Path: senator-bedfellow.mit.edu!turing!bourgin
From: dbourgin@turing.imag.fr (David Bourgin (The best player).)
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Subject: Color space FAQ
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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 rtfm.mit.edu: /pub/usenet/news.answers/graphics/colorspace-faq
or turing.imag.fr: /pub/compression/colorspace-faq
Keywords: Color space FAQ
X-Last-Updated: 1995/03/06
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Last-modified: 28/2/95
###########################################################
Color spaces FAQ - David Bourgin
Date: 28/1/95 (Major modifications)
Last update: 6/1/95 (23/1/95: minor modifications)
---------------------------
Table of contents
---------------------------
1 - Purpose of this FAQ
2 - Some definitions
3 - What is an image based on a color look-up table (LUT)?
4 - What is this gamma component?
5 - Color space conversions
5.1 - RGB, CMY, and CMYK
5.2 - HSI and related color spaces
5.3 - CIE XYZ and gray level (monochrome included) pictures
5.4 - CIE Luv and CIE Lab
5.5 - LCH and CIE LSH
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 (D. Bourgin)
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 information about that.
I aim to cover a part of the Frequently Asked Questions (FAQ) in the video
works, it means to provide some (useful?) information about the colors,
and more especially about color spaces. If you have some information
to ask/add to this document, please read item 7.
2 - Some definitions (A. Ford, D.Bourgin)
Color is defined as an experience in human perception. In physics terms, a
color is the result of an observed light on the retina of the eye. The
light must have a wavelength in the range of 400 to 700 nm. The radient
flux of observed light at each wavelength in the visible spectrum is
associated to a Spectral Power Distribution (SPD).
An SPD is created by cascading the SPD of the light source with the
Spectral Reflectance of the object in the scene. In addition the optics of
any imaging device will have an effect.
Strictly though, color is a visual sensation, so a `color' is created
when we observe a specific SPD.
We see color by means of cones in the retina. There are three types of
cones sensitive to wavelengths that approximately correspond to red, green
and blue light. Together with information from rod cells (which are not
sensitive to color) the cone information is encoded and sent to higher
brain centres along the optic nerve. The encoding, known as opponent
process theory, consists of three opponent channels, these are:
Red - Green
Blue - Yellow
Black - White
Note: Actually, recent studies show that eyes use addtionnal cone types.
(cf. "La Recherche", n.272, january, 1995)
This is different to tri-chromatic theory (e.g. Red, Green, Blue additive
color) which you may be used to, but when we describe colors we do not say
"it is a reddy green" or "that's a bluey yellow".
Perceptually we require three attributes to describe a color. Generally
any three will do, but there need's to be three.
For human purpose color descriptions these attributes have been by the CIE
recommendations, as follows:
Brightness. The attribute of a visual sensation according to which an area
appears to exhibit more or less light. You can blurry or enhance an image
by modifying this attribute.
Hue. The attribute of a visual sensation according to which an area appears
to be similar to one, or to proportions of two, of the perceived colors
red, yellow, green and blue.
Colorfulness. The attribute of a visual sensation according to which an
area appears to exhibit more or less of its hue. You can go from a sky blue
to a deep blue by changing this attribute.
So, a color is a visual sensation produced by a stimulus which is a
specific SPD. It should be noted however, that two different SPD's may
produce the same visual sensation - an effect known as metarmerism.
What is a color space?
A color space is a method by which we can specify, create and visualise
color. As human's, we may define a color by its attributes of brightness,
hue and colorfulness. A computer will define a color in terms of the
excitations of red, green and blue phosphors on the CRT faceplate. A
printing press defines color in terms of the reflectance and absorbance of
cyan, magenta, yellow and black inks on the paper.
If we imagine that each of the three attributes used to describe a color
are axes in a three dimensional space then this defines a color space.
The colors that we can percieve can be represented by the CIE system, other
color spaces are subsets of this perceptual space. For instance RGB color
space, as used by television displays, can be visualised as a cube with
red, green and blue axes. This cube lies within our perceptual space, since
the RGB space is smaller and represents less colors than we can see. CMY
space would be represented by a second cube, with a different orientation
and a different position within the perceptual space.
So, a color space is a mathematical representation of our perceptions. E.g.
RGB is a tri-dimensional space with red, green and blue axes. It's useful
to think so because computers are in fond of numbers and equations...
Why is there more than one color space?
