Amiga Format CD 40/Amiga Format CD40 (1999-05-11)(Future Publishing)(GB)(Track 1 of 3)[!][issue 1999-06].iso/-readerstuff-/paul_qureshi/info/colourspaceconversions.txt

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              Colour Space Conversions.
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Complied by Alan Roberts ([e-mail]) and Adrian Ford
([e-mail]) This document may be reproduced and
distributed freely, provided that you do not alter it in any way,
credit its source and that no charge is made for it.

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This document, containing equations relating to colour spaces
and colour transforms, is presented as an alternative to David Bourgin's
ColorSpaces FAQ. Both of the principle authors of this document have
contibuted extensivly to the ColorSpaces FAQ but have become unhappy at
the errors it contained and its maintainers unwillingness to correct them.
We recommend that this document is read in conjunction with
Charles Poynton's documents, GammaFAQ.pdf and ColorFAQ.pdf for a more
complete introduction to colour systems.

They are available from:

  ftp.inforamp.net/pub/users/poynton/doc/Colour/

in Acrobat PDF, PostScript and ASCII text formats. If you have a web
browser, consult Poynton's Gamma and Colour FAQ page;

  http://www.inforamp.net/~poynton/Poynton-colour.html

This document can always be found at

  ftp.westminster.ac.uk in directory /pub/itrg

Please send comments to Charles Poynton ([e-mail]), Alan
Roberts ([e-mail]) or Adrian Ford ([e-mail])
as appropiate.

Date of this edition: 5 May 1995
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                       Colour Equations FAQ.
                       ---------------------


Contents:

 Section [1] Some definitions and explanations.
  [1.1] What is the correct way to describe colour that we see?
  [1.2] What is a colour space?
  [1.3] Why is there more than one colour space?
  [1.4] What's the difference between device dependent and device
    independent?
  [1.5] What is a colour gamut?
  [1.6] What is the CIE System?
  [1.7] What colour space should I use?
 Section [2] Gamma and linearity.
 Section [3] Grassman's Laws of additive colour mixture.
 Section [4] Tristimuli, Chromaticity, and colorimetric systems
  [4.1] CIE XYZ (1931)
  [4.2] CIE YUV (1960)
  [4.3] CIE YU'V'
  [4.4] CIE L*u*v*
  [4.5] CIE LAB
  [4.6] CMC colour difference formula.
 Section [5]   Computer Graphics Colour Spaces.
  [5.1] Computer RGB colour space.
  [5.2] CMY(K) (Cyan Magenta Yellow (Black))
  [5.3] HSL and HSV (Hue Saturation and Lightness / Value)
 Section [6]   TV and allied non-linear systems
  [6.1] European Y'U'V' (EBU)
  [6.2] American Y'I'Q'
  [6.3] SMPTE-C RGB
  [6.4] ITU.BT-601 Y'CbCr
  [6.5] ITU.BT-709 HDTV studio production in Y'CbCr
  [6.6] SMPTE-240M Y'PbPr
  [6.7] Kodak PhotoYCC colour space for PhotoCD images.
 Section [7] Colour appearence.
 Section [8] The references and bedtime reading.
 Section [9] Footnotes & Disclaimer.

Section [1] Some definitions and explanations.

This is a chatty bit about colour spaces related to computers.

[1.1] What is the correct way to describe colour that we see?

Colour is described by three attributes. The following terms have been
defined by the CIE (see 1.6) and are given in Hunt's book "Measuring
Colour":

brightness    - the human sensation by which an area exhibits more or less
        light.
Hue           - the human sensation according to which an area appears
        to be similar to one, or to proportions of two, of the
        perceived colours red, yellow, green and blue.
Colourfulness - the human sensation according to which an area appears to
        exhibit more or less of its hue.

lightness     - the sensation of an area's brightness relative to a reference
        white in the scene.
chroma        - the colourfulness of an area relative to the brightness of a
        reference white.
saturation    - the colourfulness of an area relative to its brightness.

A `colour' is a visual sensation produced by a specific SPD (spectral
power distribution) incident on the retina. The eye senses colour using
three classes of wavelength. This mechanism means that two different
SPD's may produce the same visual sensation - an effect known as
metamerism.
A point to note, is that although the eye senses colour roughly
according to red, green and blue light (trichromatic theory), higher
visual processes in the brain code colour according to the opponent
process theory using the opponent pairs roughly termed red - green,
blue - yellow and black - white.

[1.2] What is a colour space?

A colour space is a method by which we can specify, create and visualise
colour. As humans, we may define a colour by its attributes of brightness,
hue and colourfulness. A computer will describe a colour stimulus in terms
of the excitations of red, green and blue phosphors on the CRT faceplate.
A printing press descibes a colour stimulus in terms of the reflectance and
absorbance of cyan, magenta, yellow and black inks on the paper.
Such a colour is usually specified by using three coordinates, or
attributes, which represent its position within a specific colour space.
These coordinates do not tell us what the colour looks like, only where
the colour is located within a particular colour space.

[1.3] Why is there more than one colour space?

Different colour spaces are better for different applications, some
equipment has limiting factors that dictate the size and type of colour
space that can be used.  Some colour spaces are perceptually linear,
i.e. a 10 unit change in stimulus will produce the same change in
perception wherever it is applied. Many colour spaces, particularly in
computer graphics are not linear in this way. Some colour spaces are
intuitive to use, i.e. it is easy for the user to navigate within them
and creating desired colours is relatively easy. Finally, some colour
spaces are device dependent while others are not - i.e device independent.

[1.4] What's the difference between device dependent and device independent?

A device dependent colour space is a colour space where the resultant colour
depends on the equipment and the set-up used to produce it. For example the
colour produced using pixel values of rgb = 250,134,67 will alter as
you change the brightness and contrast on your display. In the same way if
you swap your monitor the red, green and blue phosphors will have slightly
different characteristics and the colour produced will change. Thus RGB is a
colour space that is dependent on the system being used, it is device
dependent. A device independent colour space is one where the coordinates
used to specify the colour will produce the same colour wherever they are
applied. An example of a device independent colour space is the CIE L*a*b*
colour space (known as CIELab and based on the human visual system).

Another way of looking a device dependency is to imagine an RGB cube within
a colour space representing all possible colours (for example a CIE based
colour space). We define a colour by the values on the three axes, however
the exact colour will depend on the position of the cube within the
perceptual colour space, move the cube (by changing the set-up) and the
colour will change.

