ColorFAQ -- FREQUENTLY ASKED QUESTIONS ABOUT COLOR

(a.k.a. ColourFAQ -- FREQUENTLY ASKED QUESTIONS ABOUT COLOUR)

Charles Poynton
colorfaq@poynton.com
<http://www.poynton.com/ColorFAQ.txt>

Copyright (c) 2006-11-28


This document clarifies aspects of color specification and image coding
that are important to computer graphics, image processing, video, and
the transfer of digital images to print. 

The current version of this document, including a typeset version in Acrobat PDF 
format, is available on the Internet linked from 
<http://www.poynton.com/ColorFAQ.html>. 

The document "Colour Space Conversions," by Adrian Ford and Alan
Roberts, details transforms among color spaces such as RGB, HSI, CMY and
video. Find it at <http://www.poynton.com/PDFs/coloureq.pdf>. 

Steve Westland has written "Frequently asked questions about Colour
Physics", available at <http://www.colourware.co.uk/cpfaq.htm>. 

I assume that you are familiar with intensity, luminance (CIE Y),
lightness (CIE L*), and the nonlinear relationship between CRT voltage
and intensity (gamma). To learn more about these topics, read the
companion GammaFAQ, Frequently Asked Questions about Gamma. 

I retain copyright to this note. You have permission to use it, but you
may not publish it. 


CONTENTS

    0.   Where does this document live?
    1.   What is color?
    2.   What is intensity?
    3.   What is luminance?
    4.   What is lightness?
    5.   What is hue?
    6.   What is saturation?
    7.   How is color specified?
    8.   Should I use a color specification system for image data?
    9.   What weighting of red, green and blue corresponds to brightness?
    10.  Can blue be assigned fewer bits than red or green?
    11.  What is "luma"?
    12.  What are CIE XYZ components?
    13.  Does my scanner use the CIE spectral curves?
    14.  What are CIE x and y chromaticity coordinates?
    15.  What is white?
    16.  What is color temperature?
    17.  How can I characterize red, green and blue?
    18.  How do I transform between CIE XYZ and a particular set of RGB
          primaries?
    19.  Is RGB always device-dependent?
    20.  How do I transform data from one set of RGB primaries to another?
    21.  Should I use RGB or XYZ for image synthesis?
    22.  What is subtractive color?
    23.  Why did my grade three teacher tell me that the primaries are red,
          yellow and blue?
    24.  Is CMY just one-minus-RGB?
    25.  Why does offset printing use black ink in addition to CMY?
    26.  What are color differences?
    27.  How do I obtain color difference components from tristimulus values?
    28.  How do I encode Y'PBPR components?
    29.  How do I encode Y'CBCR components from R'G'B' in [0, +1]?
    30.  How do I encode Y'CBCR components from computer R'G'B' ?
    31.  How do I encode Y'CBCR components from studio video?
    32.  How do I decode R'G'B' from PhotoYCC?
    33.  Will you tell me how to decode Y'UV and Y'IQ?
    34.  How should I test my encoders and decoders?
    35.  What is perceptual uniformity?
    36.  What are HSB and HLS?
    37.  What is true color?
    38.  What is indexed color?
    39.  I want to visualize a scalar function of two variables. Should I use
          RGB values corresponding to the colors of the rainbow?
    40.  What is dithering?
    41.  How does halftoning relate to color?
    42.  What's a color management system?
    43.  How does a CMS know about particular devices?
    44.  Is a color management system useful for color specification?
    45.  I'm not a color expert. What parameters should I use to 
          code my images?
    46.  References
    47.  Contributors


0.   WHERE DOES THIS DOCUMENT LIVE?

This document resides in Toronto, linked from the Color FAQ Abstract
page, <http://www.poynton.com/colorfaq/>. Should you wish
to make a link to the Color FAQ, link to that page, not directly to
this one. This will allow me the flexibility to move it, saving
visitors the frustration of stale links.

PDF Notes

If you would like to print this document, or view it with decent typography, 
I recommend that you obtain the Acrobat PDF version of this note. The page 
indicated above contains links to the PDF version. 


1.   WHAT IS COLOR?

Color is the perceptual result of light in the visible region of the
spectrum, having wavelengths in the region of 400 nm to 700 nm, incident
upon the retina. Physical power (or radiance) is expressed in a spectral
power distribution (SPD), often in 31 components each representing a 10 nm
band.

The human retina has three types of color photoreceptor cone cells, which
respond to incident radiation with somewhat different spectral response
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
role in image reproduction.