Different color spaces are better for different applications, some
equipment has limiting factors that dictate the size and type of color
space that can be used. Some color spaces are perceptually linear, i.e. a
10 unit change in stimulus will produce the same change in perception
wherever it is applied. Many color spaces, particularly in computer
graphics are not linear in this way. Some color spaces are intuitive to
use, i.e. it is easy for the user to navigate within them and creating
desired colors is relativly easy. Finally, some color spaces are device
dependent while others are not (so called device independent).
What's the difference between device dependent and device independent?
A device dependent color space is a color space where the color produced
depends on the equipment and the set-up used to produce it. For example the
color 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
change your monitor the red, green and blue phosphors will have slightly
different SPD's and the color produced will change. Thus RGB is a color
space that is dependent on the system being used, it is device dependent.
A device indepent color space is one where the coordinates used to specify
the color will produce the same color wherever they are applied.
An example of a device independent color space (if it has been implemented
properly) is the CIE L*a*b* color space (known as CIELab). This is based on
the HVS as described by the CIE system (see below to know what CIE stands
for).
Another way of looking a device dependancy is to imagine our RGB cube
within our perceptual color space. We define a color by the values on the
three axes. However the exact color will depend on the position of the cube
within the perceptual color space, move the cube (by changing the set-up)
and the color will change even if the RGB values remain the same.
Some device dependent color spaces have their position within CIE space
defined, these are known as device callibrated color spaces and are a kind
of half way house between dependent and independent color 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. callibrated to specific devices. In other words, if you have a
device independent color space, you must adapt your device as defined in
the color space and not the color space to the device.
What is a color gamut?
A color gamut is the boundary of the color space. Gamut's are best
shown and evaluated using the CIE system.
What is the CIE System?
The CIE has defined a system that classifies color according to the HVS (it
started producing specifications in 1931). Using this system we can specify
any color in terms of its CIE coordinates.
The CIE system works by weighting the SPD of an object in terms of three
color 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 1nm
intervals. However, the illuminant, and lighting and viewing geometry are
carefully defined. This process produces three CIE tri-stimulus values,
XYZ, which describe the color.
There are many measures that can be derived from the tri-stimulus values,
these include chromaticity coordinates and color spaces.
What color space should I use?
That depends on what you want to do, but heres a list of the pros and cons
of some of the more common, computer related, color spaces - we will see
in item 5 how to convert the (most common) color spaces between
themselves - :
RGB (Red Green Blue)
Additive color system based on trichromatic theory, commonly used by CRT
displays where proportions of excitation of red, green and blue emmiting
phosphors produce colors 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 color. Used in printing and photography. Printers often include
the fourth component, black ink, to improve the color 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 color spaces, alternatives include HSI
(intensity), HSV (value), HCI (chroma / colorfulness), HVC, TSD (hue
saturation and darkness) etc etc. All these color spaces are non-linear
transforms from RGB they are thus, device dependent, non-linear but very
intuitive. In addition the seperation 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 color spaces)
YIQ, YUV, YCbCr, YCC (Luminance - Chrominance)
These are the television transmission color spaces (YIQ and YUV analogue
(NTSC and PAL) and YCbCr digital). They separate luminance from chrominance
(lightness from color) and are useful in compression and image processing
applications. YIQ and YUV are, if used according to their relative
specifications, linear. They are all device dependent and, unless you are a
TV engineer, unintuitive. Kodaks PhotoCD system uses a type of YCC color
space, PhotoYCC, which is a device calibrated color space.
CIE
The HVS based color specification system. There are two CIE based color
spaces, CIELuv and CIELab. They are near linear (as close as any color
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. CIELuv has an associated chromaticity
diagram, a two dimensional chart which makes additive color mixing very
easy to visualise, hence CIELuv is widely used in additive color
applications, like television.
CIELab has no associated two dimensional chromaticity diagram and no
correlate of saturation so only Lhc can be used.
Since there is such a wide variet of color spaces, its useful to understand
a bit more about them and how to convert between them.
The color space conversions are essentially provided for programmers. If
you are a specialist then skip to the references in item 6. Many of the
conversions are based on linear matrix transforms. (Was it Jim Blinn who
said that any problem in computer graphics can be solved by a matrix
transform ?). As an example:
E.g. RGB -> CIE XYZccir601-1 (D65) 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 1.111 |
and CIE XYZccir601-1 (D65) -> RGB provides the following matrix:
| 1.910 -0.5338 -0.2891 |
| -0.9844 1.9990 -0.0279 |
| 0.0585 -0.1187 -0.9017 |
These two matrices are the (approximate) inversion of each other. If you
are a beginner in this mathematical stuff, skip the previous explainations,
and just use the results...
