Graphics Plus/Graphics Plus.iso/info/faqs/colorspa

Internet Message Format | 1994-10-15 | 40KB

Path: bloom-beacon.mit.edu!senator-bedfellow.mit.edu!turing!bourgin
From: [e-mail] (David Bourgin (The best player).)
Newsgroups: comp.graphics,sci.image.processing,comp.answers,sci.answers,news.answers
Subject: Color space FAQ
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Date: 8 Oct 1994 16:11:14 GMT
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Sender: [e-mail] (David Bourgin)
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Expires: 29 Oct 1994 16:05:34 GMT
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Summary: This posting contains a list of Frequently Asked
         Questions (and their answers) about colors and color spaces.
         It provides an extension to the short 4 and 5 items
         of comp.graphics FAQ. Read item 1 for more details.
         A copy of this document is available by anonymous ftp in
         turing.imag.fr (129.88.31.7):/pub/compression/colorspace-faq
Keywords: Color space FAQ
X-Last-Updated: 1994/09/29
Originator: [e-mail]
Xref: bloom-beacon.mit.edu comp.graphics:31866 sci.image.processing:9461 comp.answers:7703 sci.answers:1653 news.answers:27039

Archive-name: graphics/colorspace-faq
Posting-Frequency: Weekly
Last-modified: 28/9/94

###########################################################
Color spaces FAQ - David Bourgin
Date: 28/9/94 (items 5.2 to 5.10 fully rewritten)
Last update: 29/6/94

---------------------------
     Table of contents
---------------------------
1 - Purpose of this FAQ
2 - What is a color?
3 - What is an image based on a color look-up table?
4 - What is this gamma component?
5 - Color space conversions
5.1 - RGB, CMY, and CMYK
5.2 - HSL, HSV
5.3 - CIE XYZ and gray level (monochrome included) pictures
5.4 - CIE Luv
5.5 - CIE Lab and LCH
5.6 - The associated standards: YUV, YIQ, and YCbCr
5.7 - SMPTE-C RGB
5.8 - SMPTE-240M YPbPr (HD televisions)
5.9 - Xerox Corporation YES
5.10- Kodak Photo CD YCC
6 - References
7 - Comments and thanks

---------------------------
          Contents
---------------------------
1 - Purpose of this FAQ

    I did a (too) long period of research in the video domain (video cards,
    image file formats, and so on) and I've decided to provide to all people
    who need some informations about that.
    I aim to cover a part of the Frequently Asked Questions (FAQ) in the video
    works, it means to provide some (useful?) informations about the colors,
    and more especially about color spaces. If you have some informations
    to ask/add to this document, please read item 7.

2 - What is a color?

    A color is defined from human eye capabilities. If you consider a normal
    human being, his vision of a color will be the same as for another normal
    being. Of course, to show any colored information, you need a definition
    (or a model, to use the right word). There are two kinds of color
    definitions:
    - The device-dependent: These definitions are more or less accurate.
    It means that when you display on such a device one color
    with the particular definition, you get a rendering but when you display
    on an other device the same color, you get another rendering (more or less
    dramatically different).
    - The device-independent: This means that the model is accurate and you
    must adjust your output device to get the same answer. This model is based
    on some institute works (curves of colors and associated values).

    From an absolute point of view, it means from a human visual sensation, a
    color could be defined by:
    - Hue: The perception of the nuance. It is the perception of what you see
    in a rainbow.
    - Colorfulness: The perception of saturation, vividness, purity of a color.
    You can go from a sky blue to a deep blue by changing this component.
    - Luminancy: The perception of an area to exhibit more or less light. It is
    also called brightness. You can blurry or enhance an image by modifying
    this component.

    As you see above, I describe a color with three parameters. All the
    students in maths are quickly going to say that the easier representation
    of this stuff is a space, a tri-dimensional space with the previous
    presentation. And I totally agree with that. That is why we often call
    'color space' a particular model of colors.
    With a color space, colors can be interpreted with response curves. While
    in a spectral representation of the wave lengths you have a range from
    infra red to ultra violet, in a normalized color space, we consider a range
    from black to white. All the pros use the internationally recognized
    standard CIE 1931 Standard Calorimetric Observer. This standard defines
    color curves (color matching functions) based on tristimulus values of
    human capabilities and conditions of view (enlightments, ...).
    See item 5.3.
    The CIE (Comission Internationale de l'Eclairage) defined two very useful
    references for the chromacity of the white point:
    - D50 white used as reference for reflective copy
    - D65 white used as reference for emissive devices
    - D90 white used as an approximative reference for phosphors of a monitor
    Dxx means a temperature at about xx00 Kelvins. Example, D65 is given
    at 6504 K.
    Those temperatures define the white points of particular systems. A white
    point of a system is the color at which all three of the tristimuli (RGB,
    for instance) are equal to each other. Being that a white point is
    achromatic (=it has no color), we can define some temperatures associated
    to the white references, in order we get a standard.

3 - What is an image based on a color look-up table?

