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From: "Charles A. Poynton" <poynton@inforamp.net>
Subject: colorspace-faq -- FAQ about Color and Gamma
Newsgroups: comp.graphics,comp.graphics.algorithms,sci.engr.television.advanced,sci.engr.television.broadcast,sci.image.processing,comp.answers,sci.answers,news.answers
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Organization: Poynton Vector, Toronto, ON Canada, +1 416 486 3271
Summary: This FAQ clarifies aspects of nonlinear image coding (gamma),
color specification, and image coding that are important to
computer graphics, image processing, video, and the transfer of
digital images to print.
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Archive-name: graphics/colorspace-faq
Version: 1997-02-27
URL: <http://www.inforamp.net/~poynton/Poynton-color.html>
colorspace-faq -- FREQUENTLY ASKED QUESTIONS ABOUT GAMMA AND COLOR
Charles A. Poynton
<http://www.inforamp.net/~poynton/>
Copyright (c) 1997-02-27
ntensity reproduction. The Gamma FAQ section of this document
clarifies aspects of nonlinear image coding.
The Color FAQ section of this document clarifies aspects of color
mage processing, video, and the transfer of digital images to print.
Adrian Ford and Alan Roberts have written "Colour Space Conversions"
that details transforms among color spaces such as RGB, HSI, CMY and
video. Find it at <http://www.wmin.ac.uk/ITRG/docs/coloureq/COL_.htm>.
Steve Westland has written "Frequently asked questions about Colour
may not publish it.
CONTENTS
G-0 Where do these documents live?
Frequently Asked Questions about Gamma
G-1 What is intensity?
G-2 What is luminance?
G-3 What is lightness?
G-4 What is gamma?
G-5 What is gamma correction?
G-6 Does NTSC use a gamma of 2.2?
G-7 Does PAL use a gamma of 2.8?
G-8 I pulled an image off the net and it looks murky.
G-9 I pulled an image off the net and it looks a little too contrasty.
G-10 What is luma?
G-11 What is contrast ratio?
G-12 How many bits do I need to smoothly shade from black to white?
G-13 How is gamma handled in video, computer graphics and desktop
computing?
G-14 What is the gamma of a Macintosh?
G-15 Does the gamma of CRTs vary wildly?
G-16 How should I adjust my monitor's brightness and contrast controls?
G-17 Should I do image processing operations on linear or nonlinear
image data?
G-18 What's the transfer function of offset printing?
G-19 References
Frequently Asked Questions about Color
C-1 What is color?
C-2 What is intensity?
C-3 What is luminance?
C-4 What is lightness?
C-5 What is hue?
C-6 What is saturation?
C-7 How is color specified?
C-8 Should I use a color specification system for image data?
C-9 What weighting of red, green and blue corresponds to brightness?
C-10 Can blue be assigned fewer bits than red or green?
C-11 What is "luma"?
C-12 What are CIE XYZ components?
C-13 Does my scanner use the CIE spectral curves?
C-14 What are CIE x and y chromaticity coordinates?
C-15 What is white?
C-16 What is color temperature?
C-17 How can I characterize red, green and blue?
C-18 How do I transform between CIE XYZ and a particular set of RGB
primaries?
C-19 Is RGB always device-dependent?
C-20 How do I transform data from one set of RGB primaries to another?
C-21 Should I use RGB or XYZ for image synthesis?
C-22 What is subtractive color?
C-23 Why did my grade three teacher tell me that the primaries are red,
yellow and blue?
C-24 Is CMY just one-minus-RGB?
C-25 Why does offset printing use black ink in addition to CMY?
C-26 What are color differences?
C-27 How do I obtain color difference components from tristimulus values?
C-28 How do I encode Y'PBPR components?
C-29 How do I encode Y'CBCR components from R'G'B' in [0, +1]?
C-30 How do I encode Y'CBCR components from computer R'G'B' ?
C-31 How do I encode Y'CBCR components from studio video?
C-32 How do I decode R'G'B' from PhotoYCC?
C-33 Will you tell me how to decode Y'UV and Y'IQ?
C-34 How should I test my encoders and decoders?
C-35 What is perceptual uniformity?
C-36 What are HSB and HLS?
C-37 What is true color?
C-38 What is indexed color?
C-39 I want to visualize a scalar function of two variables. Should I use
RGB values corresponding to the colors of the rainbow?
C-40 What is dithering?
C-41 How does halftoning relate to color?
C-42 What's a color management system?
C-43 How does a CMS know about particular devices?
C-44 Is a color management system useful for color specification?
C-45 I'm not a color expert. What parameters should I use to
code my images?
C-46 References
C-47 Contributors
G-0 WHERE DO THESE DOCUMENTS LIVE?
Each document GammaFAQ and ColorFAQ is available in four formats --
Adobe Acrobat (PDF), hypertext (HTML), PostScript, and plain 7-bit
ASCII text-only. You are reading the concatenation of the text versions
of GammaFAQ and ColorFAQ. The text formats are devoid of graphs and
llustrations, of course; I strongly recommend the PDF versions.
The hypertext version is linked from my color page,
<http://www.inforamp.net/~poynton/Poynton-color.html>
The PDF, PostScript and text formats are available by ftp:
<ftp://ftp.inforamp.net/pub/users/poynton/doc/color/>
s properly configured with your return address to send mail to
<ftpmail@decwrl.dec.com> with en empty subject and the single word help
n the body.
Adobe's Acrobat Reader is freely available for Windows, Mac, MS-DOS and
SPARC. If you don't already have a reader, you can obtain one from
<ftp://ftp.adobe.com/pub/adobe/acrobatreader/>
n a subdirectory and file appropriate for your platform.
On CompuServe, GO Acrobat.
On America Online, for Mac, use Keyword Adobe -> Adobe Software Library
-> New! Adobe Acrobat Reader 3.0, then choose a platform.
Transfer PDF files in binary mode, particularly to Windows or MS-DOS
machines. PDF files contain "bookmarks" corresponding to the table of
contents. Clicking a bookmark takes you to the topic. Also,
cross-references in the PDF files are links.
Acrobat Reader allows viewing on-screen on multiple platforms, printing
to both PostScript and non-PostScript printers, and permits viewing and
those people who cannot or do not wish to run Acrobat Reader, I provide
The documents use only Times, Helvetica, Palatino and Symbol fonts and
are laid out with generous margins for US Letter size paper. I confess
using A4 has suggestions to improve the PostScript please let me know.
The PostScript files are compressed with Gnu zip compression, and are
as well) is available from the usual gnu sites. If you use a Macintosh,
the freeware StuffIt Expander 4.0 will decode gnu zip files.
------------------------------
FREQUENTLY ASKED QUESTIONS ABOUT GAMMA
G-1 WHAT IS INTENSITY?
the flow of power that is radiated from, or incident on, a surface.
The voltages presented to a CRT monitor control the intensities of the
color components, but in a nonlinear manner. CRT voltages are not
color described as HSI (hue, saturation, intensity) does not accurately
formulae.
G-2 WHAT IS LUMINANCE?
Brightness is defined by the Commission Internationale de L'Eclairage (CIE)
as the attribute of a visual sensation according to which an area appears
to emit more or less light. Because brightness perception is very complex,
the CIE defined a more tractable quantity luminance, denoted Y, which is
characteristic of vision. To learn about the relationship between physical
companion Frequently Asked Questions about Color.
The magnitude of luminance is proportional to physical power. In that sense
t is like intensity. But the spectral composition of luminance is related
to the brightness sensitivity of human vision.
G-3 WHAT IS LIGHTNESS?
Human vision has a nonlinear perceptual response to brightness: a source
bright. The perceptual response to luminance is called Lightness and is
Lstar = -16 + 116 * pow(Y / Yn, 1. / 3.)
Yn is the luminance of the white reference. If you normalize luminance to
applies a linear segment with a slope of 903.3 near black, for (Y/Yn) <
you don't use it, make sure that you limit L* at zero. L* has a range of 0
to 100, and a "delta L-star" of unity is taken to be roughly the threshold
of visibility.
Stated differently, lightness perception is roughly logarithmic. You can
ntensities differs by more than about one percent.
Video systems approximate the lightness response of vision using RGB
to the 1/3 power function defined by L*.