Other definitions.
Photometric terms: illuminance - luminous flux per unit area incident on
a surface
luminance - luminous flux per unit solid angle and
per unit projected area, in a given
direction, at a point on a surface.
luminous flux - radient flux weighted by the V(landa)
function.
I.e. weighted by the eye's sensitivity.
radient flux - total power / energy of the incident
radiation.
Other terms: brightness - the human sensation by which an area
exhibits more or less light.
lightness - the sensation of an area's brightness
relative to a reference white in the
scene.
chroma - the colorfulness of an area relative to
the brightness of a reference white.
saturation - the colorfulness of an area relative to
its brightness.
Note: This list is not exhaustive, some terms have alternative meanings
but we assume these to be the fundamentals.
3 - What is an image based on a color look-up table (LUT)?
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. This table is usually small. 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 (LUT or CLUT).
4 - What is this gamma component?
Many image processing operations, and also color space transforms that
involve device independent color 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. CRTa will have a non-linear response.
The luminance of a CRT is generally modelled 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 (Richard Salmon and Alan Roberts) have shown that the actual
value of gamma is very dependent upon the accurate setting of the CRTs
black level. For correctly set-up CRTs gamma is 2.35 +/- 0.1. This
relationship is given as follows:
Luminance = voltage ^ gamma
Where luminance and voltage are normalised. For Liquid Crystal Displays the
response is more closely followed by an "S" shaped curve with a vicious
hook near black and a slow roll-off near white.
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 reciever 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 color 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 color 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 componsate 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 color channels,
however for precise applications they must be measured for each channel
separatley.
It is common to perform gamma correction by calculating the corrected value
for each possible input value and storing this in an array as a Look Up
Table (see item 3). In some cases the LUT is part of the graphics card, in
others it needs to be implemented in software.
Research by Cowan and Post (see references in item 6) has shown that not
all CRT displays can be accurately modelled by a simple power relationship.
Cowan found errors of up to 100% between measured and calculated values. To
prevent this a simple LUT generating gamma correction function cannot be
used. The best method is to measure the absolute luminance of the display
at various pixel values and to linearily interpolate between them to
produce values for the LUT.
It should be noted at this point that correct gamma correction depends on a
number of factors, in addition to the characteristics of the CRT display.
These include the gamma of the input device (scanner, video grabber etc),
the viewing conditions and target tone reproduction characteristics. In
addition linear luminance is not always desirable, for computer generated
images a system which is linear with our visual perception may be
preferable. If luminance is represented by L then lightness, our visual
sensation of an objects brightness relative to a similarly illuminated
area that appears white is given by L:
{ L=116*((Y/Yn)^(1/3))-16 if Y/Yn>0.008856
{ L=903.3*Y/Yn if Y/Yn<=0.008856
This relationship is in fact the CIE 1976 Lightness (L*) equation which will
be discussed in section 5.4.
Most un-gamma corrected displays have a near linear L* response, thus for
computer generated applications, or applications where pixel values in an
image need to be intuitivly changed, this set up may be better.
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) produced a
drop in the number of grey levels from 245 to 196. 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 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.
-> not to to be confused with gamma.
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 known as additive primary colors, because a color is produced by
adding different qunatities of the three components, red, green, and blue.
CMY are known as subtractive (or secondary) colors, because the color is
generated by subtracting different quantities of cyan, magenta and yellow
from white light.
The primaries used by artists, red, yellow and blue are different because
they are concerned with mixing pigments rather than lights or dyes.
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 transforms from CMY to CMYK (and vice
versa) are given as shown 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) |
Note, these differ to the descriptions often given, for example in Adobe
Postscript. For more information see FIELD in section 6. This is because
Adobe doesn't choose to use the most recent equations. (I don't know why!)
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 - HSI and related color spaces
The representation of the colors in the RGB and CMY(K) color spaces are
designed for specific devices. But for a human observer, they are not
useful definitions. For user interfaces a more intuitive color space,
designed for the way we actually think about color is to be preferred.
Such a color space is HSI; Hue, Saturation and Intensity, which can be
thought of as an RGB cube tipped up onto one corner. The line from RGB=min
to RGB=max becomes verticle and is the intensity axis. The position of a
point on the circumference of a circle around this axis is the hue and the
saturation is the radius from the central intensity axis to the color.