    All of the pictures don't use the full color space. That's why we often
    use another scheme to improve the encoding of the picture (especially
    to get a file which takes less space). To do so, you have two
    possibilities:
    - You reduce the bits/sample. It means you use less bits for each component
    that describe the color. The colors are described as direct colors, it
    means that all the pixels (or vectors, for vectorial descriptions) are
    directly stored with the full components. For example, with a RGB (see
    item 5.1 to know what RGB is) bitmapped image with a width of 5 pixels and
    a height of 8 pixels, you have:
    (R11,G11,B11) (R12,G12,B12) (R13,G13,B13) (R14,G14,B14) (R15,G15,B15)
    (R21,G21,B21) (R22,G22,B22) (R23,G23,B23) (R24,G24,B24) (R25,G25,B25)
    (R31,G31,B31) (R32,G32,B32) (R33,G33,B33) (R34,G34,B34) (R35,G35,B35)
    (R41,G41,B41) (R42,G42,B42) (R43,G43,B43) (R44,G44,B44) (R45,G45,B45)
    (R51,G51,B51) (R52,G52,B52) (R53,G53,B53) (R54,G54,B54) (R55,G55,B55)
    (R61,G61,B61) (R62,G62,B62) (R63,G63,B63) (R64,G64,B64) (R65,G65,B65)
    (R71,G71,B71) (R72,G72,B72) (R73,G73,B73) (R74,G74,B74) (R75,G75,B75)
    (R81,G81,B81) (R82,G82,B82) (R83,G83,B83) (R84,G84,B84) (R85,G85,B85)
    where Ryx, Gyx, Byx are respectively the Red, Green, and Blue components
    you need to render a color for the pixel located at (x;y).
    - You use a palette. In this case, all the colors are stored in a table
    called a palette and the components of all the colors for each pixel (or
    the vector data) are removed to be replaced with a number. This number is
    an index in the palette. It explains why we call the palette, a color
    look-up table.

4 - What is this gamma component?

    An important notion in image processing comes from physical properties of
    output devices. We often have to correct the colors of an image to get a
    better rendering, i.e. to sharpen or blurry the picture. With the monitors,
    this is really true because input signals - proportional to the voltage -
    don't output a linear answer curve. So, a normal monitor follows an answer
    curve with an exponential law and a monitor based on LCDs follows an "S"
    curve with a vicious hook near black and a slow roll-off near white.
    The adapted correction functions are called gamma correction.
    We will keep in mind that most of software propose a displaying correction
    based on a power law relationship. It is given as:

    Red  = a*(Red'^gamma)+b
    Green= a*(Green'^gamma)+b
    Blue = a*(Blue'^gamma)+b

    where Red', Green', and Blue' are the values of volts in input, i.e the
    values of each primary component for each pixel in the picture you have,
    Red, Green, and Blue are the adapted light components for your device,
    a and b are linear transformations to adapt the law relationship, and
    gamma is the correction factor.
    Be care: a, b, and gamma are usually real constant for *all* pixels.
    Note that the software set up a to 1 and b to 0...
    For CRTCs gray level drawing pictures, gamma is usually within the range of
    [1.2;1.8] but for true color pictures, the number is usually within the
    range of [1.8;2.2]. Normal display devices have an usual 2.35 (+/- 0.1)
    gamma value.
    I assume in the previous relationships that Red, Green, and Blue are
    given within the range of [0;1]. But if they were as well positive as
    negative, you could have, for *example*:
    Red' = -0.5
    and Red = -(abs(Red')^gamma) = -(0.5^gamma)

    In some image file formats or in graphics applications in general, you
    need sometimes some other kinds of correction. These corrections provide
    some specific processings rather than true gamma correction curves.
    This is often the case, for examples, with the printing devices or
    in animation. In the first case, it is interesting to specify that a color
    must be re-affected in order you get a better rendering, as we see it later
    in CMYK item. In the second case, some animations can need an extra
    component associated to each pixel. This component can be, for example,
    used as a transparency mask. We *improperly* call this extra component
    gamma correction.

5 - Color space conversions

    Except an historical point of view, most of you are - I hope - interested
    in color spaces to make renderings and, if possible, on your favorite
    computer. Most of computers display in the RGB color space but you may need
    sometimes the CMYK color space for printing, the YCbCr or CIE Lab to
    compress with JPEG scheme, and so on. That is why we are going to see,
    from here, what are all these color spaces and how to convert them from one
    to another (and primary from one to RGB and vice-versa, this was my purpose
    when I started this FAQ).

    I provide the color space conversions for programmers. The specialists
    don't need most of these infos or they can give a glance to all the stuff
    and read carefully the item 6. Many of the conversions are based on linear
    functions. The best example is given in item 5.3. These conversions can
    be seen in matrices. A matrix is in mathematics an array of values. And to
    go from one to another space color, you just make a matrix inversion.
    E.g. RGB -> CIE XYZrec601-1 (C illuminant) provides the following matrix
    of numbers (see item 5.3):
    |  0.607   0.174   0.200 |
    |  0.299   0.587   0.114 |
    |  0.000   0.066   1.116 |
    and CIE XYZrec601-1 (C illuminant) -> RGB provides the following matrix:
    |  1.910  -0.532  -0.288 |
    | -0.985   1.999  -0.028 |
    |  0.058  -0.118   0.898 |
    These two matrices are the (approximative) inversion of each other.
    If you are a beginner in this mathematical stuff, skip the previous
    explainations, and just use the result...

5.1 - RGB, CMY, and CMYK

    The most popular color spaces are RGB and CMY. These two acronyms stand
    for Red-Green-Blue and Cyan-Magenta-Yellow. They're device-dependent.
    The first is normally used on monitors, the second on printers.
    RGB are called primary colors because a color is produced by adding
    the three components, red, green, and blue.
    CMY is called secondary colors because to describe a color in this color
    space, you consider the reflecting result. So, you become like a painter
    who puts some (secondary) colors on a sheet of paper. A *white* light is
    received on the sheet. You have to keep in mind that white in RGB is all
    components set up to their maximum values. The white color is reflected on
    the sheet so that the components of white (primary colors) are subtracted
    from the components of the 'painting' (secondary colors). Such reflecting
    colors are called secondary colors, for the previous reasons...