The L component of a color described as HLS (hue, lightness, saturation)
any of the usual formulae. See Frequently Asked Questions about Color.
G-4 WHAT IS GAMMA?
The intensity of light generated by a physical device is not usually a
linear function of the applied signal. A conventional CRT has a power-law
approximately the applied voltage, raised to the 2.5 power. The numerical
value of the exponent of this power function is colloquially known as
As mentioned above (What is lightness?), human vision has a nonuniform
number of steps, say 256, then in order for the most effective perceptual
use to be made of the available codes, the codes must be assigned to
ntensities according to the properties of perception.
Here is a graph of an actual CRT's transfer function, at three different
contrast settings:
<< A nice graph is found in the .PDF and .PS versions. >>
This graph indicates a video signal having a voltage from zero to 700 mV.
black is at code zero and white is at code 255.
Through an amazing coincidence, vision's response to intensity is
effectively the inverse of a CRT's nonlinearity. If you apply a transfer
function to code a signal to take advantage of the properties of lightness
nverted by a CRT.
G-5 WHAT IS GAMMA CORRECTION?
video signa by gamma correction, which is universally done at the camera.
The Rec. 709 transfer function [2] takes linear-light intensity (here R) to
a nonlinear component (here Rprime), for example, voltage in a video
Rprime = ( R <= 0.018 ?
4.5 * R :
-0.099 + 1.099 * pow(R, 0.45)
);
The linear segment near black minimizes the effect of sensor noise in
function, for a signal range from zero to unity:
<< An attractive graph is presented in the .PDF and .PS versions. >>
An idealized monitor inverts the transform:
R = ( Rprime <= 0.081 ?
Rprime / 4.5 :
pow((Rprime + 0.099) / 1.099, 1. / 0.45)
);
Real monitors are not as exact as this equation suggests, and have no linear
transfer function is applied to each of the three tristimulus
(linear-light) RGB components. See Frequently Asked Questions about
Color.
By the way, the nonlinearity of a CRT is a function of the electrostatics
of the cathode and the grid of an electron gun; it has nothing to do with
the phosphor. Also, the nonlinearity is a power function (which has the
form f(x) = x^a), not an exponential function (which has the form f(x) =
a^x). For more detail, read Poynton's article [3].
G-6 DOES NTSC USE A GAMMA OF 2.2?
Television is usually viewed in a dim environment. If an images's correct
called simultaneous contrast causes the reproduced image to appear lacking
n contrast. The effect can be overcome by applying an end-to-end power
function whose exponent is about 1.1 or 1.2. Rather than having each
under-corrected at the camera by using an exponent of about 1/2.2 instead
of 1/2.5. The assumption of a dim viewing environment is built into video
coding.
G-7 DOES PAL USE A GAMMA OF 2.8?
Standards for 625/50 systems mention an exponent of 2.8 at the decoder,
exponent different from 0.45 is chosen for a power function with a linear
to maintain function and tangent continuity.
G-8 I PULLED AN IMAGE OFF THE NET AND IT LOOKS MURKY.
applied exactly once. If gamma correction is not applied and linear-light
mage data is applied to a CRT, the midtones will be reproduced too dark.
G-9 I PULLED AN IMAGE OFF THE NET AND IT LOOKS A LITTLE TOO CONTRASTY.
Viewing environments typical of computing are quite bright. When an image
s coded according to video standards it implicitly carries the assumption
of a dim surround. If it is displayed without correction in a bright
ambient, it will appear contrasty. In this circumstance you should apply a
bright surround.
Ambient lighting is rarely taken into account in the exchange of computer
mages. If an image is created in a dark environment and transmitted to a
viewer in a bright environment, the recipient will find it to have
excessive contrast.
environment, it will need no modification no matter what coding is applied.
But then it will carry an assumption of a bright surround. Video standards
are widespread and well optimized for vision, so it makes sense to code
viewing environment.
among applications, an image originator should remove the effect of his
ambient environment when he transmits an image. The recipient of an image
this data. You can correct for your own viewing environment as appropriate,
but until image interchange standards incorporate viewing conditions, you
G-10 WHAT IS LUMA?
nonlinear function of true CIE luminance, but as a weighted sum of
nonlinear R'G'B' components called luma. For more information, consult the
companion document Frequently Asked Questions about Color.
G-11 WHAT IS CONTRAST RATIO?
Contrast ratio is the ratio of intensity between the brightest white and
the darkest black of a particular device or a particular environment.
G-12 HOW MANY BITS DO I NEED TO SMOOTHLY SHADE FROM BLACK TO WHITE?
At a particular level of adaptation, human vision responds to about a
ntensities 100 and 1. Within this range, vision can detect that two
ntensities are different if the ratio between them exceeds about 1.01,
corresponding to a contrast sensitivity of one percent.
To shade smoothly over this range, so as to produce no perceptible steps,
at the black end of the scale it is necessary to have coding that
light coding is used, the "delta" of 0.01 must be maintained all the way up
the scale to white. This requires about 9,900 codes, or about fourteen bits
end of the scale applies as a ratio, not an absolute increment, and
codes, or about nine bits per component. Eight bits, nonlinearly coded
according to Rec. 709, is sufficient for broadcast-quality digital
television at a contrast ratio of about 50:1.
at code zero, then the ability of human vision to discern a 1.01 ratio
between adjacent intensity levels takes effect below code 100. If a linear
light system has only eight bits, then the top end of the scale is only
viewing conditions.
G-13 HOW IS GAMMA HANDLED IN VIDEO, COMPUTER GRAPHICS AND DESKTOP
COMPUTING?
As outlined above, gamma correction in video effectively codes into a
the camera, as shown in the top row of this diagram:
<< A nice diagram is presented in the .PDF and .PS versions. >>
Synthetic computer graphics calculates the interaction of light and
objects. These interactions are in the physical domain, and must be
calculated in linear-light values. It is conventional in computer graphics
to store linear-light values in the framebuffer, and introduce gamma
correction at the lookup table at the output of the framebuffer. This is
llustrated in the middle row above.
between codes will be perceptible as banding in smoothly-shaded images.
This is the eight-bit bottleneck in the sketch.
Desktop computers are optimized neither for image synthesis nor for video.
They have programmable "gamma" and either poor standards or no standards.
Consequently, image interchange among desktop computers is fraught with
G-14 WHAT IS THE GAMMA OF A MACINTOSH?
Apple offers no definition of the nonlinearity - or loosely speaking, gamma
- that is intrinsic in QuickDraw. But the combination of a default
QuickDraw lookup table and a standard monitor causes intensity to represent
the 1.8-power of the R, G and B values presented to QuickDraw. It is
function is different from the rest of the industry. The unconventional
QuickDraw handling of nonlinearity is the root of this misconception.
Macintosh coding is shown in the bottom row of the diagram
<< provided in the PDF and PS versions >>.
The transfer of image data in computing involves various transfer
functions: at coding, in the framebuffer, at the lookup table, and at the
monitor. Strictly speaking the term gamma applies to the exponent of the
a Mac you could call the gamma 1.4, 1.8 or 2.5 depending which part of the
for best perceptual performance and maximum ease of interchange with
ntensity with a 1/1.8-power law, anticipating QuickDraw's 1/1.4-power in
the lookup table. This coding has adequate performance in the bright
viewing environments typical of desktop applications, but suffers in darker
viewing conditions that have high contrast ratio.
G-15 DOES THE GAMMA OF CRTS VARY WILDLY?
Gamma of a properly adjusted conventional CRT varies anywhere between about
CRTs have acquired a reputation for wild variation for two reasons. First,
f the model intensity=voltage^gamma is naively fitted to a display with
black-level error, the exponent deduced will be as much a function of the
black error as the true exponent. Second, input devices, graphics libraries
and application programs all have the potential to introduce their own
transfer functions. Nonlinearities from these sources are often categorized
as gamma and attributed to the display.
G-16 HOW SHOULD I ADJUST MY MONITOR'S BRIGHTNESS AND CONTRAST CONTROLS?