Because there are exactly three types of color photoreceptor, three
numerical components are necessary and sufficient to describe a color,
providing that appropriate spectral weighting functions are used. This is
the concern of the science of colorimetry. In 1931, the Commission
Internationale de L'Eclairage (CIE) adopted standard curves for a
hypothetical Standard Observer. These curves specify how an SPD can be
transformed into a set of three numbers that specifies a color.

The CIE system is immediately and almost universally applicable to
self-luminous sources and displays. However the colors produced by
reflective systems such as photography, printing or paint are a function
not only of the colorants but also of the SPD of the ambient illumination.
If your application has a strong dependence upon the spectrum of the
illuminant, 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.


2.   WHAT IS INTENSITY?

Intensity is a measure over some interval of the electromagnetic spectrum
of the flow of power that is radiated from, or incident on, a surface.
Intensity is what I call a linear-light measure, expressed in units such as
watts per square meter.

The voltages presented to a CRT monitor control the intensities of the
color components, but in a nonlinear manner. CRT voltages are not
proportional to intensity.


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
sensitivity function that is characteristic of vision. The luminous
efficiency of the Standard Observer is defined numerically, is everywhere
positive, and peaks at about 555 nm. When an SPD is integrated using this
curve as a weighting function, the result is CIE luminance, denoted Y.

The magnitude of luminance is proportional to physical power. In that sense
it 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
per meter squared, but in practice it is often normalized to 1 or 100 units
with respect to the luminance of a specified or implied white reference.
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.


4.   WHAT IS LIGHTNESS?

Human vision has a nonlinear perceptual response to brightness: a source
having a luminance only 18% of a reference luminance appears about half as
bright. The perceptual response to luminance is called Lightness. It is
denoted L* and is defined by the CIE as a modified cube root of luminance:

  Lstar = -16 + 116 * (pow(Y / Yn), 1. / 3.)

Yn is the luminance of the white reference. If you normalize luminance to
reference white then you need not compute the fraction. The CIE definition
applies a linear segment with a slope of 903.3 near black, for (Y/Yn) <=
0.008856. The linear segment is unimportant for practical purposes but if
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
intensities differ by more than one about percent.

Video systems approximate the lightness response of vision using R'G'B'
signals that are each subject to a 0.45 power function. This is comparable
to the 1/3 power function defined by L*.


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 blue, 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.


6.   WHAT IS SATURATION?

Again from the CIE, saturation is the colorfulness of an area judged in
proportion to its brightness. Saturation runs from neutral gray through
pastel to saturated colors. Roughly speaking, the more an SPD is
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.


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
section 36.

A color specification system needs to be able to represent any color with
high precision. Since few colors are handled at a time, a specification
system can be computationally complex. Any system for color specification
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
proportions of standard (or secret) inks that can be mixed to make the
color. That's how pantone(tm) works. Although widespread, it's
proprietary. No translation to CIE is publicly available.


8.   SHOULD I USE A COLOR SPECIFICATION SYSTEM FOR IMAGE DATA?

A digitized color image is represented as an array of pixels, where each
pixel contains numerical components that define a color. Three components
are necessary and sufficient for this purpose, although in printing it is
convenient to use a fourth (black) component.

In theory, the three numerical values for image coding could be provided by
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
reasonably wide range of colors and not all of the colors. So image
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
image coding.

If you manufacture cars, you have to match the color of paint on the door
with the color of paint on the fender. A color specification system will
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].


9.   WHAT WEIGHTING OF RED, GREEN AND BLUE CORRESPONDS TO BRIGHTNESS?

Direct acquisition of luminance requires use of a very specific spectral
weighting. However, luminance can also be computed as a weighted sum of
red, green and blue components.

If three sources appear red, green and blue, and have the same radiance in
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
spectrum. The red will appear less bright, and the blue will be the darkest
of the three. As a consequence of the luminous efficiency function, all
saturated blue colors are quite dark and all saturated yellows are quite
light. If luminance is computed from red, green and blue, the coefficients
will be a function of the particular red, green and blue spectral weighting
functions employed, but the green coefficient will be quite large, the red
will have an intermediate value, and the blue coefficient will be the
smallest of the three.

Contemporary CRT phosphors are standardized in Rec. 709 [8], to be
described in section 17. The weights to compute true CIE luminance from
linear red, green and blue (indicated without prime symbols), for the Rec.
709, are these:

  Y = 0.2126 * R + 0.7152 * G + 0.0722 * 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.


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
introduce noticeable contouring in blue areas of your pictures.


11.  WHAT IS "LUMA"?

It is useful in a video system to convey a component representative of
luminance and two other components representative of color. It is
important to convey the component representative of luminance in such a way
that noise (or quantization) introduced in transmission, processing and
storage has a perceptually similar effect across the entire tone scale from
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
is 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
phosphors of 1953 are standardized in ITU-R Recommendation BT. 601-2
(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.