Some device dependent colour spaces have their position within CIE space
defined, these are known as device calibrated colour spaces and are a kind
of half way house between dependent and independent colour spaces. For
example, a graphics file that contains colorimetric information,
i.e. the white point, transfer functions, and phosphor chromaticities,
would enable device dependent RGB data to be modified for whatever
device was being used - i.e. calibrated to specific devices.

[1.5] What is a colour gamut?

A colour gamut is the area enclosed by a colour space in three dimensions.
It is usual to represent the gamut of a colour reproduction
system graphically as the range of colours available in some
device independent colour space. Often the gamut will be represented in
only two dimensions, for example on a CIE u'v' chromaticity
diagram (see 4.3).

[1.6] What is the CIE System?

The CIE has defined a system that classifies colour according to the HVS
(the human visual system). Using this system we can specify any colour in
terms of its CIE coordinates.

The CIE system works by weighting the SPD of an object in terms of three
colour matching functions. These functions are the sensitivities of a
standard observer to light of different wavelengths. The weighting is
performed over the visual spectrum, from around 360nm to 830nm in set
intervals. However, the illuminant, and lighting and viewing geometry are
carefully defined, since these all affect the appearance of a particular
colour. This process produces three CIE tri-stimulus values, XYZ, which
are the building blocks from which many colour measurements are made.

[1.7] What colour space should I use?

That depends on what you want to do, but here is a list of the pros and cons
of some of the more common, computer related, colour spaces;

RGB (Red Green Blue)

Additive colour system based on trichromatic theory, used by CRT
displays where proportions of excitation of red, green and blue emitting
phosphors produce colours when visually fused. Easy to implement, non linear,
device dependent, unintuitive, common (used in television cameras, computer
graphics etc).

CMY(K) (Cyan Magenta Yellow (Black))

Subtractive colour. Used in printing and photography. Printers often include
the fourth component, black ink, to improve the colour gamut (by increasing
the density range), improving blacks, saving money and speeding drying (less
ink to dry). Fairly easy to implement, difficult to transfer *properly* from
RGB (simple transforms are, well, simple), device dependent, non-linear,
unintuitive.

HSL (Hue Saturation and Lightness)

This represents a wealth of similar colour spaces, alternatives include HSI
(intensity), HSV (value), HCI (chroma / colourfulness),  HVC, TSD (hue
saturation and darkness) etc etc. Most of these colour spaces are linear
transforms from RGB and are thus, device dependent, non-linear but very
intuitive. In addition the separation of the luminance component has
advantages in image processing and other applications. (But take care, the
complete isolation of the separate components will require a space optimised
for your device. See later notes on CIE colour spaces)

YIQ, YUV, YCbCr, YCC  (Luminance - Chrominance)

These are the television transmission colour spaces, also known as
transmission primaries. (YIQ and YUV are analogue for NTSC and PAL, and
YCbCr is digital). They separate luminance from chrominance (lightness
from colour) and are useful in compression and image processing applications.
They are device dependent and, unless you are a TV engineer, unintuitive.
Kodaks PhotoCD system uses a type of YCC colour space, PhotoYCC, which is a
device calibrated colour space.

CIE

There are two CIE based colour spaces, CIELuv and CIELab. They are near
linear (as close as any colour space is expected to sensibly get), device
independent (unless your in the habit of swapping your eye balls with aliens),
but not very intuitive to use.

From CIELuv you can derive CIELhs or CIELhc where h is the hue (an angle),
s the saturation and c the chroma. This is more intuitive to work with when
specifying colours. CIELuv also has an associated chromaticity diagram, a two
dimensional chart which makes additive colour mixing very easy to visualise,
hence CIELuv is widely used in additive colour applications, like television.

CIELab has no associated two dimensional chromaticity diagram and no
correlate of saturation so only CIELhc can be used.

Section [2] Gamma and linearity.

Many image processing operations, and also colour space transforms that
involve device independent colour spaces, like the CIE system based
ones, must be performed in a linear luminance domain.
By this we really mean that the relationship between pixel
values specified in software and the luminance of a specific area on the CRT
display must be known. In most cases the CRT will have a non-linear response.
The luminance of a CRT is generally modeled using a power function with an
exponent, gamma, somewhere between 2.2 (NTSC and SMPTE specifications) and
2.8 (as given by Hunt and Sproson). Recent measurements performed at the BBC
in the UK (by Richard Salmon and Alan Roberts) have shown that the actual
value of gamma is very dependent upon the accurate setting of the CRT's black
level. For correctly set-up CRT's, gamma is 2.35 +/- 0.1. This relationship
is given as follows;

Luminance = voltage ^ gamma

Where luminance and voltage are normalised.

In order to display image information as linear luminance  we need to modify
the voltages sent to the CRT. This process stems from television systems
where the camera and receiver had different transfer functions (which,
unless corrected, would cause problems with tone reproduction). The
modification applied is known as gamma correction and is given below;

New_Voltage = Old_Voltage ^ (1/gamma)

(both voltages are normalised and gamma is the value of the exponent of the
power function that most closely models the luminance-voltage relationship
of the display being used.)

For a colour computer system we can replace the voltages by the pixel values
selected, this of course assumes that your graphics card converts digital
values to analogue voltages in a linear way. (For precision work you should
check this). The colour relationships are;

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

where Red', Green', and Blue' are the normalised input RGB pixel values and
Red, Green, and Blue are the normalised gamma corrected signals sent to the
graphics card. The values of the constants a and b compensate for the overall
system gain and system offset respectively. (essentially gain is contrast and
offset is intensity.) For basic applications the value of a, b and gamma can
be assumed to be consistent between colour channels, however for precise
applications they must be measured for each channel separately.

A more accurate description of the gamma relationship has recently been given
in a paper by Berns. See also Charles Poynton's paper and his
document GammaFAQ. The implementation of gamma correction for television
standards is discussed more fully in section 6.

Note: Gamma correction performed in integer maths is prone to large
quantisation errors. For example, applying a gamma correction of 1/2.2 to
an image with an original gamma of one (linear luminance) produces a drop
in the number of grey levels from 245 to 196. Therefore take care not to
alter the transfer characteristics more than is necessary, if you need to
gamma correct images try to keep the originals so that you can pass them
on to others without passing on the degradations that you've produced ;-).
In addition, any implementation of gamma correction which takes no account
of the transfer function of the image acquisition system, is an incomplete
implementation.