On a CRT monitor, the control labelled contrast controls overall intensity,
and the control labelled brightness controls offset (black level). Display
a picture that is predominantly black. Adjust brightness so that the
monitor reproduces true black on the screen, just at the threshold where it
s not so far down as to "swallow" codes greater than the black code, but
not so high that the picture sits on a "pedestal" of dark grey. When the
critical point is reached, put a piece of tape over the brightness control.
Then set contrast to suit your preference for display intensity.
For more information, consult "Black Level" and "Picture",
<ftp://ftp.inforamp.net/pub/users/poynton/doc/color/Black_and_Picture.pdf>.
G-17 SHOULD I DO IMAGE PROCESSING OPERATIONS ON LINEAR OR NONLINEAR IMAGE
DATA?
necessary. For example, if you want to produce a numerical simulation of a
lens performing a Fourier transform, you should use linear coding. If you
lens by a video camera, you will have to "remove" the nonlinear gamma
correction that was imposed by the camera, to convert the image data back
nto its linear-light representation.
On the other hand, if your computation involves human perception, a
nonlinear representation may be required. For example, if you perform a
compression, as in JPEG, then you ought to use nonlinear coding that
exhibits perceptual uniformity, because you wish to minimize the
The image processing literature rarely discriminates between linear and
nonlinear coding. In the JPEG and MPEG standards there is no mention of
transfer function, but nonlinear (video-like) coding is implicit:
unacceptable results are obtained when JPEG or MPEG are applied to
linear-light data. In computer graphic standards such as PHIGS and CGM
there is no mention of transfer function, but linear-light coding is
mplicit. These discrepancies make it very difficult to exchange image data
between systems.
When you ask a video engineer if his system is linear, he will say "Of
course!" referring to linear voltage. If you ask an optical engineer if her
But when a nonlinear transform lies between the two systems, as in video, a
linear transformation performed in one domain is not linear in the other.
G-18 WHAT'S THE TRANSFER FUNCTION OF OFFSET PRINTING?
A image destined for halftone printing conventionally specifies each pixel
n terms of dot percentage in film. An imagesetter's halftoning machinery
Two phenomena distort the requested dot coverage values. First, printing
nvolves a mechanical smearing of the ink that causes dots to enlarge.
Second, optical effects within the bulk of the paper cause more light to be
absorbed than would be expected from the surface coverage of the dot alone.
These phenomena are collected under the term dot gain, which is the
Standard offset printing involves a dot gain at 50% of about 24%: when 50%
absorption is requested, 74% absorption is obtained. The midtones print
Correction of dot gain is conceptually similar to gamma correction in
video: physical correction of the "defect" in the reproduction process is
very well matched to the lightness perception of human vision. Coding an
mage in terms of dot percentage in film involves coding into a roughly
North America and Europe correspond to intensity being reproduced as a
exponent is about 1.75, compared to about 2.2 for video. This is lower than
the optimum for perception, but works well for the low contrast ratio of
offset printing.
The Macintosh has a power function that is close enough to printing practice
that raw QuickDraw codes sent to an imagesetter produce acceptable results.
High-end publishing software allows the user to specify the parameters of
corrections.
G-19 REFERENCES
[1] Publication CIE No 15.2, Colorimetry, Second Edition (1986), Central
Bureau of the Commission Internationale de L'Eclairage, Vienna, Austria.
[2] ITU-R Recommendation BT.709, Basic Parameter Values for the HDTV
Standard for the Studio and for International Programme Exchange (1990),
[formerly CCIR Rec. 709], ITU, 1211 Geneva 20, Switzerland.
[3] Charles A. Poynton, "Gamma and Its Disguises" in Journal of the Society
of Motion Picture and Television Engineers, Vol. 102, No. 12 (December
[4] Charles A. Poynton, "Gamma on the Apple Macintosh",
<ftp://ftp.inforamp.net/pub/users/poynton/doc/Mac/>.
------------------------------
FREQUENTLY ASKED QUESTIONS ABOUT COLOR
C-1 WHAT IS COLOR?
Color is the perceptual result of light in the visible region of the
upon the retina. Physical power (or radiance) is expressed in a spectral
band.
The human retina has three types of color photoreceptor cone cells, which
curves. A fourth type of photoreceptor cell, the rod, is also present in
the retina. Rods are effective only at extremely low light levels
(colloquially, night vision), and although important for vision play no
Because there are exactly three types of color photoreceptor, three
numerical components are necessary and sufficient to describe a color,
the concern of the science of colorimetry. In 1931, the Commission
transformed into a set of three numbers that specifies a color.
The CIE system is immediately and almost universally applicable to
not only of the colorants but also of the SPD of the ambient illumination.
lluminant, you may have to resort to spectral matching.
Sir Isaac Newton said, "Indeed rays, properly expressed, are not coloured."
SPDs exist in the physical world, but color exists only in the eye and the
brain.
C-2 WHAT IS INTENSITY?
of the flow of power that is radiated from, or incident on, a surface.
The voltages presented to a CRT monitor control the intensities of the
color components, but in a nonlinear manner. CRT voltages are not
C-3 WHAT IS LUMINANCE?
Brightness is defined by the CIE as the attribute of a visual sensation
according to which an area appears to emit more or less light. Because
brightness perception is very complex, the CIE defined a more tractable
quantity luminance which is radiant power weighted by a spectral
efficiency of the Standard Observer is defined numerically, is everywhere
curve as a weighting function, the result is CIE luminance, denoted Y.
The magnitude of luminance is proportional to physical power. In that sense
t is like intensity. But the spectral composition of luminance is related
to the brightness sensitivity of human vision.
Strictly speaking, luminance should be expressed in a unit such as candelas
For example, a studio broadcast monitor has a white reference whose
luminance is about 80 cd*m -2, and Y = 1 refers to this value.
C-4 WHAT IS LIGHTNESS?
Human vision has a nonlinear perceptual response to brightness: a source
bright. The perceptual response to luminance is called Lightness. It is
Lstar = -16 + 116 * (pow(Y / Yn), 1. / 3.)
Yn is the luminance of the white reference. If you normalize luminance to
applies a linear segment with a slope of 903.3 near black, for (Y/Yn) <=
you don't use it, make sure that you limit L* at zero. L* has a range of 0
to 100, and a "delta L-star" of unity is taken to be roughly the threshold
of visibility.
Stated differently, lightness perception is roughly logarithmic. An
observer can detect an intensity difference between two patches when their
ntensities differ by more than one about percent.
Video systems approximate the lightness response of vision using R'G'B'
to the 1/3 power function defined by L*.
C-5 WHAT IS HUE?
According to the CIE [1], hue is the attribute of a visual sensation
according to which an area appears to be similar to one of the perceived
colors, red, yellow, green and bue, or a combination of two of them.
Roughly speaking, if the dominant wavelength of an SPD shifts, the hue of
the associated color will shift.
C-6 WHAT IS SATURATION?
Again from the CIE, saturation is the colorfulness of an area judged in
concentrated at one wavelength, the more saturated will be the associated
color. You can desaturate a color by adding light that contains power at
all wavelengths.
C-7 HOW IS COLOR SPECIFIED?
The CIE system defines how to map an SPD to a triple of numerical
components that are the mathematical coordinates of color space. Their
function is analagous to coordinates on a map. Cartographers have different
map projections for different functions: some map projections preserve
areas, others show latitudes and longitudes as straight lines. No single
map projection fills all the needs of map users. Similarly, no single
color system fills all of the needs of color users.
The systems useful today for color specification include CIE XYZ, CIE xyY,
CIE L*u*v* and CIE L*a*b*. Numerical values of hue and saturation are not
very useful for color specification, for reasons to be discussed in
A color specification system needs to be able to represent any color with
must be intimately related to the CIE specifications.
You can specify a single "spot" color using a color order system such as
Munsell. Systems like Munsell come with swatch books to enable visual
color matches, and have documented methods of transforming between
coordinates in the system and CIE values. Systems like Munsell are not
useful for image data. You can specify an ink color by specifying the
color. That's how pantone(tm) works. Although widespread, it's
C-8 SHOULD I USE A COLOR SPECIFICATION SYSTEM FOR IMAGE DATA?