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 (Intensity=0 at the top of the apex and =1 at the base of the cone)
The big disadvantage of this model is the conversion which is mainly
because the hue is expressed as an angle. The transforms are given below:
Hue = (Alpha-arctan((Red-intensity)*(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
Intensity = (Red+Green+Blue)/3
Note that you have to compute Intensity *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
(steyaert@vvs.innet.be).
Another model close to HSI 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. ;-)
Actually, here are many variations on HSI, e.g. HSL, HSV, HCI (chroma /
colorfulness), HVC, TSD (hue saturation and darkness) etc. But they all
do basically the same thing.
5.3 - CIE XYZ and gray level pictures
The CIE (presented in the item 2) has defined a human "Standard Observer",
based on measurements of the colour-matching abilities of the average human
eye. Using data from measurements made in 1931, a system of three primaries,
XYZ, was developed in which all visible colours can be represented using
only positive values of XY and Z. The Y primary is identical to Luminance,
X and Z give colouring information. This forms the basis of the CIE 1931
XYZ colour space, which is fundamental to all colorimetry. It is completely
device-independant and values are normally assumed to lie in the range
[0;1]. Colours are rarely specified in XYZ terms, it is far more common to
use "chromaticity coordinates" which are independant of the Luminance (Y).
The main advantage of CIE XYZ, and any color space or color definition
based on it, is that it is completely device independent. The main
disadvantage with CIE based spaces is the complexity of implementing them,
in addition some are not user intuitive. A complete description of the CIE
system is beyond the scope of this FAQ, we simply present useful formula to
convert between CIE values and between CIE and non-CIE color spaces. We
cannot recommend too highly that anyone wishing to implement any of the CIE
system in the digital domain reads the refs in section 6, specifically HUNT
1, SPROSON, BERNS and CIE 1.
Chromaticity coordinates are derived from tristimulus values (the amounts
of the primaries) by normalising thus:
x = X/(X+Y+Z)
y = Y/(X+Y+Z)
z = Z/(X+Y+Z)
Chromaticity coordinates are *always* used in lower case. Because they have
been normalised, only two values are needed to specify the colour, and so z
is normally discarded (because x+y+z=1). Colours can be plotted on a
"chromaticity diagram" using x and y as coordinates, with Y (Luminance)
normal to the diagram. When a colour is specified in this form, it is
referred to as CIE 1931 Yxy. Tristimulus values can always be derived from
Yxy values:
X = x*Y/y
Z = (1-x-y)*Y/y
For scientists and programers, it is possible to convert between RGB as
displayed on a CRT and CIE tristimulus values.
The first step is to ensure that you have either linear luminance
information, or that you know the transfer function (gamma correction) of
the display device. For further details on this see section 4. This will
give you the luminances of the red, green and blue phosphor emissions from
the red, green and blue pixel values that you specify.
The second stage is to perform a matrix transform (see item 5) to convert
the red, green, blue luminance information to CIE XYZ tristimulus values,
essentially. We can apply Grassman's Laws to establish conversion matrices
between the XYZ primaries and any other set of primaries, for instance (if
we consider RGB):
|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 (phosphors on *your* CRT).
Ideally you would measure these - if you have a colorimeter or a
spectroradiometer / spectrophotometer handy. Alternativly you could assume
that your system corresponds to a particular specification, e.g. NTSC, and
use the figures given by the standard, however this is often not a valid
assumption - and if you need to make it it's probably not worth going to
the effort of implementing the transforms, the error's induced would outway
any advantages of the CIE system. The third method is to derive the figures
from other data.
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, we just consider:
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|
(1) becomes by invoking the white balance condition (Red=Green=Blue=1 for
white):
|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|
Now, xn, yn, zn, xr, yr, zr, xg, yg, zg, xb, yb, and zb are all known
because they are supplied. Multiplying the chromaticity coordinates by
these values gives the the matrix in equation (1) (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
You should remember that these transforms are only valid if you have
equipment that matches these specifications, or you have images that you
know have been encoded to these standards. If this is not the case, the
CIE values you calculate will not be true CIE.
All these conversions are presented noit just as demonstrations, they can
be used for conversion between systems ;-).
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, alternativly, you can average the three color components so:
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 loss.
5.4 - CIE Luv and CIE Lab
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)) with Y/Yn>0.008856
{ L* = 903.3*Y/Yn with 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.
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))-16 if Y/Yn>0.008856
{ L=903.3*Y/Yn if 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) with Y/Yn>0.008856
{ f(t)=7.787*t+16/116 with Y/Yn<=0.008856
See also item 5.3 about Xn, Yn, and Zn.