    RGB -> CMY                | CMY -> RGB
    Red   = 1-Cyan    (0<=Cyan<=1)    | Cyan    = 1-Red (0<=Red<=1)
    Green = 1-Magenta    (0<=Magenta<=1)    | Magenta = 1-Green (0<=Green<=1)
    Blue  = 1-Yellow    (0<=Yellow<=1)    | Yellow  = 1-Blue (0<=Blue<=1)

    On printer devices, a component of black is added to the CMY, and the
    second color space is then called CMYK (Cyan-Magenta-Yellow-blacK). This
    component is actually used because cyan, magenta, and yellow set up to the
    maximum should produce a black color. (The RGB components of the white are
    completly substracted from the CMY components.) But the resulting color
    isn't physically a 'true' black. The most usual definition for the CMYK
    color space is given below:
    CMY -> CMYK                | CMYK -> CMY
    Black=minimum(Cyan,Magenta,Yellow)    | Cyan=minimum(1,Cyan*(1-Black)+Black)
    Cyan=(Cyan-Black)/(1-Black)        | Magenta=minimum(1,Magenta*(1-Black)+Black)
    Magenta=(Magenta-Black)/(1-Black)    | Yellow=minimum(1,Yellow*(1-Black)+Black)
    Yellow=(Yellow-Black)/(1-Black)    |

    RGB -> CMYK                | CMYK -> RGB
    Black=minimum(1-Red,1-Green,1-Blue)    | Red=1-minimum(1,Cyan*(1-Black)+Black)
    Cyan=(1-Red-Black)/(1-Black)    | Green=1-minimum(1,Magenta*(1-Black)+Black)
    Magenta=(1-Green-Black)/(1-Black)    | Blue=1-minimum(1,Yellow*(1-Black)+Black)
    Yellow=(1-Blue-Black)/(1-Black)    |

    Of course, I assume that C, M, Y, K, R, G, and B  have a range of [0;1].

5.2 - HSL, HSV

    The representation of the colors in the RGB space is quite adapted for
    monitors but from a human being, this is not a useful definition. To
    provide a user representation in the user interfaces, we preferr the HSL
    color space. The acronym stand for Hue (see definition of Hue in item 2),
    Saturation (see definition of Colorfulness in item 2), and Luminosity
    (see definition of Luminancy in item 2).
    The HSV model can be represented by a trigonal cone, as:
                 Green
                  /\
                /    \    ^
              /V=1 x   \   \ Hue (angle, so that Hue(Red)=0, Hue(Green)=120, and Hue(blue)=240 deg)
       Blue -------------- Red
            \      |     /
             \     |-> Saturation (distance from the central axis)
              \    |   /
               \   |  /
                \  | /
                 \ |/
               V=0 x (Value=0 at the top of the apex and =1 at the base of the cone)
    The big disadvantage of this model is the conversion. Most of publishings
    (Microsoft, and Foley's "Computer Graphics: Principles and Practice",
    included) give unaccurate transforms. Actually, the transforms are really
    complicate, as given below:
    Hue = (Alpha-arctan((Red-Luminosity)*(3^0.5)/(Green-Blue)))/(2*PI)
    with { Alpha=PI/2 if Green>Blue
         { Aplha=3*PI/2 if Green<Blue
         { Hue=1 if Green=Blue
    Saturation = (Red^2+Green^2+Blue^2-Red*Green-Red*Blue-Blue*Green)^0.5
    Luminosity = (Red+Green+Blue)/3

    Note that you have to compute Luminosity *before* Hue. If not, you must
    assume that Hue = (Alpha-arctan((2*Red-Green-Blue)/((Green-Blue)*(3^0.5))))/(2*PI).

    I assume that H, S, L, R, G, and B are within range of [0;1].

    Another point of view of this cone is to project the coordinates onto the
    base. The 2D projection is:
    Red:   (1;0)
    Green: (cos(120 deg);sin(120 deg)) = (-0.5; 0.866)
    Blue:  (cos(240 deg);sin(240 deg)) = (-0.5;-0.866)
    Now you need intermediate coordinates:
    a = Red-0.5*(Green+Blue)
    b = 0.866*(Green-Blue)
    Finally, you have:
    Hue = arctan2(x,y)/(2*PI) ; Just one formula, always in the correct quadrant
    Saturation = (x^2+y^2)^0.5
    Luminosity = (Red+Green+Blue)/3
    This interesting point of view was provided by Christian Steyaert
    ([e-mail]).

    Another model close to HSV is HSL. It's actually a double cone with black
    and white points placed at the two apexes of the double cone.
    I don't provide formula, but feel free to send me the formula you could
    find. ;-)