A digitized color image is represented as an array of pixels, where each
are necessary and sufficient for this purpose, although in printing it is
convenient to use a fourth (black) component.
a color specification system. But a practical image coding system needs to
be computationally efficient, cannot afford unlimited precision, need not
be intimately related to the CIE system and generally needs to cover only a
coding uses different systems than color specification.
The systems useful for image coding are linear RGB, nonlinear R'G'B',
nonlinear CMY, nonlinear CMYK, and derivatives of nonlinear R'G'B' such
as Y'CBCR. Numerical values of hue and saturation are not useful in color
mage coding.
be necessary. But to convey a picture of the car, you need image coding.
You can afford to do quite a bit of computation in the first case because
you have only two colored elements, the door and the fender. In the second
case, the color coding must be quite efficient because you may have a
million colored elements or more.
For a highly readable short introduction to color image coding, see
DeMarsh and Giorgianni [2]. For a terse, complete technical treatment, read
Schreiber [3].
C-9 WHAT WEIGHTING OF RED, GREEN AND BLUE CORRESPONDS TO BRIGHTNESS?
Direct acquisition of luminance requires use of a very specific spectral
the visible spectrum, then the green will appear the brightest of the three
because the luminous efficiency function peaks in the green region of the
of the three. As a consequence of the luminous efficiency function, all
light. If luminance is computed from red, green and blue, the coefficients
functions employed, but the green coefficient will be quite large, the red
Contemporary CRT phosphors are standardized in Rec. 709 [8], to be
linear red, green and blue (indicated without prime symbols), for the Rec.
Y = 0.212671 * R + 0.715160 * G + 0.072169 * B;
This computation assumes that the luminance spectral weighting can be
formed as a linear combination of the scanner curves, and assumes that the
component signals represent linear-light. Either or both of these
conditions can be relaxed to some extent depending on the application.
Some computer systems have computed brightness using (R+G+B)/3. This is at
odds with the properties of human vision, as will be discussed under What
are HSB and HLS? in section 36.
The coefficients 0.299, 0.587 and 0.114 properly computed luminance for
monitors having phosphors that were contemporary at the introduction of
NTSC television in 1953. They are still appropriate for computing video
luma to be discussed below in section 11. However, these coefficients do
not accurately compute luminance for contemporary monitors.
C-10 CAN BLUE BE ASSIGNED FEWER BITS THAN RED OR GREEN?
Blue has a small contribution to the brightness sensation. However, human
vision has extraordinarily good color discrimination capability in blue
colors. So if you give blue fewer bits than red or green, you will
ntroduce noticeable contouring in blue areas of your pictures.
C-11 WHAT IS "LUMA"?
luminance and two other components representative of color. It is
mportant to convey the component representative of luminance in such a way
that noise (or quantization) introduced in transmission, processing and
black to white. The ideal way to accomplish these goals would be to form a
luminance signal by matrixing RGB, then subjecting luminance to a nonlinear
transfer function similar to the L* function.
There are practical reasons in video to perform these operations in the
opposite order. First a nonlinear transfer function - gamma correction - is
applied to each of the linear R, G and B. Then a weighted sum of the
nonlinear components is computed to form a signal representative of
luminance. The resulting component is related to brightness but is not CIE
luminance. Many video engineers call it luma and give it the symbol Y'. It
s often carelessly called luminance and given the symbol Y. You must be
careful to determine whether a particular author assigns a linear or
nonlinear interpretation to the term luminance and the symbol Y.
The coefficients that correspond to the "NTSC" red, green and blue CRT
(formerly CCIR Rec. 601-2). I call it Rec. 601. To compute nonlinear video
luma from nonlinear red, green and blue:
Yprime = 0.299 * Rprime + 0.587 * Gprime + 0.114 * Bprime;
The prime symbols in this equation, and in those to follow, denote
nonlinear components.
C-12 WHAT ARE CIE XYZ COMPONENTS?
The CIE system is based on the description of color as a luminance
component Y, as described above, and two additional components X and Z. The
based on statistics from experiments involving human observers. XYZ
tristimulus values can describe any color. (RGB tristimulus values will be
The magnitudes of the XYZ components are proportional to physical energy,
but their spectral composition corresponds to the color matching
characteristics of human vision.
The CIE system is defined in Publication CIE No 15.2, Colorimetry, Second
Edition (1986) [4].
C-13 DOES MY SCANNER USE THE CIE SPECTRAL CURVES?
components of color information. The usual task of a scanner is not
than filters that adhere to the principles of colorimetry.
"original" SPDs that are not already a record of three components, chances
are your scanner will not very report accurate RGB values. This is because
most scanners do not conform very closely to CIE standards.
C-14 WHAT ARE CIE x AND y CHROMATICITY COORDINATES?
brightness. The CIE defines a normalization process to compute "little" x
and y chromaticity coordinates:
x = X / (X + Y + Z);
y = Y / (X + Y + Z);
A color plots as a point in an (x, y) chromaticity diagram. When a
narrowband SPD comprising power at just one wavelength is swept across the
y) coordinates. The sensation of purple cannot be produced by a single
light. The line of purples on a chromaticity diagram joins extreme blue to
extreme red. All colors are contained in the area in (x, y) bounded by the
line of purples and the spectral locus.
A color can be specified by its chromaticity and luminance, in the form of
an xyY triple. To recover X and Z from chromaticities and luminance, use
these relations:
X = (x / y) * Y;
Z = (1 - x - y) / y * Y;
The bible of color science is Wyszecki and Styles, Color Science [5]. But
t's daunting. For Wyszecki's own condensed version, see Color in Business,
Science and Industry, Third Edition [6]. It is directed to the color
ndustry: ink, paint and the like. For an approachable introduction to the
a copy of R.W.G. Hunt, The Reproduction of Colour [7]. But sorry to report,
as I write this, it's out of print.
C-15 WHAT IS WHITE?
color reproduced by equal red, green and blue components. White point is a
function of the ratio (or balance) of power among the primaries. In
by the SPD of the media. There is no unique physical or perceptual
uniform SPD. This white reference is known as the equal-energy illuminant,
or CIE Illuminant E.
A more realistic reference that approximates daylight has been specified
numerically by the CIE as Illuminant D65. You should use this unless you
D50 and photography commonly uses D55. These represent compromises between
the conditions of indoor (tungsten) and daylight viewing.
C-16 WHAT IS COLOR TEMPERATURE?
Many sources of illumination have, at their core, a heated object, so it is
often useful to characterize an illuminant by specifying the temperature
(in units of kelvin, K) of a black body radiator that appears to have the
Although an illuminant can be specified informally by its color
temperature, a more complete specification is provided by the chromaticity
coordinates of the SPD of the source.
Modern blue CRT phosphors are more efficient with respect to human vision
than red or green. In a quest for brightness at the expense of color
accuracy, it is common for a computer display to have excessive blue
content, about twice as blue as daylight, with white at about 9300 K.
Human vision adapts to white in the viewing environment. An image viewed in
solation - such as a slide projected in a dark room - creates its own
objectionable.
Complete adaptation seems to be confined to the range 5000 K to 5500 K. For
most people, D65 has a little hint of blue. Tungsten illumination, at about
C-17 HOW CAN I CHARACTERIZE RED, GREEN AND BLUE?
Additive reproduction is based on physical devices that produce
all-positive SPDs for each primary. Physically and mathematically, the
that appear red, green and blue. Human color vision obeys the principle of
the XYZ components of the primaries: the colors that can be mixed from a
the primaries by themselves. Subtractive reproduction is much more
complicated: the colors of mixtures are determined by the primaries and by
the colors of their combinations.
An additive RGB system is specified by the chromaticities of its primaries
and its white point. The extent (gamut) of the colors that can be mixed
from a given set of RGB primaries is given in the (x, y) chromaticity
RGB image but have no information about its chromaticities, you cannot
accurately reproduce the image.
The NTSC in 1953 specified a set of primaries that were representative of
years, primarily in response to market pressures for brighter receivers,
and by the time of the first the videotape recorder the primaries in use
NTSC primary chromaticities documented, they are of no use today.
Contemporary studio monitors have slightly different standards in North
America, Europe and Japan. But international agreement has been obtained on
closely representative of contemporary monitors in studio video, computing
and computer graphics. The primaries and the D65 white point of Rec. 709
[8] are:
x y z
R 0.6400 0.3300 0.0300
G 0.3000 0.6000 0.1000
B 0.1500 0.0600 0.7900
For a discussion of nonlinear RGB in computer graphics, see Lindbloom [9].