5.5 - LCH and CIE LSH
CIELab and CIELuv both have a disadvantage if used for a user interface,
they are unintuitive to use. To solve this we can use CIE definitions for
chroma, c, Hue angle, h and saturation, s (see section 1). Hue, chroma and
saturation can be derived from CIELuv, and Hue and chroma but *NOT*
saturation can be derived from CIELab (this is because CIELab has no
associated chromaticity diagram and so no correlation of saturation is
possible).
To distinguish between LCH derived from CIELuv and CIELab the values of
Hue, H, and Chroma, C, are given the subscripts uv if from CIELuv and ab
if from CIELab.
CIELab -> LCH
L = L*
C = (a*^2+b*^2)^0.5
{ H=0 if a=0
{ H=(arctan((b*)/(a*))+k*PI/2)/(2*PI) if 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
CIELuv -> LCH
L = L*
C = (u*^2 + v*^2)^0.5 or C = L*s
H = arctan[(v*)/(u*)]
{ H=0 if u=0
{ H=(arctan((v*)/(u*))+k*PI/2)/(2*PI) if u#0 (add PI/2 to H if H<0)
{ and { k=0 if u*>=0 and v*>=0
{ or k=1 if u*>0 and v*<0
{ or k=2 if u*<0 and v*<0
{ or k=3 if u*<0 and v*>0
CIELuv -> CIE LSH
L = L*
s = 13[(u' - u'n)^2 + (v' - v'n)^2]^0.5
H = arctan[(v*)/(u*)]
{ H=0 if u=0
{ H=(arctan((v*)/(u*))+k*PI/2)/(2*PI) if u#0 (add PI/2 to H if H<0)
{ and { k=0 if u*>=0 and v*>=0
{ or k=1 if u*>0 and v*<0
{ or k=2 if u*<0 and v*<0
{ or k=3 if u*<0 and v*>0
5.6 - The associated standards: YUV, YIQ, and YCbCr
YUV and YIQ are standard color spaces used for analogue television
transmission. YUV is used in European TVs (PAL) and YIQ in North American
TVs (NTSC). These colors spaces are device-dependent, like RGB, but they
are callibrated. This is because the primaries used in these television
systems are specified by the relative standards authorities. Y is the
luminance component and is usually referred to as the luma component (it
comes from CIE standard), U,V or I,Q are the chrominance components (i.e.
the color signals).
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 | 0.2989 | 0.5867 | 0.1144 |
| Rec 709 | 0.2126 | 0.7152 | 0.0722 |
| ITU | 0.2220 | 0.7067 | 0.0713 |
+----------------+---------------+-----------------+----------------+
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+0.5867*Green+0.1144*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
Additional note: Tom Lane provided me implementation of the Baseline JPEG
compression system but after a close look I understood that their values
was an approximation of the previous values (you should preferr mine ;-).).
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 gives 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
The Kodak PhotoYCC color space was designed for encoding images with the
PhotoCD system. It is based on both ITU Recommendations 709 and 601-1,
having a color gamut defined by the ITU 709 primaries and a luminance -
chrominance representation of color like ITU 601-1's YCbCr. The main
attraction of PhotoYCC is that it calibrated color space, each image being
tracable to Kodak's standard image-capturing device and the CIE Standard
Illuminant for daylight, D65. In addition PhotoYCC provides a color gamut
that is greater than that which can currently be displayed, thus it is
suitable not only for both additive and subtractive (RGB and CMY(K))
reproduction, but also for archieving since it offers a degree of
protection against future progress in display technology.
Images are scanned by a standardised image-capturing device, calibrated
accoring to the type of photographic material being scanned. The scanner is
sensitive to any color currently producable by photographic materials (and
more besides). The image is encoded into a color space based on the ITU
Rec 709 reference primaries and the CIE standard illuminant D65 (standard
daylight). The extended color gamut obtainable by the PhotoCD system is
achieved by allowing both positive and negative values for each primary.
This means that whereas conventional ITU 709 encoded data is limited by
the boundary of the triangle linking the three primaries (the color gamut),
PhotoYCC can encode data outside the boundary, thus colors that are not
realiseable by the CCIR primary set can be recorded. This feature means
that PhotoCD stores more information (as a larger color gamut) than
current display devices, such as CRT monitors and dye-sublimination
printers, can produce. In this respect it is good for archieval storage of
images since the pictures we see now will keep up with improving display
technology.