Section [3]  Grassman's Laws of additive colour mixture.

Any colour (source C) can be matched by a linear combination of three other
colours (primaries eg. RGB), provided that none of those three can be matched
by a combination of the other two. This is fundamental to colorimetry and is
Grassman's first law of colour mixture. So a colour C can be matched by Rc
units of red, Gc units of green and Bc units of blue. The units are can be
measured in any form that quantifies light power.

   C = Rc(R) + Gc(G) + Bc(B)

A mixture of any two colours (sources C1 and C2) can be matched by linearly
adding together the mixtures of any three other colours that individually
match the two source colours. This is Grassman's second law of colour
mixture. It can be extended to any number of source colours.

   C3(C3) = C1(C1) + C2(C2) = [R1+R2](R) + [G1+G2](G) + [B1+B2](B)

Colour matching persists at all luminances. This is Grassman's third law. It
fails at very low light levels where rod cell vision (scoptopic) takes over
from cone cell vision (photopic).

   kC3(C3) = kC1(C1) + kC2(C2).

The symbols in square brackets are the names of the colours, and not numerical
values. The equality sign should not be used to signify an identity, in
colorimetry it means a colour matching, the colour on one side of the equality
looks the same as the colour on the other side.

These laws govern all aspects of additive colour work, but they apply only
signals in the "linear-light" domain. They can be extended into subtractive
colour work.

Section [4]   Tristimuli, Chromaticity, and colorimetric systems

A colour can be described as a mixture of three other colours or "Tristimuli".
Typically RGB for CRT based systems (TV, computer) or XYZ (fundamental
measurements). The amounts of each stimulus define the colour. However, it is
frequently useful to separate the colour definition into "luminance" and
"chromaticity". Lower case is always used to signify chromaticity coordinates,
upper case always signifies tristimulus values (or amounts of the primaries).
Chromaticity coordinates can be plotted on a two-dimensional diagram that
defines all the visible colours, luminance is normal to that diagram.

[4.1] CIE XYZ (1931)

The CIE XYZ (1931) system is at the root of all colorimetry. It is defined
such  that all visible colours can be defined using only positive values,
and, the Y value is luminance. Consequently, the colours of the XYZ
primaries themselves are not visible. The chromaticity diagram is highly
non-linear, in that a vector of unit magnitude representing the difference
between two chromaticities is not uniformly visible. A colour defined in this
system is referred to as Yxy. A third coordinate, z, can also be defined but
is redundant since x+y+z=1 for all colours.

    x = X / (X + Y + Z)
    y = Y / (X + Y + Z)

[4.2] CIE YUV (1960)

This is a linear transformation of Yxy, in an attempt to produce a
chromaticity diagrams in which a vector of unit magnitude (difference between
two points representing two colours) is equally visible at all colours. Y is
unchanged from XYZ or Yxy. Difference non-uniformity is reduced considerably,
but not enough. A third coordinate, w, can also be defined but is redundant.

    u = 2x / (6y - x + 1.5)
    v = 3y / (6y - x + 1.5)


[4.3] CIE YU'V'

This is another linear transformation of Yxy. Y remains unchanged.
Difference non-uniformity is further reduced, but still not enough. Again,
a third coordinate, w', can be defined, but is redundant.

    u' = u    = 2x / (6y - x + 1.5)
    v' = 1.5v = 4.5y / (6y - x + 1.5)


[4.4] CIE L*u*v*

This is based on CIE Yu'v' (1976) and is a further attempt to linearise
the perceptibility of unit vector colour differences. It is a non-linear
colour space, but the conversions are reversible. Colouring information is
centered on the colour of the white point of the system, subscript n, (D65
in most TV systems). The non-linear relationship for Y* is intended to mimic
the logarithmic response of the eye.

    L* = 116*((Y/Yn)^(1/3))     for Y/Yn>0.008856
    L* = 903.3*Y/Yn             for Y/Yn<=0.008856
    u* = 13*(L*)*(u'-u'n)
    v* = 13*(L*)*(v'-v'n)

L* scales from 0 to 100 for relative luminance (Y/Yn) scaling 0 to 1.

There are three other, more meaningful polar parameters which more closely
match  the human visual experience than do the Cartesian parameters.

    Chroma                     C* = (u*^2 + v*^2) ^ 0.5
    Hue                       huv = arctan(v* / u*)
    Psychometric Saturation   suv = C* / L*

Hue is an angle in four quadrants.

[4.5] CIE LAB

This is based directly on CIE XYZ (1931) and is another attempt to linearise
the perceptibility of unit vector colour differences. Again, it is non-linear,
and the conversions are still reversible. Colouring information is referred
to the colour of the white point of the system, subscript n. The non-linear
relationships for L* a* and b* are the same as for CIELUV and are intended
to mimic the logarithmic  response of the eye.

    L*=116*((Y/Yn)^(1/3))       for Y/Yn>0.008856
    L*=903.3*Y/Yn               for 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)          for t>0.008856
      f(t)=7.787*t+16/116   for t<=0.008856

Again, L* scales from 0 to 100.

Again, there are polar parameters that more closely match the visual
experience of colours.

    Chroma C*  = (a*^2 + b*^2)^ 0.5
    Hue    hab = arctan(b*/a)

Hue is an angle in four quadrants, and there is no saturation term in this
system.


[4.6] CMC colour difference formula.

The CMC colour difference formula is better than CIE Lab for evaluating
small colour differences.

Colour difference = [(D_L / l * Sl)^2 + (D_C / c * Sc)^2 + (D_H / Sh)^"2]^0.5

where; Sl = 0.040975L / (1+0.01765L) unless L < 16 when Sl = 0.511
       Sc = 0.0638C / (1+0.0131C) + 0.638
       Sh = (f*T + 1 - f)Sc

where; f = (C^4 / (C^4 + 1900))^0.5
       T = 0.36 + | 0.4 cos(h + 35| unless h is between 164 and 345
     degrees when
        T = 0.56 + | 0.2 cos(h + 168) |

D_L is delta E star, D_C is delta C star, D_H delta H star, L is L star
and h hue angle.a:

for predicting colour differences, the weights l and c are set to unity,
and the colour difference is referred to as the CMC(1:1) difference.

Section [5]   Computer Graphics Colour Spaces.