For technical details on monitor calibration, consult Cowan [10].
C-18 HOW DO I TRANSFORM BETWEEN CIE XYZ AND A PARTICULAR SET OF RGB
PRIMARIES?
RGB values in a particular set of primaries can be transformed to and from
CIE XYZ by a three-by-three matrix transform. These transforms involve
tristimulus values, that is, sets of three linear-light components that
conform to the CIE color matching functions. CIE XYZ is a special case of
tristimulus values. In XYZ, any color is represented by a positive set of
values.
Details can be found in SMPTE RP 177-1993 [11].
To transform from CIE XYZ into Rec. 709 RGB (with its D65 white point), put
an XYZ column vector to the right of this matrix, and multiply:
[ R709 ] [ 3.240479 -1.53715 -0.498535 ] [ X ]
[ G709 ]=[-0.969256 1.875991 0.041556 ]*[ Y ]
[ B709 ] [ 0.055648 -0.204043 1.057311 ] [ Z ]
As a convenience to C programmers, here are the coefficients as a C array:
{{ 3.240479,-1.53715 ,-0.498535},
{-0.969256, 1.875991, 0.041556},
{ 0.055648,-0.204043, 1.057311}}
This matrix has some negative coefficients: XYZ colors that are out of
components is negative or greater than unity.
Here's the inverse matrix. Because white is normalized to unity, the
middle row sums to unity:
[ X ] [ 0.412453 0.35758 0.180423 ] [ R709 ]
[ Y ]=[ 0.212671 0.71516 0.072169 ]*[ G709 ]
[ Z ] [ 0.019334 0.119193 0.950227 ] [ B709 ]
{{ 0.412453, 0.35758 , 0.180423},
{ 0.212671, 0.71516 , 0.072169},
{ 0.019334, 0.119193, 0.950227}}
To recover primary chromaticities from such a matrix, compute little x and
y for each RGB column vector. To recover the white point, transform RGB=[1,
C-19 IS RGB ALWAYS DEVICE-DEPENDENT?
Video standards specify abstract R'G'B' systems that are closely
matched to the characteristics of real monitors. Physical devices that
consider the monitor to be device-independent.
The importance of Rec. 709 as an interchange standard in studio video,
broadcast television and high definition television, and the perceptual
basis of the standard, assures that its parameters will be used even by
CRTs.
C-20 HOW DO I TRANSFORM DATA FROM ONE SET OF RGB PRIMARIES TO ANOTHER?
RGB values in a system employing one set of primaries can be transformed
nto another set by a three-by-three linear-light matrix transform.
Generally these matrices are normalized for a white point luminance of
unity. For details, see Television Engineering Handbook [12].
As an example, here is the transform from SMPTE 240M (or SMPTE RP 145) RGB
to Rec. 709:
[ R709 ] [ 0.939555 0.050173 0.010272 ] [ R240M ]
[ G709 ]=[ 0.017775 0.965795 0.01643 ]*[ G240M ]
[ B709 ] [-0.001622 -0.004371 1.005993 ] [ B240M ]
{{ 0.939555, 0.050173, 0.010272},
{ 0.017775, 0.965795, 0.01643 },
{-0.001622,-0.004371, 1.005993}}
All of these terms are close to either zero or one. In a case like this, if
the transform is computed in the nonlinear (gamma-corrected) R'G'B'
Here's another example. To transform EBU 3213 RGB to Rec. 709:
[ R709 ] [ 1.044036 -0.044036 0. ] [ R240M ]
[ G709 ]=[ 0. 1. 0. ]*[ G240M ]
[ B709 ] [ 0. 0.011797 0.988203 ] [ B240M ]
{{ 1.044036,-0.044036, 0. },
{ 0. , 1. , 0. },
{ 0. , 0.011797, 0.988203}}
Transforming among RGB systems may lead to an out of gamut RGB result where
one or more RGB components is negative or greater than unity.
C-21 SHOULD I USE RGB OR XYZ FOR IMAGE SYNTHESIS?
Once light is on its way to the eye, any tristimulus-based system will
tristimulus values. In synthetic computer graphics, the calculations are
actually simulating sampled SPDs, even if only three components are used.
Details concerning the resultant errors are found in Hall [13].
C-22 WHAT IS SUBTRACTIVE COLOR?
Subtractive systems involve colored dyes or filters that absorb power from
amount of cyan dye (or ink), you modulate the amount of red in the image.
multiply, so this method of color reproduction should really be called
"multiplicative". Photographers and printers have for decades measured
transmission in base-10 logarithmic density units, where transmission of
unity corresponds to a density of 0, transmission of 0.1 corresponds to a
When a printer or photographer computes the effect of filters in tandem, he
calls the system subtractive.
To achieve a wide range of colors in a subtractive system requires filters
that appear colored cyan, yellow and magenta (CMY). Cyan in tandem with
magenta produces blue, cyan with yellow produces green, and magenta with
yellow produces red. Smadar Nehab suggests this memory aid:
----+ ----------+
R | G B R G | B
| |
Cy | Mg Yl Cy Mg | Yl
+---------- +-----
Additive primaries are at the top, subtractive at the bottom. On the left,
magenta and yellow filters combine to produce red. On the right, red and
C-23 WHY DID MY GRADE THREE TEACHER TELL ME THAT THE PRIMARIES ARE RED,
YELLOW AND BLUE?
To get a wide range of colors in an additive system, the primaries must
appear red, green and blue (RGB). In a subtractive system the primaries
must appear yellow, cyan and magenta (CMY). It is complicated to predict
the colors produced when mixing paints, but roughly speaking, paints mix
additively to the extent that they are opaque (like oil paints), and
This question also relates to color names: your grade three "red" was
For a discussion of paint mixing from a computer graphics perspective,
consult Haase [14].
C-24 IS CMY JUST ONE-MINUS-RGB?
absorption curves with no overlap. The color reproduction of the system
combination.
absorption curves that overlap significantly. Most magenta dyes absorb
mediumwave (green) light as expected, but incidentally absorb about half
that amount of shortwave (blue) light. If reproduction of a color, say
brown, requires absorption of all shortwave light then the incidental
absorption from the magenta dye is not noticed. But for other colors, the
"one minus RGB" formula produces mixtures with much less blue than
expected, and therefore produce pictures that have a yellow cast in the mid
tones. Similar but less severe interactions are evident for the other pairs
of practical inks and dyes.
Due to the spectral overlap among the colorants, converting CMY using the
"one-minus-RGB" method works for applications such as business graphics
Multiplicative mixture in a CMY system is mathematically nonlinear, and the
effect of the unwanted absorptions cannot be easily analyzed or
compensated. The colors that can be mixed from a particular set of CMY
themselves, but are also a function of the colors of the sets of
combinations of the primaries.
n the response of the three (or four) channels. In offset printing, the
for print, a black code of 128 (on a scale of 0 to 255) produces a
For a detailed discussion of transferring colorimetric image data to print
media, see Stone [15].
C-25 WHY DOES OFFSET PRINTING USE BLACK INK IN ADDITION TO CMY?
Replacing colored ink by black ink - which is primarily carbon - makes
economic sense. Second, printing three ink layers causes the printed paper
to become quite wet. If three inks can be replaced by one, the ink will dry
more quickly, the press can be run faster, and the job will be less
expensive. Third, if black is printed by combining three inks, and
mechanical tolerances cause the three inks to be printed slightly out of
Other printing processes may or may not be subject to similar constraints.
C-26 WHAT ARE COLOR DIFFERENCES?
This term is ambiguous. In its first sense, color difference refers to
numerical differences between color specifications. The perception of
color differences in XYZ or RGB is highly nonuniform. The study of
color differences at the threshold of perceptibility (just noticeable
brightness is "removed". Vision has poor response to spatial detail in
colored areas of the same luminance, compared to its response to luminance
transmit luminance with full detail and to form two color difference
components each having no contribution from luminance. The two color
components can then have spatial detail removed by filtering, and can be
transmitted with substantially less information capacity than luminance.
ubiquitous for practical reasons to use a luma signal that is computed
nonlinearly as outlined above ( What is luma? ).