When an image is scanned it is stored in terms of the three reference
primaries, these values, Rp, Gp and Bp are defined as follows:
Rp = kr {integral of (Planda planda rlanda) dlanda}
Gp = kg{integral of (Planda planda glanda) dlanda}
Bp = kb{integral of (Planda planda blanda) dlanda}
where Rp Gp and Bp are the CCIR 709 primaries although not constrained to
positive values.
kr kg kb are normalising constants;
Planda is the spectral power distribution of the light source (CIE D65);
planda is the spectral power distribution of the scene at a specific point
(pixel);
rlanda glanda and blanda are the spectral power distributions of the
scanner components primaries.
kr kg kb are specified as kr = 1 / {integral of (Planda * rlanda) dlanda}
as similairly for kg and kb replacing rlanda with glanda and blanda
respectivly.
Let's stop with the theory and let's see how to make transforms.
To be stored on a CD rom, the Rp Gp and Bp values are transformed into
Kodak's PhotoYCC color space. This is performed in three stages. Firstly a
non-linear transform is applied to the image signals (this is because
scanners tend to be linear devices while CRT displays are not), the
transform used is as follows:
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.
Converting stored 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)
Assuming your display uses phosphors that are, or are very close to, ITU
Rec 709 primaries in their chromaticities, then (* see below)
Rdisplay = L + Chroma2
Gdisplay = L - 0.194Chroma1 - 0.509Chroma2
Bdisplay = 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) if this is simply ignored the resulting clipping will cause severe
loss of highlight information in the displayed image, 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
independedent color space such as CIE XYZ.
* as a note -> do the phosphors need to match with regard to their
chromaticities or is a spectral match required? Two different spectral
distributed phosphors may have same chromaticites but may not be a
metameric match since metarimerism only applies to spectral distribution of
color matching functions.
Another point to note is that PhotoCD images are chroma subsampled, that is
to say for each 2 x 2 block of pixels, 4 luma and 1 of each chroma
component are sampled (i.e. chroma data is averaged over 2x2 pixel blocks).
This technique uses the fact that the HVS is less sensitive to luminance
than chromaince diferences so color information can be stored at a lower
precision without percievable loss in visual quality.
6 - References (most of them are provided by Adrian Ford)
"An inexpensive scheme for calibration of a color 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
SPROSON: "Color 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 talk about it as a reference)
CIE 1: "CIE Colorimetry" Official recommendations of the International
Commission on Illumination, Publication 15.2 1986
BERNS: "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 CIE implementations on CRT's)
"Effective Color Displays. Theory and Practice", Travis, D, Academic Press,
1991. ISBN 0-12-697690-2
(Color applications in computer graphics)
FIELD: Field, G.G., Color and Its Reproduction, Graphics Arts Technical
Foundation, 1988, pp. 320-9
(Read this about CMY/CMYK)
POYNTON: "Gamma and its disguises: The nonlinear mappings of intensity in
perception, CRT's, Film and Video" C. A. Poynton, SMPTE Journal, December
1993
HUNT 1: "Measuring Color" 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
CIE 2: "The colorimetry of self luminous displays - a bibliography" CIE
Publication n.87, Central Bureau of the CIE, Vienna 1990
HUNT 2: "The Reproduction of Color in PhotoGraphy, Printing and
Television", R. W. G. Hunt, Fountain Press, Tolworth, England, 1987
"Fully Utilizing Photo CD Images, Article No. 4, PhotoYCC Color Encoding
and Compression Schemes" Eastman Kodak Company, Rochester NY (USA) (1993).
7 - Comments and thanks
Whenever you would like to comment or suggest me some information about
this or about the color space transformations in general, please use email:
dbourgin@ufrima.imag.fr (David Bourgin)
Special thanks to the following persons (there are actually many other
people to cite) for contributing to valid, see even to write some part of
the items:
- Adrian Ford (ajoec1@westminster.ac.uk)
- Tom Lane (Tom_Lane@G.GP.CS.CMU.EDU)
- Alan Roberts and Richard Salmon (Alan.Roberts@rd.bbc.co.uk,
Richard.Salmon@rd.eng.bbc.co.uk)
- Grant Sayer (grants@research.canon.oz.au)
- Steve Westland (coa23@potter.cc.keele.ac.uk)
Note: I'm doing my national service on 4 next months, it means up to the
begining of july. I'll try to read and answer to my e-mails.
Thanks to not be in a hurry ;-).
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