Traditionally colour spaces for computer graphics have been designed for
specific devices - RGB for displays or CMY for printers. As such they
are device dependent (and meaningless if applied to different devices or
the same device in different conditions). Most computer graphics colour
spaces are perceptually non-linear, i.e. colour differences vary
throughout the space, this makes them inefficient for coding colour
information. Another problem is that they can be unintuitive, by this we
mean that a novice may find it difficult to specify a desired colour -
for example selecting the colour brown in an RGB space.

A caveat.

The transforms in this section are generally simplifications of the
real world. We strongly recommend reading the references at the end of
this FAQ as well as Charles Poynton's ColorFAQ and GammaFAQ.

We assume all values are normalised to 1 unless otherwise stated.

[5.1] Computer RGB colour space.

This is the colour space produced on a CRT (or similar) display when
pixel values are applied to a graphics card. To convert RGB pixel values
to CIE XYZ tri-stimulus values is a two stage process.

1) Calculate the displayed luminance for each pixel value, this is done
by applying the gamma correction factor to the signal. Ideally this
should be calculated for each channel independently, (see sections 2 and 6).

2) Perform a matrix transform from the linear RGB to CIE XYZ values.
This transform takes the following form.

       |X|       |Xr  Xg  Xb|     |R|
       |Y|   =   |Yr  Yg  Yb|  *  |G|
       |Z|       |Zr  Zg  Zb|     |B|

where Xr,Yr,Zr, are the CIE XYZ tristimulus values of the red phosophor
at full emission measured from the CRT faceplate.
Xg,Yg,Zg, are the CIE XYZ tristimulus values of the green phosophor
at full emission measured from the CRT faceplate.
and Xb,Yb,Zb, are the CIE XYZ tristimulus values of the blue phosophor
at full emission measured from the CRT faceplate.
R, G and B are the corrected pixel values obtained from the previous step
(by gamma correction).
X, Y and Z are the resultant CIE XYZ tristimulus values of the displayed
colour.

To convert from XYZ to RGB use the inverse matrix.

       |R|       |Xr  Xg  Xb|(-1)     |X|
       |G|   =   |Yr  Yg  Yb|     *   |Y|
       |B|       |Zr  Zg  Zb|         |Z|

In section 6.1 this relationship is given for a typical television system,
for this system the matrix to convert RGB to XYZ is as follows...

       |X|    |0.431 0.342 0.178|      |R|
       |Y| =  |0.222 0.707 0.071|   *  |G|
       |Z|    |0.020 0.130 0.939|      |B|

which gives;

        X = 0.431*R + 0.342*G + 0.178*B
        Y = 0.222*R + 0.707*G + 0.071*B
        Z = 0.020*R + 0.130*G + 0.939*B

Which, given specific RGB values, can be used to calculate CIE XYZ.
Source code is given in Travis' book for matrix transforms between RGB and
CIE XYZ. (see references).

Often, it is not possible to measure the phosphors of your particluar
display, as this requires either a spectroradiometer or a colorimeter.
You can get round this if you have published data for your display's
CIE xy chromaticity coordinates of each phosphor and the white point.
Since the CIE Y tristimulus value always has a value of one you can
calculate CIE XYZ for the white point and then (assuming additivity)
CIE XYZ for the three phosphors by solving the three simultanous
equations.

[The white point of a display system is the displayed colour that is
produced when all three channels are driven to maximum. (eg RGB = 255,
255,255). The white point is usually expressed as either CIE xy
chromaticity coordinates or a correlated colour temperature in Kelvin.]

There can be problems with converting between RGB and XYZ which result
in differences between values calculated and those measured from the
screen. Assuming that the correction for the display gamma is correct
and that you have the right CIE XYZ tristimulus values the following
may apply:

  spatial non-linearity - the colour on a CRT display often differs with
                          the spatial location across the faceplate.
  channel dependence    - there may be interactions between channels,
                          for instance the green signal may cause
                          excitation in the red phosphors.
  spatial dependence    - the exact displayed colour often depends on what
                          else is being displayed on screen at the same
                          time. For instance a central red patch will have
                          a different colour depending on whether the
                          surround is black or white. (Note this is in
                          addition to visual effects in the HVS.)
  lack of additivity    - many displays do not strictly obey the rules of
                          additivity, the sum of the measurements of red
                          green and blue differs from the measured white.
                          Ideally they should be identical. (See section 3).

These errors mean that although greater accuracy can be obtained by using
the actual display system transfer function rather than gamma (which is an
approximation) the effort probably isn't worth it.
See Berns et al for a details of possible problems and descriptions of some
solutions, also Sproson for more detailed theory of RGB to CIE conversions
in television systems.


[5.2] CMY(K) (Cyan Magenta Yellow (Black))

CMY(K) is device dependent, unintuitive and perceptually non-linear;

To convert from RGB to CMY for printing, the simplest method is to
convert from RGB to CIE XYZ and then from CIE XYZ to CMY(K). This is not
a trivial process and ideally takes into consideration other factors -
such as the printing inks being used, the type of press and screening,
the paper, viewing conditions, lighting, etc.

Simple (and incorrect) transforms for RGB to CMY are given below;

RGB to CMY
Cyan    = 1-Red
Magenta = 1-Green
Yellow  = 1-Blue

CMY to RGB
Red   = 1-Cyan
Green = 1-Magenta
Blue  = 1-Yellow

CMY to CMYK
Black   = minimum (Cyan,Magenta,Yellow)
Cyan    = (Cyan-Black)/(1-Black)
Magenta = (Magenta-Black)/(1-Black)
Yellow  = (Yellow-Black)/(1-Black)

CMYK to CMY
Cyan    = minimum(1,Cyan*(1-Black)+Black)
Magenta = minimum(1,Magenta*(1-Black)+Black)
Yellow  = minimum(1,Yellow*(1-Black)+Black)

These transforms may be sufficient if you simply want to specify CMY
colours on an RGB display's user interface, but for printing, where any
kind of colour match between display and print is desired, they are
totally inaccurate.

If you want to try this kind of thing you're getting into the domain of
colour management systems and should be reading Charle's Poynton's
ColorFAQ.

[5.3] HSL and HSV (Hue Saturation and Lightness / Value)

Other similar colour spaces include HSI (intensity), HCI (chroma /
colourfulness), HVC, TSD (hue saturation and darkness) etc etc

As linear transforms from RGB they are device dependent, non-linear but very
intuitive. The separation of the luminance component has some advantages in
image processing. There appears to be little point in using these
associated colour spaces, a better alternative is CIELch, which although
more complex offers a more accurate, but equally intuitive way of
specifying colours.