The easiest way to "remove" brightness information to form two color
channels is to subtract it. The luma component already contains a large
fraction of the green information from the image, so it is standard to form
the other two components by subtracting luma from nonlinear blue (to form
B'-Y') and by subtracting luma from nonlinear red (to form R'-Y').
These are called chroma.
Various scale factors are applied to (B'-Y') and (R'-Y') for different
applications. The Y 'PBPR scale factors are optimized for component analog
video. The Y 'CBCR scaling is appropriate for component digital video such
as studio video, JPEG and MPEG. Kodak's PhotoYCC(tm) uses scale factors
optimized for the gamut of film colors. Y'UV scaling is appropriate as an
ntermediate step in the formation of composite NTSC or PAL video signals,
but is not appropriate when the components are kept separate. The Y'UV
nomenclature is now used rather loosely, and it sometimes denotes any
The subscripts in CBCR and PBPR are often written in lower case. I find
this to compromise readability, so without introducing any ambiguity I
"prime" these quantities to indicate their nonlinear nature, but because no
t safe to omit the primes.
C-27 HOW DO I OBTAIN COLOR DIFFERENCE COMPONENTS FROM TRISTIMULUS
VALUES?
Here is the block diagram for luma/color difference encoding and
<< A nice diagram is included in the .PDF and .PS versions. >>
From linear XYZ - or linear R1 G1 B1 whose chromaticity coordinates are
to obtain linear RGB according to the interchange primaries. Apply a a
nonlinear transfer function ("gamma correction") to each of the components
to get nonlinear R'G'B'. Apply a 3x3 matrix to obtain color
apply a color subsampling filter to obtain subsampled color difference
components. To decode, invert the above procedure: run through the block
conforms to the interchange primaries, decoding need not explicitly use a
transfer function or the tristimulus 3x3.
The block diagram emphasizes that 3x3 matrix transforms are used for two
for which task it is intended.
C-28 HOW DO I ENCODE Y'PBPR COMPONENTS?
Although the following matrices could in theory be used for tristimulus
To encode Y'PBPR , start with the basic Y', (B'-Y') and (R'-Y')
Eq 1
[ Y' 601 ] [ 0.299 0.587 0.114 ] [ R' ]
[ B'-Y' 601 ]=[-0.299 -0.587 0.886 ]*[ G' ]
[ R'-Y' 601 ] [ 0.701 -0.587 -0.114 ] [ B' ]
{{ 0.299, 0.587, 0.114},
{-0.299,-0.587, 0.886},
{ 0.701,-0.587,-0.114}}
Y'PBPR components have unity excursion, where Y' ranges [0..+1] and each
of PB and PR ranges [-0.5..+0.5]. The (B'-Y') and (R'-Y') rows need to
be scaled. To encode from R'G'B' where reference black is 0
and reference white is +1:
Eq 2
[ Y' 601 ] [ 0.299 0.587 0.114 ] [ R' ]
[ PB 601 ]=[-0.168736 -0.331264 0.5 ]*[ G' ]
[ PR 601 ] [ 0.5 -0.418688 -0.081312 ] [ B' ]
{{ 0.299 , 0.587 , 0.114 },
{-0.168736,-0.331264, 0.5 },
{ 0.5 ,-0.418688,-0.081312}}
The first row comprises the luma coefficients; these sum to unity. The
components. The +0.5 entries reflect the maximum excursion of PB and PR of
+0.5, for the blue and red primaries [0, 0, 1] and [1, 0, 0].
The inverse, decoding matrix is this:
[ R' ] [ 1. 0. 1.402 ] [ Y' 601 ]
[ G' ]=[ 1. -0.344136 -0.714136 ]*[ PB 601 ]
[ B' ] [ 1. 1.772 0. ] [ PR 601 ]
{{ 1. , 0. , 1.402 },
{ 1. ,-0.344136,-0.714136},
{ 1. , 1.772 , 0. }}
C-29 HOW DO I ENCODE Y'CBCR COMPONENTS FROM R'G'B' IN [0, +1]?
Rec. 601 specifies eight-bit coding where Y' has an excursion of 219 and
an offset of +16. This coding places black at code 16 and white at code
footroom. CB and CR have excursions of +/-112 and offset of +128, for a
To compute Y'CBCR from R'G'B' in the range [0..+1], scale the rows of
the matrix of Eq 2 by the factors 219, 224 and 224, corresponding to the
excursions of each of the components:
Eq 3
{{ 65.481, 128.553, 24.966},
{ -37.797, -74.203, 112. },
{ 112. , -93.786, -18.214}}
Add [16, 128, 128] to the product to get Y'CBCR.
Summing the first row of the matrix yields 219, the luma excursion from
black to white. The two entries of 112 reflect the positive CBCR extrema of
the blue and red primaries.
Clamp all three components to the range 1 through 254 inclusive, since Rec.
To recover R'G'B' in the range [0..+1] from Y'CBCR, subtract [16, 128, 128]
from Y'CBCR, then multiply by the inverse of the matrix in Eq 3 above:
{{ 0.00456621, 0. , 0.00625893},
{ 0.00456621,-0.00153632,-0.00318811},
{ 0.00456621, 0.00791071, 0. }}
This looks scary, but the Y'CBCR components are integers in eight
bits and the reconstructed R'G'B' are scaled down to the range
[0..+1].
C-30 HOW DO I ENCODE Y'CBCR COMPONENTS FROM COMPUTER R'G'B' ?
and white at 255. To encode Y'CBCR from R'G'B' in the range [0..255], using
eight-bit binary arithmetic, scale the Y'CBCR matrix of Eq 3 by 256/255:
{{ 65.738, 129.057, 25.064},
{ -37.945, -74.494, 112.439},
{ 112.439, -94.154, -18.285}}
The entries in this matrix have been scaled up by 256, assuming that you will
mplement the equation in fixed-point binary arithmetic, using a shift by eight
bits. Add [16, 128, 128] to the product to get Y'CBCR.
To decode R'G'B' in the range [0..255] from Rec. 601 Y'CBCR, using
eight-bit binary arithmetic , subtract [16, 128, 128] from Y'CBCR,
then multiply by the inverse of the matrix above, scaled by 256:
Eq 4
{{ 298.082, 0. , 408.583},
{ 298.082, -100.291, -208.12 },
{ 298.082, 516.411, 0. }}
You can remove a factor of 1/256 from these coefficients, then accomplish the
multiplication by shifting. Some of the coefficients, when scaled by 256, are
larger than unity. These coefficients will need more than eight multiplier
bits.
For implementation in binary arithmetic the matrix coefficients have to be
The matrix of Eq 4 will decode standard Y'CBCR components to RGB
components in the range [0..255], subject to roundoff error. You must take
care to avoid overflow due to roundoff error. But you must protect against
overflow in any case, because studio video signals use the extremes of the
coding range to handle signal overshoot and undershoot, and these will
footroom.
C-31 HOW DO I ENCODE Y'CBCR COMPONENTS FROM STUDIO VIDEO?
Studio R'G'B' signals use the same 219 excursion as the luma component
of Y'CBCR. To encode Y'CBCR from R'G'B' in the range [0..219], using
eight-bit binary arithmetic, scale the Y'CBCR encoding matrix of Eq 3
above by 256/219. Here is the encoding matrix for studio video:
{{ 65.481, 128.553, 24.966},
{ -37.797, -74.203, 112. },
{ 112. , -93.786, -18.214}}
To decode R'G'B' in the range [0..219] from Y'CBCR, using eight-bit
binary arithmetic, use this matrix:
{{ 256. , 0. , 350.901},
{ 256. , -86.132, -178.738},
{ 256. , 443.506, 0. }}
When scaled by 256, the first column in this matrix is unity, indicating
that the corresponding component can simply be added: there is no need for
a multiplication operation. This matrix contains entries larger than 256;
the corresponding multipliers will need capability for nine bits.
