is an excellent resource, especially with respect to the | |
161 | mathematics behind colorspace conversions. The wikipedia | |
162 | `CIE 1931 colorspace <http://en.wikipedia.org/wiki/CIE_1931_color_space#CIE_xy_chromaticity_diagram_and_the_CIE_xyY_color_space>`__ | |
163 | article is also very useful. |