If you think of RGB space as a simple cube, with the red, green and blue
vectors as the three axis and imagine a line drawn through the cube centre
from black (0,0,0) to white (1,1,1) then HSI space is this cube tipped up
onto one corner so that the black - white line is vertical. Then the black
- white line becomes the intensity axis, the hue is given by an angle from
the intensity axis and the saturation is the distance from the central
intensity axis out to the colour point (the radius).
If you only want a simple way of selecting colour on an RGB display the
following transforms can be useful:

RGB to HSI

  I = (1/3)(R+G+B)

  S = 1 - (3/(R+G+B))*a    where a is the minimum of R, G and B

  H = cos^(-1) [(0.5*(R-G)+(R-B)) / ( ((R-G)^2 + (R-B)(G-B))^(0.5) )]

    If S = 0, H is meaningless.

    If (B/I) > (G/I) then H = 360 - H since H is an angle in degrees we
    then normalise to 0,1 with H=H/360

HSI to RGB

  First we restore H to degrees with H = 360H

  If 0 < H <= 120 then

      B = 1/3(1-S)
      R = 1/3(1+(S cos H) / ( cos(60 - H))
      G = 1 - (B+R)

  If 120 < H <= 240 then

      H = H - 120
      R = 1/3(1-S)
      G = 1/3(1+(S cos H) / ( cos(60 - H))
      B = 1 - (R+G)

  If 240 < H <= 360 then

      H = H - 240
      G = 1/3(1-S)
      B = 1/3(1+(S cos H) / ( cos(60 - H))
      R = 1 - (G+B)

for details of other HSI related spaces (HSL) see Foley and VanDam -
full reference in section 8.

Section [6]   TV and allied non-linear systems

All TV standards use non-linear signals, pre-corrected for the non-linear
transfer characteristic of the display CRT. It is here that the most
confusion exists, and so this is a VERY important section to understand.

A typical CRT has a non-linear voltage-to-light transfer function with a
power law usually denoted by gamma. The value of gamma is theoretically
2.5, but is specified as 2.2 in NTSC systems, 2.8 in PAL systems, and is
actually nearer to 2.35 for real CRTs. Any signal destined for display on
a CRT must be distorted by an inverse law. In practice, that is impossible
because a pure power law has infinite slope (gain) at zero (black). TV
systems limit the gain near black to a value between 4 and 5 by offsetting
the power law. This has the side advantage of increasing saturation in a way
that compensates for the display having a dark surround. For example the
ITU-BT.709 specification is:-

    Volts = (1 + a) * Light ^ (law) - a        for Light > b
    Volts = slope * Light                      for Light <= b
          where a=0.099, law=0.45, b=0.018.

and the gain at zero is 4.5. This law is similar to the formula used for L*
(see above).

So for accurate colour calculations, this law (or whichever law was actually
applied) must be undone to return to linear signals before doing conversions.
The law should be reapplied to the results to get the drive signals for the
actual display.

A signal that has been gamma-corrected is shown primed (Y', R', G', B' etc).
In general, undoing the gamma law will return to linear signals, but that
is not always true, especially with the Y' signal, which is not directly
related to the CIE Y value. It is a shame that the TV industry used Y' for
the luminance channel, because it created a great deal of confusion, most
of which still exists. But careful reading of the following section shows
the way to performing totally accurate colour calculations using any colour
system.

[6.1] European Y'U'V' (EBU)

European TV (PAL and SECAM coded) uses Y'U'V' components. Y' is similar to
perceived luminance, U' and V' carry the colour information and some
luminance information and are bipolar (they go negative as well as positive).
The symbols U and V here are not related to the U and V of CIE YUV (1960).

This coding is also used in some 525 line systems with PAL subcarriers,
particularly in parts of the Americas. The specification here is that of the
European Broadcasting Union (EBU). Y' has a bandwidth of 5 MHz in Europe,
5.5 MHz in UK. The U' and V' signals usually have up to 2.5 MHz bandwidth
in a component studio system, but can be as little as 600 kHz or less in a
VHS recorder. U' and V' always have the same bandwidth as each other. The
CRT gamma law is assumed to be 2.8, but camera correction laws are the same
as in all other systems (approximately 0.45). The system white point is D65,
the chromaticity coordinates are:

    R:      xr=0.64      yr=0.33
    G:      xg=0.29      yg=0.60
    B:      xb=0.15      yb=0.06
    White:  xn=0.312713  yn=0.329016

The conversion equations for linear signals are:-
    X = 0.431*R + 0.342*G + 0.178*B
    Y = 0.222*R + 0.707*G + 0.071*B
    Z = 0.020*R + 0.130*G + 0.939*B

    R = 3.063*X - 1.393*Y - 0.476*Z
    G =-0.969*X + 1.876*Y + 0.042*Z
    B = 0.068*X - 0.229*Y + 1.069*Z

the coding equations for non-linear signals are:
    Y'= 0.299*R' + 0.587*G' + 0.114*B'
    U'= 0.493*(B' - Y') =-0.147*R' - 0.289*G' + 0.436*B'
    V'= 0.877*(R' - Y') = 0.615*R' - 0.515*G' - 0.100*B'

    R'= Y' + 0.000*U' + 1.140*V'
    G'= Y' - 0.396*U' - 0.581*V'
    B'= Y' + 2.029*U' + 0.000*V'

The conversion equations between linear 709 RGB signals
(see later) and EBU RGB signals are:
    Re= 0.9578*R7 + 0.0422*G7 + 0.0000*B7
    Ge= 0.0000*R7 + 1.0000*G7 + 0.0000*B7
    Be= 0.0000*R7 + 0.0118*G7 + 0.9882*B7

    R7= 1.0440*Re - 0.0440*Ge + 0.0000*Be
    G7= 0.0000*Re + 1.0000*Ge + 0.0000*Be
    B7= 0.0000*Re - 0.0119*Ge + 1.0119*Be


[6.2] American Y'I'Q'

American TV (NTSC coded) uses Y'I'Q' components. Again Y' is similar to
perceived luminance, I' and Q' carry colour information and some luminance
information and are derived by rotating the U'V' vector formed by colour
coding as described in section 3.1 by 33 degrees. The Y' signal usually has
4.2 MHz bandwidth in a 525 line system. Originally the I' and Q' signals
were to have different bandwidths (0.5 and 1.5 MHz) but they now commonly
have the same bandwidth (1 MHz). The coding is also used in some 625 line
countries with NTSC subcarriers, again mostly in the Americas. The CRT
gamma law is assumed to 2.2. The system white pointis Illuminant C, the
chromaticity coordinates are:-
    R:      xr=0.67      yr=0.33
    G:      xg=0.21      yg=0.71
    B:      xb=0.14      yb=0.08
    White: xn=0.310063 yn=0.316158 zn=0.373779