The matrices in this section conform to Rec. 601 and apply directly to
conventional 525/59.94 and 625/50 video. It is not yet decided whether
emerging HDTV standards will use the same matrices, or adopt a new set of
matrices having different luma coefficients. In my view it would be
unfortunate if different matrices were adopted, because then image coding
and decoding would depend on whether the picture was small (conventional
video) or large (HDTV).
and CR components are subsampled horizontally by a factor of two with
n the vertical dimension as well, denoted 4:2:0.
Color difference coding is standardized in Rec. 601. For details on color
C-32 HOW DO I DECODE R'G'B' FROM PHOTOYCC?
Kodak's PhotoYCC uses the Rec. 709 primaries, white point and transfer
function. Reference white codes to luma 189; this preserves film
because YCC is closely associated with the PhotoCD(tm) system whose
compression methods are proprietary. But just in case, the following
equation is comparable to in that it produces R'G'B' in the range
[0..+1] from integer YCC. If you want to return R'G'B' in a different
techniques in the section above.
[ R'709 ] [ 0.0054980 0.0000000 0.0051681 ] [ Y'601,189 ] [ 0 ]
[ G'709 ]=[ 0.0054980 -0.0015446 -0.0026325 ]* ( [ C1 ] - [ 156 ] )
[ B'709 ] [ 0.0054980 0.0079533 0.0000000 ] [ C2 ] [ 137 ]
{{ 0.0054980, 0.0000000, 0.0051681},
{ 0.0054980, -0.0015446, -0.0026325},
{ 0.0054980, 0.0079533, 0.0000000}}
Decoded R'G'B' components from PhotoYCC can exceed unity or go below
zero. PhotoYCC extends the Rec. 709 transfer function above unity, and
C-33 WILL YOU TELL ME HOW TO DECODE Y'UV AND Y'IQ?
No, I won't! Y'UV and Y'IQ have scale factors appropriate to composite
NTSC and PAL. They have no place in component digital video! You shouldn't
code into these systems, and if someone hands you an image claiming it's
Y'UV, chances are it's actually Y'CBCR, it's got the wrong scale factors,
or it's linear-light.
Well OK, just this once. To transform Y', (B'-Y') and (R'-Y')
components from Eq 1 to Y'UV, scale (B'-Y') by 0.492111 to get U and
composite NTSC or PAL amplitude for all legal R'G'B' values:
<< Equation omitted -- see PostScript or PDF version. >>
To transform to Y'IQ to Y'UV, perform a 33 degree rotation and an exchange
of color difference axes:
<< Equation omitted -- see PostScript or PDF version. >>
C-34 HOW SHOULD I TEST MY ENCODERS AND DECODERS?
To test your encoding and decoding, ensure that colorbars are handled
correctly. A colorbar signal comprises a binary RGB sequence ordered for
[ 1 1 0 0 1 1 0 0 ]
[ 1 1 1 1 0 0 0 0 ]
[ 1 0 1 0 1 0 1 0 ]
To ensure that your scale factors are correct and that clipping is not
being invoked, test 75% bars, a colorbar sequence having 75%-amplitude
bars instead of 100%.
C-35 WHAT IS PERCEPTUAL UNIFORMITY?
A system is perceptually uniform if a small perturbation to a component
value is approximately equally perceptible across the range of that value.
The volume control on your radio is designed to be perceptually uniform:
ncrement in volume anywhere across the range of the control. If the
control were physically linear, the logarithmic nature of human loudness
bottom of its range.
The XYZ and RGB systems are far from exhibiting perceptual uniformity.
Finding a transformation of XYZ into a reasonably perceptually-uniform
could be agreed. So the CIE standardized two systems, L*u*v* and L*a*b*,
and V.) Both L*u*v* and L*a*b* improve the 80:1 or so perceptual
nonuniformity of XYZ to about 6:1. Both demand too much computation to
accommodate real-time display, although both have been successfully applied
to image coding for printing.
Computation of CIE L*u*v* involves intermediate u' and v ' quantities,
uprime = 4 * X / (X + 15 * Y + 3 * Z);
vprime = 9 * Y / (X + 15 * Y + 3 * Z);
First compute un' and vn' for your reference white Xn , Yn and Zn. Then
compute u' and v ' - and L* as discussed earlier - for your colors.
Finally, compute:
ustar = 13 * Lstar * (uprime - unprime);
vstar = 13 * Lstar * (vprime - vnprime);
L*a*b* is computed as follows, for (X/Xn, Y/Yn, Z/Zn) > 0.01:
astar = 500 * (pow(X / Xn, 1./3.) - pow(Y / Yn, 1./3.));
bstar = 200 * (pow(Y / Yn, 1./3.) - pow(Z / Zn, 1./3.));
These equations are great for a few spot colors, but no fun for a million
nonlinear R'G'B' coding used in video is quite perceptually uniform,
and has the advantage of being fast enough for interactive applications.
C-36 WHAT ARE HSB AND HLS?
HSB and HLS were developed to specify numerical Hue, Saturation and
Brightness (or Hue, Lightness and Saturation) in an age when users had to
flawed with respect to the properties of color vision. Now that users can
choose colors visually, or choose colors related to other media (such as
HLS should be abandoned.
Here are some of problems of HSB and HLS. In color selection where
"lightness" runs from zero to 100, a lightness of 50 should appear to be
HLS make no reference to the linearity or nonlinearity of the underlying
RGB, and make no reference to the lightness perception of human vision.
The usual formulation of HSB and HLS compute so-called "lightness" or
"brightness" as (R+G+B)/3. This computation conflicts badly with the
more intense than blue with the same "lightness" value (say L=50).
HSB and HSL are not useful for image computation because of the
of colors expressed in polar coordinates.
Nearly all formulations of HSB and HLS involve different computations
around 60 degree segments of the hue circle. These calculations introduce
visible discontinuities in color space.
Although the claim is made that HSB and HLS are "device independent", the
ubiquitous formulations are based on RGB components whose chromaticities
and white point are unspecified. Consequently, HSB and HLS are useless for
conveyance of accurate color information.
v*: h*uv for hue angle and c*uv for chroma.
C-37 WHAT IS TRUE COLOR?
True color is the provision of three separate components for additive red,
for each of the three components, so true color is sometimes referred to
as 24-bit color.
A true color system usually interposes a lookup table between each
component of the framestore and each channel to the display. This makes it
coding. In the X Window System, direct color refers to fixed lookup tables,
and truecolor refers to lookup tables that are under the control of
application software.
C-38 WHAT IS INDEXED COLOR?
number, say 256, of discrete colors in a colormap or palette. The
framebuffer stores, at each pixel, the index number of a color. At the
output of the framebuffer, a lookup table uses the index to retrieve red,
The colors in the map may be fixed systematically at the design of a
can be partitioned systematically into a 6x6x6 "cube" to implement what
amounts to a direct color system where each of red, green and blue has a
value that is an integer in the range zero to five.
An RGB image can be converted to a predetermined colormap by choosing, for
each pixel in the image, the colormap index corresponding to the "closest"
RGB triple. With a systematic colormap such as a 6x6x6 colorcube this
s straightforward. For an arbitrary colormap, the colormap has to be
"Closeness" should be determined according to the perceptibility of color
computationally prohibitive, but in practice it is adequate to use a
Euclidean distance metric in R'G'B' components coded nonlinearly
according to video practice.
A direct color image can be converted to indexed color with an
mage-dependent colormap by a process of color quantization that searches
through all of the triples used in the image, and chooses the palette for
the image based on the colors that are in some sense most "important".
Again, the decisions should be made according to the perceptibility of
color differences. Adobe Photoshop(tm) can perform this conversion.
UNIX(tm) users can employ the pbm package.
the maps associated with other windows may be disturbed. In window system
maps can cause annoying colormap flashing.
An eight-bit indexed color system requires less data to represent a
comes at a high price. The truecolor system can represent each of its
three components according to the principles of sampled continuous signals.
This makes it possible to accomplish, with good quality, operations such as
artifacts because the underlying representation lacks the properties of a
continuous representation, even if converted back to RGB.
accompanied by its colormap. Generally such a colormap has RGB entries that
are gamma corrected: the colormap's RGB codes are intended to be presented
C-39 I WANT TO VISUALIZE A SCALAR FUNCTION OF TWO VARIABLES. SHOULD I USE RGB
VALUES CORRESPONDING TO THE COLORS OF THE RAINBOW?