5.3 - CIE XYZ and gray level pictures

    The CIE (a committee I presented in the item 2) has defined in 1931 a
    standard called CIE 1931 based on tristimuli of the Joe eye capabilities.
    These tristimuli are given by three components X, Y and Z.
    X, Y, and Z are respectively linked to the red, green, and blue stimulus.
    These coordinates are absolute, device-independent and normalized to the
    range of [0;1]. To be useful for scientists and programers, some committees
    defined some relations to convert RGB to CIE XYZ and vice-versa. We saw
    in item 5 that color space conversions can be expressed by using matrices.
    You've got:
    |Red  |      -1 |X|     |X|       |Red  |
    |Green| = |M|  *|Y| and |Y| = |M|*|Green|
    |Blue |         |Z|     |Z|       |Blue |
    The matrix M is 3 by 3, and consists of the tristimulus values of the RGB
    primaries in terms of the XYZ primaries.
    To solve this system we need some more data. The first data is the color
    reference we use. With the CIE standard the reference of your rendering is
    the white. White point is achromatic and is defined so that Y=1, and
    Red=Green=Blue. To get the white point coordinates and put it into our
    previous matrix system we use the CIE xyY diagram. This diagram is a 2D
    diagram (based on tristimuli in regard with the wave lengths) where you get
    a color as (x;y). To transform this 2D diagram into a 3D, you have:
    z=1-(x+y)
    X=x*Y/y
    Z=z*Y/y
    (Take care on these letters because these are case sensitive. Otherwise
    you'd get unaccurate results!)
    From there we must consider the coordinates of the vertices in your
    triangle reference. The three vertices in your triangle reference are
    of course the red, the green, and the blue in CIE xyY diagram. Those colors
    are "pure values", it means the chromacity coordinates of red, green, and
    blue are defined in the CIE xyY diagram:
    Red:   (xr; yr; zr=1-(xr+yr))
    Green: (xg; yg; zg=1-(xg+yg))
    Blue:  (xb; yb; zb=1-(xb+yb))
    And the white is defined as:
    |Xn|   |r1 g1 b1|   |Redn  |   |r1 g1 b1|   |1|
    |Yn| = |r2 g2 b2| * |Greenn| = |r2 g2 b2| * |1| (1)
    |Zn|   |r3 g3 b3|   |Bluen |   |r3 g3 b3|   |1|
    (Don't forget that Red=Green=Blue=1 for white.)
    (1) becomes:
    |Xn|   |ar*xr ag*xg ab*xb|   |1|   |xr xg xb|   |ar|
    |Yn| = |ar*yr ag*yg ab*yb| * |1| = |yr yg yb| * |ag| (2)
    |Zn|   |ar*zr ag*zg ab*zb|   |1|   |zr zg zb|   |ab|
    But Xn, Yn, and Zn are also defined as (xn;yn) from the CIE xyY diagram:
    zn=1-(xn+yn)
    Xn=xn*Yn/yn=xn/yn
    Yn=1 (always for white!)
    Zn=zn*Yn/yn=zn/yn
    So (2) becomes:
    |xn/yn|   |xr xg xb|   |ar|
    |  1  | = |yr yg yb| * |ag| (3)
    |zn/yn|   |zr zg zb|   |ab|
    In this system, xn, yn, zn, xr, yr, zr, xg, yg, zg, xb, yb, and zb are all
    known (from the CIE xyY diagram). You just solve it (with a HP pocket
    computer, for example) and get ar, ag, and ab. So:
    |X|   |xr*ar xg*ag xb*ab|   |Red  |
    |Y| = |yr*ar yg*ag xb*ab| * |Green|
    |Z|   |zr*ar zg*ag xb*ab|   |Blue |
    Let's take some examples. The CCIR (Comite Consultatif International des
    Radiocommunications) defined several recommendations. The most popular
    (they shouldn't be used anymore, we will see later why) are CCIR 601-1
    and CCIR 709.
    The CCIR 601-1 is the old NTSC (National Television System Committee)
    standard. It uses a white point called "C Illuminant". The white point
    coordinates in the CIE xyY diagram are (xn;yn)=(0.310063;0.316158). The
    red, green, and blue chromacity coordinates are:
    Red:   xr=0.67 yr=0.33 zr=1-(xr+yr)=0.00
    Green: xg=0.21 yg=0.71 zg=1-(xg+yg)=0.08
    Blue:  xb=0.14 yb=0.08 zb=1-(xb+yb)=0.78
    zn=1-(xn+yn)=1-(0.310063+0.316158)=0.373779
    Xn=xn/yn=0.310063/0.316158=0.980722
    Yn=1 (always for white)
    Zn=zn/yn=0.373779/0.316158=1.182254
    We introduce all that in (3) and get:
    ar=0.981854
    ab=0.978423
    ag=1.239129
    Finally, we have RGB -> CIE XYZccir601-1 (C illuminant):
    |X|   |0.606881 0.173505 0.200336|   |Red  |
    |Y| = |0.298912 0.586611 0.114478| * |Green|
    |Z|   |0.000000 0.066097 1.116157|   |Blue |
    Because I'm a programer, I preferr to round these values up or down (in
    regard with the new precision) and I get:
    RGB -> CIE XYZccir601-1 (C illuminant)    | CIE XYZccir601-1 (C illuminant) -> RGB
    X = 0.607*Red+0.174*Green+0.200*Blue    | Red   =  1.910*X-0.532*Y-0.288*Z
    Y = 0.299*Red+0.587*Green+0.114*Blue    | Green = -0.985*X+1.999*Y-0.028*Z
    Z = 0.000*Red+0.066*Green+1.116*Blue    | Blue  =  0.058*X-0.118*Y+0.898*Z
    The other common recommendation is the 709. The white point is D65 and have
    coordinates fixed as (xn;yn)=(0.312713;0.329016). The RGB chromacity
    coordinates are:
    Red:   xr=0.64 yr=0.33
    Green: xg=0.30 yg=0.60
    Blue:  xb=0.15 yb=0.06
    Finally, we have RGB -> CIE XYZccir709 (709):
    |X|   |0.412411 0.357585 0.180454|   |Red  |
    |Y| = |0.212649 0.715169 0.072182| * |Green|
    |Z|   |0.019332 0.119195 0.950390|   |Blue |
    This provides the formula to transform RGB to CIE XYZccir709 and vice-versa:
    RGB -> CIE XYZccir709 (D65)            | CIE XYZccir709 (D65) -> RGB
    X = 0.412*Red+0.358*Green+0.180*Blue    | Red   =  3.241*X-1.537*Y-0.499*Z
    Y = 0.213*Red+0.715*Green+0.072*Blue    | Green = -0.969*X+1.876*Y+0.042*Z
    Z = 0.019*Red+0.119*Green+0.950*Blue    | Blue  =  0.056*X-0.204*Y+1.057*Z
    Recently (about one year ago), CCIR and CCITT were both absorbed into their
    parent body, the International Telecommunications Union (ITU). So you must
    *not* use CCIR 601-1 and CCIR 709 anymore. Furthermore, their names have
    changed  respectively to Rec 601-1 and Rec 709 ("Rec" stands for
    Recommendation). Here is the new ITU recommendation.
    The white point is D65 and have coordinates fixed as (xn;yn)=(0.312713;
    0.329016). The RGB chromacity coordinates are:
    Red:   xr=0.64 yr=0.33
    Green: xg=0.29 yg=0.60
    Blue:  xb=0.15 yb=0.06
    Finally, we have RGB -> CIE XYZitu (D65):
    |X|   |0.430574 0.341550 0.178325|   |Red  |
    |Y| = |0.222015 0.706655 0.071330| * |Green|
    |Z|   |0.020183 0.129553 0.939180|   |Blue |
    This provides the formula to transform RGB to CIE XYZitu and vice-versa:
    RGB -> CIE XYZitu (D65)            | CIE XYZitu (D65) -> RGB
    X = 0.431*Red+0.342*Green+0.178*Blue    | Red   =  3.063*X-1.393*Y-0.476*Z
    Y = 0.222*Red+0.707*Green+0.071*Blue    | Green = -0.969*X+1.876*Y+0.042*Z
    Z = 0.020*Red+0.130*Green+0.939*Blue    | Blue  =  0.068*X-0.229*Y+1.069*Z