The conversion equations for linear signals are:-
    X = 0.607*R + 0.174*G + 0.200*B
    Y = 0.299*R + 0.587*G + 0.114*B
    Z = 0.000*R + 0.066*G + 1.116*B

    R = 1.910*X - 0.532*Y - 0.288*Z
    G =-0.985*X + 1.999*Y - 0.028*Z
    B = 0.058*X - 0.118*Y + 0.898*Z

The coding equations for non-linear signals are:-
    Y'= 0.299*R' + 0.587*G' + 0.114*B'
    I'=-0.27*(B' - Y') + 0.74*(R' - Y') = 0.596*R' - 0.274*G' + 0.322*B'
    Q'= 0.41*(B' - Y') + 0.48*(R' - Y') = 0.212*R' - 0.523*G' - 0.311*B'

    R'= Y' + 0.956*I' + 0.621*Q'
    G'= Y' - 0.272*I' - 0.647*Q'
    B'= Y' - 1.105*I' + 1.702*Q'

It is possible to define a transformation matrix between EBU Y'U'V' and NTSC
Y'I'Q'. However, this only makes sense if the primaries are the same for the
two systems, and clearly they are defined differently. However, over the
years, the American NTSC system has changed its primaries several times
until they are now very similar to those of the EBU systems. The non-linear
connecting equations are:
     I'=-0.27/0.493*U' + 0.74/0.877*V' =-0.547667343*U' +  0.843785633*V'
     Q'= 0.41/0.493*U' + 0.48/0.877*V' = 0.831643002*U' +  0.547320410*V'

and:
     U'=-0.546512701*I' +  0.842540416*Q'
     V'= 0.830415704*I' +  0.546859122*Q'

To all intents and purposes these equations are identical and so one practical
set of equations can be used in either direction:
     I'=-0.547*U' + 0.843*V'
     Q'= 0.831*U' + 0.547*V'

     U'=-0.547*I' + 0.843*Q'
     V'= 0.831*I' + 0.547*Q'

The conversion equations relating NTSC RGB signals to EBU and 709 are:
    Rntsc= 0.6984*Rebu + 0.2388*Gebu + 0.0319*Bebu
    Gntsc= 0.0193*Rebu + 1.0727*Gebu - 0.0596*Bebu
    Bntsc= 0.0169*Rebu + 0.0525*Gebu + 0.8450*Bebu

    Rebu= 1.4425*Rntsc - 0.3173*Gntsc - 0.0769*Bntsc
    Gebu=-0.0275*Rntsc + 0.9350*Gntsc + 0.0670*Bntsc
    Bebu=-0.0272*Rntsc - 0.0518*Gntsc + 1.1081*Bntsc

and:
    Rntsc= 0.6698*R709 + 0.2678*G709 + 0.0323*B709
    Gntsc= 0.0185*R709 + 1.0742*G709 - 0.0603*B709
    Bntsc= 0.0162*R709 + 0.0432*G709 + 0.8551*B709

    R709= 1.5073*Rntsc - 0.3725*Gntsc - 0.0832*Bntsc
    G709=-0.0275*Rntsc + 0.9350*Gntsc + 0.0670*Bntsc
    B709=-0.0272*Rntsc - 0.0401*Gntsc + 1.1677*Bntsc

[6.3] SMPTE-C RGB

SMPTE-C is the current colour standard for broadcasting in America, the old
NTSC standard for primaries is no longer in wide use because the primaries
of the system have gradually shifted towards those of the EBU
(see section 6.2). In all other respects, SMPTE-C is the same as NTSC.
The CRT gamma law is assumed to be 2.2. The white point is now D65, and
the chromaticities are:

    R:     xr=0.630     yr=0.340
    G:     xg=0.310     yg=0.595
    B:     xb=0.155     yb=0.070
    White: xn=0.312713  yn=0.329016

The conversion equations for linear signals are:
    X = 0.3935*R + 0.3653*G + 0.1916*B
    Y = 0.2124*R + 0.7011*G + 0.0866*B
    Z = 0.0187*R + 0.1119*G + 0.9582*B

    R = 3.5058*X - 1.7397*Y - 0.5440*Z
    G =-1.0690*X + 1.9778*Y + 0.0352*Z
    B = 0.0563*X - 0.1970*Y + 1.0501*Z

The coding equations for non-linear signals are the same as for NTSC:
    Y'= 0.299*R' + 0.587*G' + 0.114*B'
    I'=-0.27*(B' - Y') + 0.74*(R' - Y') = 0.596*R' - 0.274*G' + 0.322*B'
    Q'= 0.41*(B' - Y') + 0.48*(R' - Y') = 0.212*R' - 0.523*G' - 0.311*B'

    R'= Y' + 0.956*I' + 0.621*Q'
    G'= Y' - 0.272*I' - 0.647*Q'
    B'= Y' - 1.105*I' + 1.702*Q'

and the same conversion equations work between EBU and SMPTE-C components:
    I'=-0.547*U' + 0.843*V'
    Q'= 0.831*U' + 0.547*V'

    U'=-0.547*I' + 0.843*Q'
    V'= 0.831*I' + 0.547*Q'

The conversion equations relating SMPTE-C RGB signals to EBU and 709 signals
are:
    Rsmptec= 1.1123*Rebu - 0.1024*Gebu - 0.0099*Bebu
    Gsmptec=-0.0205*Rebu + 1.0370*Gebu - 0.0165*Bebu
    Bsmptec= 0.0017*Rebu + 0.0161*Gebu + 0.9822*Bebu

    Rebu= 0.9007*Rsmptec + 0.0888*Gsmptec + 0.0105*Bsmptec
    Gebu= 0.0178*Rsmptec + 0.9658*Gsmptec + 0.0164*Bsmptec
    Bebu=-0.0019*Rsmptec - 0.0160*Gsmptec + 1.0178*Bsmptec

and:
    Rsmptec= 1.0654*R709 - 0.0554*G709 - 0.0010*B709
    Gsmptec=-0.0196*R709 + 1.0364*G709 - 0.0167*B709
    Bsmptec= 0.0016*R709 + 0.0044*G709 + 0.9940*B709