When you look at a rainbow you do not see a smooth gradation of colors.
or 600 nm. If you use the rainbow's colors to represent data, the
visibility of differences among your data values will depend on where they
lie in the spectrum.
uniformity. This an open research problem, but basing your system on CIE
L*a*b* or L*u*v*, or on nonlinear video-like RGB, would be a good start.
C-40 WHAT IS DITHERING?
A display device may have only a small number of choices of greyscale
values or color values at each device pixel. However if the viewer is
be set so that the viewer's eye integrates several pixels to achieve an
apparent improvement in the number of levels or colors that can be
Computer displays are generally viewed from distances where the device
visual acuity. Applying dither to a conventional computer display often
ntroduces objectionable artifacts. However, careful application of dither
can be effective. For example, human vision has poor acuity for blue
be dithered across two-by-two pixel arrays to produce four times the number
of blue levels, with no perceptible penalty at normal viewing distances.
C-41 HOW DOES HALFTONING RELATE TO COLOR?
The processes of offset printing and conventional laser printing are
ntrinsically bilevel: a particular location on the page is either covered
closely-spaced dots of variable size. An array of small dots produces the
This process is called halftoning or screening. In a sense this is
Halftone dots are usually placed in a regular grid, although stochastic
black grids that have exactly the same dot pitch but different
carefully-chosen screen angles. The recently introduced technique of
Flamenco screening uses the same screen angles for all screens, but its
Agfa's booklet [17] is an excellent introduction to practical concerns of
algorithms is Ulichney [18], but that work does not detail the
nonlinearities found in practical printing systems. For details about
Asked Questions about Gamma for an introduction to the transfer function of
offset printing.
C-42 WHAT'S A COLOR MANAGEMENT SYSTEM?
Software and hardware for scanner, monitor and printer calibration have had
limited success in dealing with the inaccuracies of color handling in
cannot address the end-to-end system. Certain application developers have
added color transformation capability to their applications, but the
majority of application developers have insufficient expertise and
nsufficient resources to invest in accurate color.
A color management system (CMS) is a layer of software resident on a
computer that negotiates color reproduction between the application and
color devices. It cooperates with the operating system and the graphics
library components of the platform software. Color management systems
between diverse devices, in various color coding systems including RGB,
CMYK and CIE L*a*b*.
The CMS makes available to the application a set of facilities whereby the
application can determine what color devices and what color spaces are
available. When the application wishes to access a particular device, it
abstract color spaces such as CIE XYZ, CIE L*a*b* or calibrated RGB.
Alternatively a color space can be associated with a particular device. In
the second case the Color manager needs access to characterization data
for the device, and perhaps also to calibration data that reflects the
Sophisticated color management systems are commercially available from
Kodak, Electronics for Imaging (EFI) and Agfa. Apple's ColorSync(tm)
management capabilities either built-in to ColorSync or provided by a
version of Solaris.
The basic CMS services provided with desktop operating systems are likely
to be adequate for office users, but are unlikely to satisfy high-end users
transform machinery. Advanced color management modules will be
commercially available from third parties.
C-43 HOW DOES A CMS KNOW ABOUT PARTICULAR DEVICES?
A CMS needs access to information that characterizes the color
characterization data for a device is called a device profile. Industry
agreement has been reached on the format of device profiles, although
the forthcoming ColorSync version 2.0 will adhere to this agreement.
Vendors of color peripherals will soon provide industry-standard profiles
characterization services.
Agfa's FotoTune(tm) software - part of Agfa's FotoFlow(tm) color manager -
can create device profiles.
C-44 IS A COLOR MANAGEMENT SYSTEM USEFUL FOR COLOR SPECIFICATION?
Not yet. But color management system interfaces in the future are likely
to include the ability to accommodate commercial proprietary color
are likely to provide their color specification systems in shrink-wrapped
form to plug into color managers. In this way, users will have guaranteed
color accuracy among applications and peripherals, and application vendors
C-45 I'M NOT A COLOR EXPERT. WHAT PARAMETERS SHOULD I USE TO CODE MY
IMAGES?
Use the CIE D65 white point (6504 K) if you can.
Use the Rec. 709 primary chromaticities. Your monitor is probably already
quite close to this. Rec. 709 has international agreement, offers excellent
use the Rec. 709 transfer function, with its 0.45-power law. If you need
Mac compatibility you will have to suffer a penalty in perceptual
them to QuickDraw.
To code luma, use the Rec. 601 luma coefficients 0.299, 0.587 and 0.114.
Use Rec. 601 digital video coding with black at 16 and white at 235.
Use prime symbols (') to denote all of your nonlinear components!
Y'CBCR coding with Rec. 601 studio video (16..235/128+/-112) excursion.
Tag your image data with the primary and white chromaticity, transfer
function and luma coefficients that you are using. TIFF 6.0 tags have been
or in the future, to determine the parameters of your coded image and give
you the best possible results.
C-46 REFERENCES
[1] Publication CIE No 17.4, International Lighting Vocabulary. Central
Bureau of the Commission Internationale de L'Eclairage, Vienna, Austria.
[2] LeRoy E. DeMarsh and Edward J. Giorgianni, "Color Science for Imaging
Systems", Physics Today, September 1989, 44-52.
[3] W.F. Schreiber, Fundamentals of Electronic Imaging Systems, Second
Edition (Springer-Verlag, 1991).
[4] Publication CIE No 15.2, Colorimetry, Second Edition (1986), Central
Bureau of the Commission Internationale de L'Eclairage, Vienna, Austria.
[5] Guenter Wyszecki and W.S. Styles, Color Science: Concepts and Methods,
Quantitative Data and Formulae, Second Edition (New York: John
Wiley & Sons, 1982).
[6] Guenter Wyszecki and D.B. Judd, Color in Business, Science and
[7] R.W.G. Hunt, The Reproduction of Colour in Photography, Printing and
Television, Fourth Edition (Fountain Press, Tolworth, England, 1987).
[8] ITU-R Recommendation BT.709, Basic Parameter Values for the HDTV
Standard for the Studio and for International Programme Exchange (1990),
[formerly CCIR Rec. 709], ITU, 1211 Geneva 20, Switzerland.
[9] Bruce J. Lindbloom, "Accurate Color Reproduction for Computer Graphics
Applications", Computer Graphics, Vol. 23, No. 3 (July 1989), 117-126
(proceedings of SIGGRAPH '89).
[10] William B. Cowan, "An Inexpensive Scheme for Calibration of a Colour
Monitor in terms of CIE Standard Coordinates", Computer Graphics, Vol. 17,
No. 3 (July 1983), 315-321.
[11] SMPTE RP 177-1993, Derivation of Basic Television Color Equations.
[12] Television Engineering Handbook, Featuring HDTV Systems, Revised
Edition by K. Blair Benson, revised by Jerry C. Whitaker (McGraw-Hill,
[13] Roy Hall, Illumination and Color in Computer Generated Imagery
(Springer-Verlag, 1989).
[14] Chet S. Haase and Gary W. Meyer, "Modelling Pigmented Materials for
Realistic Image Synthesis", ACM Transactions on Graphics, Vol. 11, No. 4,
[15] Maureen C. Stone, William B. Cowan and John C. Beatty, "Color Gamut
Mapping and the Printing of Digital Color Images", ACM Transactions on
Graphics, Vol. 7, No. 3, October 1988.
[16] Charles A. Poynton, A Technical Introduction To Digital Video.
New York: John Wiley & Sons, 1996.
[17] Agfa Corporation, An introduction to Digital Color Prepress, Volumes 1
and 2 (1990), Prepress Education Resources, P.O. Box 7917 Mt. Prospect, IL
[18] Robert Ulichney, Digital Halftoning (Cambridge, Mass.: MIT Press,
[19] Peter Fink, PostScript Screening: Adobe Accurate Screens (Mountain
View, Calif.: Adobe Press, 1992).
C-47 CONTRIBUTORS
Thanks to Norbert Gerfelder, Alan Roberts and Fred Remley for their
Giorgianni, Junji Kumada and Bill Cowan. Thanks!
Charles A. Poynton
<http://www.inforamp.net/~poynton/>
.