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
spectral weighting curves of X and Z have been standardized by the CIE
based on statistics from experiments involving human observers. XYZ
tristimulus values can describe any color. (RGB tristimulus values will be
described later.)

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].


13.  DOES MY SCANNER USE THE CIE SPECTRAL CURVES?

Probably not. Scanners are most often used to scan images such as color
photographs and color offset prints that are already "records" of three
components of color information. The usual task of a scanner is not
spectral analysis but extraction of the values of the three components that
have already been recorded. Narrowband filters are more suited to this task
than filters that adhere to the principles of colorimetry.

If you place on your scanner an original colored object that has
"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.


14.  WHAT ARE CIE x AND y CHROMATICITY COORDINATES?

It is often convenient to discuss "pure" color in the absence of
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
range 400 nm to 700 nm, it traces a shark-fin shaped spectral locus in (x,
y) coordinates. The sensation of purple cannot be produced by a single
wavelength: to produce purple requires a mixture of shortwave and longwave
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
it's daunting. For Wyszecki's own condensed version, see Color in Business,
Science and Industry, Third Edition [6]. It is directed to the color
industry: ink, paint and the like. For an approachable introduction to the
same theory, accompanied by descriptions of image reproduction, try to find
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.


15.  WHAT IS WHITE?

In additive image reproduction, the white point is the chromaticity of the
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
subtractive reproduction, white is the SPD of the illumination, multiplied
by the SPD of the media. There is no unique physical or perceptual
definition of white, so to achieve accurate color interchange you must
specify the characteristics of your white.

It is often convenient for purposes of calculation to define white as a
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
have a good reason to use something else. The print industry commonly uses
D50 and photography commonly uses D55. These represent compromises between
the conditions of indoor (tungsten) and daylight viewing.


16.  WHAT IS COLOR TEMPERATURE?

Planck determined that the SPD radiated from a hot object - a black body
radiator - is a function of the temperature to which the object is heated.
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
same hue.

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
isolation - such as a slide projected in a dark room - creates its own
white reference, and a viewer will be quite tolerant of errors in the white
point. But if the same image is viewed in the presence of an external white
reference or a second image, then differences in white point can be
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
3200 K, always appears somewhat yellow.


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
spectra add. The largest range of colors will be produced with primaries
that appear red, green and blue. Human color vision obeys the principle of
superposition, so the color produced by any additive mixture of three
primary spectra can be predicted by adding the corresponding fractions of
the XYZ components of the primaries: the colors that can be mixed from a
particular set of RGB primaries are completely determined by the colors of
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
diagram by a triangle whose vertices are the chromaticities of the
primaries.

In computing there are no standard primaries or white point. If you have an
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
phosphors used in color CRTs of that era. But phosphors changed over the
years, primarily in response to market pressures for brighter receivers,
and by the time of the first the videotape recorder the primaries in use
were quite different than those "on the books". So although you may see the
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
primaries for high definition television (HDTV), and these primaries are
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
 
white    0.3127  0.3290  0.3582

For a discussion of nonlinear RGB in computer graphics, see Lindbloom [9]. 
For technical details on monitor calibration, consult Cowan [10].


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
gamut for a particular RGB transform to RGB where one or more RGB
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,
1, 1] to XYZ, then compute x and y.


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
produce additive color involve tolerances and uncertainties, but if you
have a monitor that conforms to Rec. 709 within some tolerance, you can
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
devices such as flat-panel displays that do not have the same physics as
CRTs.


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
into 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'
domain the resulting errors will be insignificant.

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.


21.  SHOULD I USE RGB OR XYZ FOR IMAGE SYNTHESIS?

Once light is on its way to the eye, any tristimulus-based system will
work. But the interaction of light and objects involves spectra, not
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].


22.  WHAT IS SUBTRACTIVE COLOR?

Subtractive systems involve colored dyes or filters that absorb power from
selected regions of the spectrum. The three filters are placed in tandem. A
dye that appears cyan absobs longwave (red) light. By controlling the
amount of cyan dye (or ink), you modulate the amount of red in the image.

In physical terms the spectral transmission curves of the colorants
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
density of 1, transmission of 0.01 corresponds to a density of 2 and so on.
When a printer or photographer computes the effect of filters in tandem, he
subtracts density values instead of multiplying transmission values, so 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
green sources add to produce yellow.


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
subtractively to the extent that they are transparent (like watercolors).
This question also relates to color names: your grade three "red" was
probably a little on the magenta side, and "blue" was probably quite cyan.
For a discussion of paint mixing from a computer graphics perspective,
consult Haase [14].