    R709= 0.9395*Rsmptec + 0.0502*Gsmptec + 0.0103*Bsmptec
    G709= 0.0178*Rsmptec + 0.9658*Gsmptec + 0.0164*Bsmptec
    B709=-0.0016*Rsmptec - 0.0044*Gsmptec + 1.0060*Bsmptec

[6.4] ITU.BT-601 Y'CbCr

This is the international standard for digital coding of TV pictures at 525
and 625 line rates. It is independent of the scanning standard and the
system primaries, therefore there are no chromaticity coordinates, no CIE
XYZ matrices, and no assumptions about white point or CRT gamma. It deals
only with the digital representation of R'G'B' signals in Y'CbCr form.
The non-linear coding matrices are:

    Y'= 0.299*R' + 0.587*G' + 0.114*B'
    Cb=-0.169*R' - 0.331*G' + 0.500*B'
    Cr= 0.500*R' - 0.419*G' - 0.081*B'

    R'= Y' + 0.000*U' + 1.403*V'
    G'= Y' - 0.344*U' - 0.714*V'
    B'= Y' + 1.773*U' + 0.000*V'


[6.5] ITU.BT-709 HDTV studio production in Y'CbCr

This is a recent standard, defined only as an interim standard for HDTV
studio production. It was defined by the CCIR (now the ITU) in 1988, but is
not yet recommended for use in broadcasting. The primaries are the R and B
from the EBU, and a G which is midway between SMPTE-C and EBU. The CRT gamma
law is assumed to be 2.2. White is D65. The chromaticities are:
    R:      xr=0.64       yr=0.33
    G:      xg=0.30       yg=0.60
    B:      xb=0.15       yb=0.06
    White:  xn=0.312713   yn=0.329016

The conversion equations for linear signals are:
    X = 0.412*R + 0.358*G + 0.180*B
    Y = 0.213*R + 0.715*G + 0.072*B
    Z = 0.019*R + 0.119*G + 0.950*B

    R = 3.241*X - 1.537*Y - 0.499*Z
    G =-0.969*X + 1.876*Y + 0.042*Z
    B = 0.056*X - 0.204*Y + 1.057*Z

The coding equations for non-linear signals are:
    Y'= 0.2215*R' + 0.7154*G' + 0.0721*B'
    Cb=-0.1145*R' - 0.3855*G' + 0.5000*B'
    Cr= 0.5016*R' - 0.4556*G' - 0.0459*B'

    R'= Y' + 0.0000*Cb + 1.5701*Cr
    G'= Y' - 0.1870*Cb - 0.4664*Cr
    B'= Y' - 1.8556*Cb + 0.0000*Cr

The conversion equations between linear 709 RGB signals and EBU RGB signals
are:
    Re= 0.9578*R7 + 0.0422*G7 + 0.0000*B7
    Ge= 0.0000*R7 + 1.0000*G7 + 0.0000*B7
    Be= 0.0000*R7 + 0.0118*G7 + 0.9882*B7

    R7= 1.0440*Re - 0.0440*Ge + 0.0000*Be
    G7= 0.0000*Re + 1.0000*G7 + 0.0000*Be
    B7= 0.0000*Re - 0.0119*Ge + 1.0119*Be


[6.6] SMPTE-240M Y'PbPr

This one of the developments of NTSC component coding, in which the B primary
and white point were changed. The CRT gamma law is assumed to be 2.2. The
white point is D65, chromaticity coordinates are:
    R:      xr=0.67     yr=0.33
    G:      xg=0.21     yg=0.71
    B:      xb=0.15     yb=0.06
    White:  xn=0.312713 yn=0.329016

The conversion equations for linear signals are:
    X = 0.567*R + 0.190*G + 0.193*B
    Y = 0.279*R + 0.643*G + 0.077*B
    Z = 0.000*R + 0.073*G + 1.016*B

    R = 2.042*X - 0.565*Y - 0.345*Z
    G =-0.894*X + 1.815*Y + 0.032*Z
    B = 0.064*X - 0.129*Y + 0.912*Z

The coding equations for non-linear signals are:
   Y'= 0.2122*R' + 0.7013*G' + 0.0865*B'
   Pb=-0.1162*R' - 0.3838*G' + 0.5000*B'
   Pr= 0.5000*R' - 0.4451*G' - 0.0549*B'

   R'= Y + 0.0000*Pb + 1.5756*Pr
   G'= Y - 0.2253*Pb + 0.5000*Pr
   B'= Y + 1.8270*Pb + 0.0000*Pr

The conversion equations relating SMPTE 240 RGB to EBU and 709 primaries are:
    R240= 0.7466*Re + 0.2534*Ge + 0.0000*Be
    G240= 0.0187*Re + 0..9813*Ge + 0.0000*Be
    B240= 0.0185*Re + 0.0575*Ge + 0.9240*Be

    Re= 1.3481*R240 - 0.3481*G240 + 0.0000*B240
    Ge=-0.0257*R240 + 1.0257*G240 + 0.0000*B240
    Be=-0.0254*R240 - 0.0568*G240 + 1.0822*B240

and:
    R240= 0.7151*R709 + 0.2849*G709 + 0.0000*B709
    G240= 0.0179*R709 + 0.9821*G709 + 0.0000*B709
    B240= 0.0177*R709 + 0.0472*G709 + 0.9350*B709

    R709= 1.4086*R240 - 0.4086*G240 + 0.0000*B240
    G709=-0.0257*R240 + 1.0457*G240 + 0.0000*B240
    B709=-0.0254*R240 - 0.0440*G240 + 1.0695*B240


[6.7] Kodak PhotoYCC colour space for PhotoCD images.

The Kodak PhotoYCC colour space was designed for encoding images with the
PhotoCD system. It is based on both CCIR Recommendations 709 and 601-1,
having a colour gamut defined by the CCIR 709 primaries and a luminance
- chrominance representation of colour like CCIR 601-1's YCbCr.