    All the conversions I presented until there in this item are not just for
    fun ;-). They can really be useful. For example, in most of your
    applications you have true color images in RGB color space. How to render
    them fastly on your screen or on your favorite printer. This is simple.
    You can convert your picture instantaneously in gray scale pictures see
    even in a black and white pictures as a magician.
    To do so, you just need to convert your RGB values into the Y component.
    Actually, Y is linked to the luminosity (Y is an achromatic component) and
    X and Z are linked to the colorfulness (X and Z are two chromatic
    components). Old softwares used Rec 601-1 and produced:
    Gray scale=Y=(299*Red+587*Green+114*Blue)/1000
    With Rec 709, we have:
    Gray scale=Y=(213*Red+715*Green+72*Blue)/1000
    Some others do as if:
    Gray scale=Green (They don't consider the red and blue components at all)
    Or Gray scale=(Red+Green+Blue)/3
    But now all people *should* use the most accurate, it means ITU standard:
    Gray scale=Y=(222*Red+707*Green+71*Blue)/1000
    (That's very close to Rec 709!)
    I made some personal tests and have sorted them in regard with the global
    resulting luminosity of the picture (from my eye point of view!). The
    following summary gives what I found ordered increasingly:
    +-----------------------------+----------------+
    |Scheme                       |Luminosity level|
    +-----------------------------+----------------+
    |Gray=Green                   |        1       |
    |Gray=ITU (D65)               |        2       |
    |Gray=Rec 709 (D65)           |        3       |
    |Gray=Rec 601-1 (C illuminant)|        4       |
    |Gray=(Red+Green+Blue)/3      |        5       |
    +-----------------------------+----------------+
    So softwares with Gray=Rec 709 (D65) produce a more dark picture than with
    Gray=Green. Even if you theorically lose many details with Gray=Green
    scheme, in fact, and with the 64-gray levels of a VGA card of a PC it is
    hard to distinguish the losts.

5.4 - CIE Luv

    In 1976, the CIE defined two new color spaces to enable us to get more
    uniform and accurate models. The first of these two color spaces is the
    CIE Luv which component are L*, u* and v*. L* component defines the
    luminancy, and u*, v* define chrominancy. CIE Luv is very used in
    calculation of small colors or color differences, especially with additive
    colors. The CIE Luv color space is defined from CIE XYZ.

    CIE XYZ -> CIE Lab
    { L* = 116*((Y/Yn)^(1/3)) whether Y/Yn>0.008856
    { L* = 903.3*Y/Yn whether Y/Yn<=0.008856
    u* = 13*(L*)*(u'-u'n)
    v* = 13*(L*)*(v'-v'n)
    where u'=4*X/(X+15*Y*+3*Z) and v'=9*Y/(X+15*Y+3*Z)
    and u'n and v'n have the same definitions for u' and v' but applied to the
    white point reference. So, you have:
    u'n=4*Xn/(Xn+15*Yn*+3*Zn) and v'n=9*Yn/(Xn+15*Yn+3*Zn)

    See also item 5.3 about Xn, Yn, and Zn.

5.5 - CIE Lab and LCH

    As CIE Luv, CIE Lab is a color space introduced by CIE in 1976. It's a new
    incorporated color space in TIFF specs. In this color space you use three
    components: L* is the luminancy, a* and b* are respectively red/blue and
    yellow/blue chrominancies.
    This color space is also defined with regard to the CIE XYZ color spaces.

    CIE XYZ -> CIE Lab
    { L=116*((Y/Yn)^(1/3)) whether Y/Yn>0.008856
    { L=903.3*Y/Yn whether Y/Yn<=0.008856
    a=500*(f(X/Xn)-f(Y/Yn))
    b=200*(f(Y/Yn)-f(Z/Zn))
    where { f(t)=t^(1/3) whether Y/Yn>0.008856
          { f(t)=7.787*t+16/116

    See also item 5.3 about Xn, Yn, and Zn.

    The CIE Lab has the same problem as RGB, it is not very useful for user
    interface. That's why you will preferr the LCH, a color space based on
    CIE Lab (accurate and useful...). LCH stand for Luminosity (see this term
    in item 2), Chroma (see Colourfulness in item 2), and Hue (see this term
    in item 2).
    CIE Lab -> LCH
    L = L*
    C = (a*^2+b*^2)^0.5
    { H=0 whether a=0
    { H=(arctan((b*)/(a*))+k*PI/2)/(2*PI) whether a#0 (add PI/2 to H if H<0)
    { and { k=0 if a*>=0 and b*>=0
          { or k=1 if a*>0 and b*<0
          { or k=2 if a*<0 and b*<0
          { or k=3 if a*<0 and b*>0

5.6 - The associated standards: YUV, YIQ, and YCbCr

    YUV is used in European TVs and YIQ in North American TVs (NTSC).
    Y is linked to the component of luminancy, and U,V and I,Q are linked
    to the components of chrominancy. Y come from the standard CIE 1931 XYZ.

    YUV uses D65 white point which coordinates are (xn;yn)=(0.312713;0.329016).
    The RGB chromacity coordinates are:
    Red:   xr=0.64 yr=0.33
    Green: xg=0.29 yg=0.60
    Blue:  xb=0.15 yb=0.06
    See item 5.3 to understand why the above values.

    RGB -> YUV                    | YUV -> RGB
    Y =  0.299*Red+0.587*Green+0.114*Blue    | Red   = Y+0.000*U+1.140*V
    U = -0.147*Red-0.289*Green+0.436*Blue    | Green = Y-0.396*U-0.581*V
    V =  0.615*Red-0.515*Green-0.100*Blue    | Blue  = Y+2.029*U+0.000*V

    RGB -> YIQ                    | YUV -> RGB
    Y =  0.299*Red+0.587*Green+0.114*Blue    | Red   = Y+0.956*I+0.621*Q
    I =  0.596*Red-0.274*Green+0.322*Blue    | Green = Y-0.272*I-0.647*Q
    Q =  0.212*Red-0.523*Green-0.311*Blue    | Blue  = Y-1.105*I+1.702*Q

    YUV -> YIQ                | YIQ -> YUV
    Y = Y (no changes)            | Y = Y (no changes)
    I = -0.2676*U+0.7361*V        | U = -1.1270*I+1.8050*Q
    Q =  0.3869*U+0.4596*V        | V =  0.9489*I+0.6561*Q

    Note that Y has a range of [0;1] (if red, green, and blue have a range of
    [0;1]) but U, V, I, and Q can be as well negative as positive. I can't give
    the range of U, V, I, and Q because it depends on precision from Rec specs
    To avoid such problems, you'll preferr the YCbCr. This color space is
    similar to YUV and YIQ without the disadvantages. Y remains the component
    of luminancy but Cb and Cr become the respective components of blue and
    red. Futhermore, with YCbCr color space you can choose your luminancy from
    your favorite recommendation. The most popular are given below:
    +----------------+---------------+-----------------+----------------+
    | Recommendation | Coef. for red | Coef. for Green | Coef. for Blue |
    +----------------+---------------+-----------------+----------------+
    | Rec 601-1      | 0.299         | 0.587           | 0.114          |
    | Rec 709        | 0.2125        | 0.7154          | 0.0721         |
    | ITU            | 0.2125        | 0.7154          | 0.0721         |
    +----------------+---------------+-----------------+----------------+
    RGB -> YCbCr
    Y  = Coef. for red*Red+Coef. for green*Green+Coef. for blue*Blue
    Cb = (Blue-Y)/(2-2*Coef. for blue)
    Cr = (Red-Y)/(2-2*Coef. for red)
    YCbCr -> RGB
    Red   = Cr*(2-2*Coef. for red)+Y
    Green = (Y-Coef. for blue*Blue-Coef. for red*Red)/Coef. for green
    Blue  = Cb*(2-2*Coef. for blue)+Y
    (Note that the Green component must be computed *after* the two other
    components because Green component use the values of the two others.)
    Usually, you'll need the following conversions based on Rec 601-1
    for TIFF and JPEG works:
    RGB -> YCbCr (with Rec 601-1 specs)        | YCbCr (with Rec 601-1 specs) -> RGB
    Y=  0.2989*Red+0.5866*Green+0.1145*Blue    | Red=  Y+0.0000*Cb+1.4022*Cr
    Cb=-0.1687*Red-0.3312*Green+0.5000*Blue    | Green=Y-0.3456*Cb-0.7145*Cr
    Cr= 0.5000*Red-0.4183*Green-0.0816*Blue    | Blue= Y+1.7710*Cb+0.0000*Cr

    I assume Y is within the range [0;1], and Cb and Cr are within the range
    [-0.5;0.5].