To encode data, a transfer function (gamma correction) is first applied;

For R,G,B > 0.018
R' = 1.099*R ^0.45 - 0.099
G' = 1.099*G ^0.45 - 0.099
B' = 1.099*B ^0.45 - 0.099

For R,G,B, <= 0.018
R' = 4.5*R
G' = 4.5*G
B' = 4.5*B

Secondly the R'G'B' data is transformed into PhotoYCC data,

    Luma    = 0.299R'  + 0.587G' + 0.114B'
    Chroma1 = -0.299R' - 0.587G' + 0.886B'
    Chroma2 = 0.701R'  - 0.587G' - 0.114B'

Finally the floating point values are stored as 8 bit integers;

    Luma_8bit       = (255 / 1.402)Luma
    Chroma1_8bit    = 111.40*Chroma1 + 156
    Chroma2_8bit    = 135.64*Chroma2 + 137

The unbalanced scale difference between Chroma1 and Chroma2 is designed,
according to Kodak, to follow the typical distribution of colours in
real scenes.

Kodak YCC can store more information than current display devices can cope
with (it allows negative RGB values), the transforms from YCC to RGB are
therefore not simply the inverse of RGB to YCC, they depend on the target
display system.

Converting PhotoYCC data to RGB 24bit data for display by computers on CRT's
is achieved as follows;

Firstly normal Luma and Chroma data are recovered;

    Luma            = 1.3584 * Luma_8bit
    Chroma1         = 2.2179 * (Chroma1_8bit - 156)
    Chroma2         = 1.8215 * (Chroma2_8bit - 137)

For display primaries that are, or are very close to, CCIR
Recommendation 709 primaries in their chromaticities, then

    R'      = L + Chroma2
    G'      = L - 0.194Chroma1 - 0.509Chroma2
    B'      = L + Chroma1
Two things to watch are;

a) this results in RGB values from 0 to 346 (instead of the more usual 0 to
255) a look-up-table is usually used to convert these through a non-linear
function to 8 bit data. For example;

    Y  = (255/1.402)*Y'
    C1 = 111.40*C1'+156
    C2 = 135.64*C2'+137

b) if the display phosphors differ from CCIR 709 primaries then further
conversion will be necessary, possibly through an intermediate device
independent colour space such as CIE XYZ.

Converting stored PhotoYCC data to RGB signal voltages for display on
television's is achieved as follows;

Firstly  normal Luma and Chroma data are recovered;

    Luma            = 1.3584 * Luma_8bit
    Chroma1         = 2.2179 * (Chroma1_8bit - 156)
    Chroma2         = 1.8215 * (Chroma2_8bit - 137)

the RGB display voltages are then as follows;

    R'      = (L + Chroma2) / 353.2
    G'      = (L - 0.194Chroma1 - 0.509Chroma2) / 353.2
    B'      = (L + Chroma1) / 353.2

Note, the gamma corrected RGB values (R'G'B') are fine so long as you haven't
done anything silly - like calibrate you CRT for linear luminance :)

Section [7] Colour appearence.

When a colour is measured using the CIE system it can be defined in such a
way that it can be reproducted exactly. This is because the CIE system
defines the conditions and mechanism of the measurement of a colour, for
example the exact type of illumination and geometry is specified. However,
even though a colour has set CIE co-ordinates, it will still appear to
an observer to be different as its surround or the ambient lighting change.
This has serious consequences for digital colour spaces. For example
when printing the conversion from RGB to CMY(K) may be perfect but the
viewing conditions of the screen and hard copy will be different. The
display may have a white point of around 8000k with ambient lighting
provided by fluorescent tubes while the print may by displayed in a
tungsten lit gallerey - oh dear! So although you may have a colour
match in terms of CIE co-ordinates, the colours may _appear_ to differ.

There is a possible solution, but it is complex so a brief summary only is
given here. Essentially a colour appearence space (as opposed to a simple
colour space) is required. There are a few of these around, for example
Hunt's colour appearence space with is based on his model of colour vision
and is explained in his book "Measuring Colour". Hunt's model is designed
to predict the appearence of a colour under different viewing conditions
based on colorimetry of five different regions of the visible scene.

Section [8] The references and bedtime reading.

[*]'ed are recommended.

   Notes on conversion between RGB pixel values and CIE co-ordinates.

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

"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.

[*] "CRT Colorimetry:Part 1 Theory and Practice, Part 2 Metrology", Berns,
R.S., Motta, R.J. and Gorzynski, M.E., Color Research and Application, 18,
(1993).

   Standard references on colour science.

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

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

[*] "Measuring Colour" second edition, R.W.G. Hunt, Ellis Horwood 1991.

   References specific to colour in television and in computers.

[*] "Colour Science in Television and Display Systems" Sproson, W, N,
Adam Hilger Ltd, 1983. ISBN 0-85274-413-7

[*] "Effective Color Displays. Theory and Practice", Travis, D, Academic Press,
1991. ISBN 0-12-697690-2
This contains C source code for many colour space conversions.


[pearson]

[computer generated colour]

   Colour and printing.

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

   Display non-linearity and gamma.

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

   Colour in Digital Image Processing and Computer Graphics.

"Digital Image Processing", Rafael C. Gonzalez and Richard E. Woods,
Addision Wesley, 1992. Chapter 4.6

"Fundamentals of Digital Image Processing", Anil K. Jain, Prentice-Hall
International, 1989. Chapter 3.

"Computer graphics : principles and practices" James D. Foley, et al.
2nd ed. Addison-Wesley, c1990.

   Others.

"On the Gun Independence and Phosphor Consistency 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

"Fully Utilizing Photo CD Images, Article No. 4,
PhotoYCC Colour Encoding and Compression Schemes" Eastman Kodak Company,
Rochester NY (USA) (1993).

   On-line references and links.

CIE
   http://www.hike.te.chiba-u.ac.jp/ikeda/CIE/home.html

Charles Poynton's Color and Gamma FAQ page
   http://www.inforamp.net/~poynton/Poynton-colour.html

University of Derby, Colour Research Group. (RWG Hunt)
   http://ziggy.derby.ac.uk:80/colour/

This document
   ftp://ftp.wmin.ac.uk/pub/itrg/coloureq.txt
   or via http://www.wmin.ac.uk/ITRG

Section [8] Footnotes & Disclaimer.

Thanks to everyone who contributed, especially to Charles Poynton
([e-mail]) and David Wooding ([e-mail]) for
helpful comments. Feel free to send comments, suggestions, additions,
flames, etc to [e-mail].

Bits to add.

 Proper details of CMY(K) conversions
 Colour Management Systems
 Gamut Mapping
 Add your topics here!

If we've made any mistakes, please let us know, however we take no
reponsibility for them. Opinions expressed are not those of either
the British Broadcasting Corporation nor the University of Westminster.
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