5.7 - SMPTE-C RGB

    SMPTE is an acronym which stands for Society of Motion Picture and Television
    Engineers. They give a gamma (=2.2 with NTSC, and =2.8 with PAL) corrected
    color space with RGB components (about RGB, see item 5.1).
    The white point is D65. The white point coordinates are (xn;yn)=(0.312713;
    0.329016). The RGB chromacity coordinates are:
    Red:   xr=0.630 yr=0.340
    Green: xg=0.310 yg=0.595
    Blue:  xb=0.155 yb=0.070
    See item 5.3 to understand why the above values.
    To get the conversion from SMPTE-C RGB to CIE XYZ or from CIE XYZ to
    SMPTE-C RGB, you have two steps:
    SMPTE-C RGB -> CIE XYZ (D65)        | CIE XYZ (D65) -> SMPTE-C RGB
    - Gamma correction                | - Linear transformations:
    Red=f1(Red')                | Red  = 3.5058*X-1.7397*Y-0.5440*Z
    Green=f1(Green')                | Green=-1.0690*X+1.9778*Y+0.0352*Z
    Blue=f1(Blue')                | Blue = 0.0563*X-0.1970*Y+1.0501*Z
    where { f1(t)=t^2.2 whether t>=0.0        | - Gamma correction
          { f1(t)-(abs(t)^2.2) whether t<0.0    | Red'=f2(Red)
    - Linear transformations:            | Green'=f2(Green)
    X=0.3935*Red+0.3653*Green+0.1916*Blue    | Blue'=f2(Blue)
    Y=0.2124*Red+0.7011*Green+0.0866*Blue    | where { f2(t)=t^(1/2.2) whether t>=0.0
    Z=0.0187*Red+0.1119*Green+0.9582*Blue    |       { f2(t)-(abs(t)^(1/2.2)) whether t<0.0

5.8 - SMPTE-240M YPbPr (HD televisions)

    SMPTE give a gamma (=0.45) corrected color space with RGB components (about
    RGB, see item 5.1). With this space color, you have three components Y, Pb,
    and Pr respectively linked to luminancy (see item 2), green, and blue.
    The white point is D65. The white point coordinates are (xn;yn)=(0.312713;
    0.329016). The RGB chromacity coordinates are:
    Red:   xr=0.67 yr=0.33
    Green: xg=0.21 yg=0.71
    Blue:  xb=0.15 yb=0.06
    See item 5.3 to understand why the above values.
    Conversion from SMPTE-240M RGB to CIE XYZ (D65) or from CIE XYZ (D65) to
    SMPTE-240M RGB, you have two steps:
    YPbPr -> RGB                | RGB -> YPbPr
    - Gamma correction                | - Linear transformations:
    Red=f(Red')                    | Red  =1*Y+0.0000*Pb+1.5756*Pr
    Green=f(Green')                | Green=1*Y-0.2253*Pb+0.5000*Pr
    Blue=f(Blue')                | Blue =1*Y+1.8270*Pb+0.0000*Pr
    where { f(t)=t^0.45 whether t>=0.0        | - Gamma correction
          { f(t)-(abs(t)^0.45) whether t<0.0    | Red'=f(Red)
    - Linear transformations:            | Green'=f(Red)
    Y=  0.2122*Red+0.7013*Green+0.0865*Blue    | Blue'=f(Red)
    Pb=-0.1162*Red-0.3838*Green+0.5000*Blue    | where { f(t)=t^(1/0.45) whether t>=0.0
    Pr= 0.5000*Red-0.4451*Green-0.0549*Blue    |       { f(t)-(abs(t)^(1/0.45)) whether t<0.0

5.9 - Xerox Corporation YES

    YES have three components which are Y (see Luminancy, item 2), E (chrominancy
    of red-green axis), and S (chrominancy of yellow-blue axis)
    Conversion from YES to CIE XYZ (D50) or from CIE XYZ (D50) to YES, you have two
    steps:
    YES -> CIE XYZ (D50)            | CIE XYZ (D50) -> YES
    - Gamma correction                | - Linear transformations:
    Y=f1(Y')                    | Y= 0.000*X+1.000*Y+0.000*Z
    E=f1(E')                    | E= 1.783*X-1.899*Y+0.218*Z
    S=f1(S')                    | S=-0.374*X-0.245*Y+0.734*Z
    where { f1(t)=t^2.2 whether t>=0.0        | - Gamma correction
          { f1(t)-(abs(t)^2.2) whether t<0.0    | Y'=f2(Y)
    - Linear transformations:            | E'=f2(E)
    X=0.964*Y+0.528*E-0.157*S            | S'=f2(S)
    Y=1.000*Y+0.000*E+0.000*S            | where { f2(t)=t^(1/2.2) whether t>=0.0
    Z=0.825*Y+0.269*E+1.283*S            |       { f2(t)-(abs(t)^(1/2.2)) whether t<0.0

    Conversion from YES to CIE XYZ (D65) or from CIE XYZ (D65) to YES, you have two
    steps:
    YES -> CIE XYZ (D65)            | CIE XYZ (D65) -> YES
    - Gamma correction                | - Linear transformations:
    Y=f1(Y')                    | Y= 0.000*X+1.000*Y+0.000*Z
    E=f1(E')                    | E=-2.019*X+1.743*Y-0.246*Z
    S=f1(S')                    | S= 0.423*X+0.227*Y-0.831*Z
    where { f1(t)=t^2.2 whether t>=0.0        | - Gamma correction
          { f1(t)-(abs(t)^2.2) whether t<0.0    | Y'=f2(Y)
    - Linear transformations:            | E'=f2(E)
    X=0.782*Y-0.466*E+0.138*S            | S'=f2(S)
    Y=1.000*Y+0.000*E+0.000*S            | where { f2(t)=t^(1/2.2) whether t>=0.0
    Z=0.671*Y-0.237*E-1.133*S            |       { f2(t)-(abs(t)^(1/2.2)) whether t<0.0

    Usually, you should use YES <-> CIE XYZ (D65) conversions because your
    screen and the usual pictures have D65 as white point. Of course, sometime
    you'll need the first conversions. Just take care on your pictures.

5.10- Kodak Photo CD YCC

    YCC is a color space intented for Kodak Photo CD. It uses Rec 709 as gamma
    correction but its components are defined with the D65 white point and are
    Y (see Luminancy, item 2) and C1 and C2 (both are linked to chrominancy).
    YC1C2->RGB                        | RGB->YC1C2
    - Gamma correction:                    | Y' =1.3584*Y
    Red  =f(red')                    | C1'=2.2179*(C1-156)
    Green=f(Green')                    | C2'=1.8215*(C2-137)
    Blue =f(Blue')                    | Red  =Y'+C2'
    where { f(t)=-1.099*abs(t)^0.45+0.999 if t<=-0.018    | Green=Y'-0.194*C1'-0.509*C2'
          { f(t)=4.5*t if -0.018<t<0.018        | Blue =Y'+C1'
          { f(t)=1.099*t^0.45-0.999 if t>=0.018        |
    - Linear transforms:                |
    Y' = 0.299*Red+0.587*Green+0.114*Blue        |
    C1'=-0.299*Red-0.587*Green+0.886*Blue        |
    C2'= 0.701*Red-0.587*Green-0.114*Blue        |
    - To fit it into 8-bit data:            |
    Y =(255/1.402)*Y'                    |
    C1=111.40*C1'+156                    |
    C2=135.64*C2'+137                    |

    Finally, I assume Red, Green, Blue, Y, C1, and C2 are in the range of
    [0;255]. Take care that your RGB values are not constrainted to positive
    values. So, some colors can be outside the Rec 709 display phosphor
    limit, it means some colors can be outside the trangle I defined in
    item 5.3. This can be explained because Kodak want to preserve some
    accurate infos, such as specular highlight information.
    You can note that the relations to transform YC1C2 to RGB is not exactly
    the reverse to transform RGB to YC1C2. This can be explained (from Kodak
    point of view) because the output displays are limited in the range of
    their capabilities.

6 - References (most of them are provided by Adrian Ford)

    "An inexpensive scheme for calibration of a colour monitor in terms of CIE
    standard coordinates" W.B. Cowan, Computer Graphics, Vol. 17 No. 3, 1983

    "Calibration of a computer controlled color monitor", Brainard, D.H, Color
    Research & Application, 14, 1, pp 23-34 (1989).

    "Color Monitor Colorimetry", SMPTE Recommended Practice RP 145-1987

    "Color Temperature for Color Television Studio Monitors", SMPTE Recommended
    Practice RP 37

    "Colour Science in Television and Display Systems" Sproson, W, N,
    Adam Hilger Ltd, 1983. ISBN 0-85274-413-7
    (Color measuring from soft displays.
    Alan Roberts and Richard Salmon talked about it as a reference)

    "CIE Colorimetry" Official recommendations of the International Commission
    on Illumination, Publication 15.2 1986

    "CRT Colorimetry:Part 1 Theory and Practice, Part 2 Metrology", Berns,
    R.S., Motta, R.J. and Gorzynski, M.E., Color Research and Appliation, 18,
    (1993).
    (Adrian Ford talks about it as a must about color spaces)

    "Effective Color Displays. Theory and Practice", Travis, D, Academic Press,
    1991. ISBN 0-12-697690-2
    (Color applications in computer graphics)

    Field, G.G., Color and Its Reproduction, Graphics Arts Technical
    Foundation, 1988, pp. 320-9
    (Read this about CMY/CMYK)

    "Gamma and its disguises: The nonlinear mappings of intensity in
    perception, CRT's, Film and Video" C. A. Poynton, SMPTE Journal, December
    1993

    "Measuring Colour" second edition, R. W. G. Hunt, Ellis Horwood 1991,
    ISBN 0-13-567686-x
    (Calculation of CIE Luv and other CIE standard colors spaces)

    "On the Gun Independance and Phosphor Consistancy of Color Video Monitors"
    W.B. Cowan N. Rowell, Color Research and Application, V.11 Supplement 1986

    "Precision requirements for digital color reproduction" M Stokes
    MD Fairchild RS Berns, ACM Transactions on graphics, v11 n4 1992

    "The colorimetry of self luminous displays - a bibliography" CIE
    Publication n.87, Central Bureau of the CIE, Vienna 1990

    "The Reproduction of Colour in PhotoGraphy, Printing and Television", R. W.
    G. Hunt, Fountain Press, Tolworth, England, 1987

7 - Comments and thanks

    Whenever you would like to comment or suggest me some informations about
    this or about the color space transformations in general, please use email:
    [e-mail] (David Bourgin)

    Special thanks to the following persons (there are actually many other
    people to cite) for contributing to valid these data:
    - Adrian Ford ([e-mail])
    - Tom Lane ([e-mail])
    - Alan Roberts and Richard Salmon ([e-mail],
                                       [e-mail])
    - Grant Sayer ([e-mail])
    - Steve Westland ([e-mail])

    Note: We are installing some new devices in our net and it could be
    disturbed for some time. Furthermore, I think there's a lot of chances
    I'm going for my national service on next month, it means from 4/10/94.
    (Yes I'm young. :-).) It will take 10 months but I'll try to read and
    answer to my e-mails. Thanks to not be in a hurry ;-).

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