24.  IS CMY JUST ONE-MINUS-RGB?

In a theoretical subtractive system, CMY filters could have spectral
absorption curves with no overlap. The color reproduction of the system
would correspond exactly to additive color reproduction using the red,
green and blue primaries that resulted from pairs of filters in
combination.

Practical photographic dyes and offset printing inks have spectral
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
where accurate color need not be preserved, but the method fails to
produce acceptable color images.

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
primaries cannot be determined from the colors of the primaries
themselves, but are also a function of the colors of the sets of
combinations of the primaries.

Print and photographic reproduction is also complicated by nonlinearities
in the response of the three (or four) channels. In offset printing, the
physical and optical processes of dot gain introduce nonlinearity that is
roughly comparable to gamma correction in video. In a typical system used
for print, a black code of 128 (on a scale of 0 to 255) produces a
reflectance of about 0.26, not the 0.5 that you would expect from a linear
system. Computations cannot be meaningfully performed on CMY components
without taking nonlinearity into account.

For a detailed discussion of transferring colorimetric image data to print
media, see Stone [15].


25.  WHY DOES OFFSET PRINTING USE BLACK INK IN ADDITION TO CMY?

Printing black by overlaying cyan, yellow and magenta ink in offset
printing has three major problems. First, colored ink is expensive.
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
register, then black edges will suffer colored tinges. Vision is most
demanding of spatial detail in black and white areas. Printing black with a
single ink minimizes the visibility of registration errors.

Other printing processes may or may not be subject to similar constraints.


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
perceptual uniformity concerns numerical differences that correspond to
color differences at the threshold of perceptibility (just noticeable
differences, or JNDs).

In its second sense, color difference refers to color components where
brightness is "removed". Vision has poor response to spatial detail in
colored areas of the same luminance, compared to its response to luminance
spatial detail. If data capacity is at a premium it is advantageous to
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.

Instead of using a true luminance component to represent brightness, it is
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
intermediate 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
scaling of (B'-Y') and (R'-Y'). Y  'IQ coding is obsolete.

The subscripts in CBCR and PBPR are often written in lower case. I find
this to compromise readability, so without introducing any ambiguity I
write them in uppercase. Authors with great attention to detail sometimes
"prime" these quantities to indicate their nonlinear nature, but because no
practical image coding system employs linear color differences I consider
it safe to omit the primes.


27.  HOW DO I OBTAIN COLOR DIFFERENCE COMPONENTS FROM TRISTIMULUS
      VALUES?

Here is the block diagram for luma/color difference encoding and
decoding:

<< A nice diagram is included in the .PDF and .PS versions. >>

From linear XYZ - or linear R1 G1 B1 whose chromaticity coordinates are
different from the interchange standard - apply a 3x3 matrix transform
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
difference components such as Y'PBPR , Y'CBCR or PhotoYCC. If necessary,
apply a color subsampling filter to obtain subsampled color difference
components. To decode, invert the above procedure: run through the block
diagram right-to-left using the inverse operations. If your monitor
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
distinctly different tasks. When someone hands you a 3x3, you have to ask
for which task it is intended.


28.  HOW DO I ENCODE Y'PBPR COMPONENTS?

Although the following matrices could in theory be used for tristimulus
signals, it is ubiquitous to use them with gamma-corrected signals.

To encode Y'PBPR , start with the basic Y', (B'-Y') and (R'-Y')
relationships:

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
second and third rows each sum to zero, a necessity for color difference
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.      }}


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
235, reserving the extremes of the range for signal processing headroom and
footroom. CB and CR have excursions of +/-112 and offset of +128, for a
range of 16 through 240 inclusive.

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.
601 reserves codes 0 and 255 for synchronization signals.

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].


30.  HOW DO I ENCODE Y'CBCR COMPONENTS FROM COMPUTER R'G'B' ?

In computing it is conventional to use eight-bit coding with black at code 0
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
implement 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
rounded. When you round, take care to preserve the row sums of [1, 0, 0].

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
require clipping when decoded to an RGB range that has no headroom or
footroom.


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).

In digital video, Rec. 601 standardizes subsampling denoted 4:2:2, where CB
and CR components are subsampled horizontally by a factor of two with
respect to luma. JPEG and MPEG conventionally subsample by a factor of two
in the vertical dimension as well, denoted 4:2:0.

Color difference coding is standardized in Rec. 601. For details on color
difference coding as used in video, consult Poynton [16].


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
highlights. The color difference coding is asymmetrical, to encompass film
gamut. You are unlikely to encounter any raw image data in PhotoYCC form
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
range, or implement the equation in eight-bit integer arithmetic, use the
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
reflects it around zero, to accommodate wide excursions of R'G'B'. To
decode to CRT primaries, clip R'G'B' to the range zero to one.


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
scale R'-Y' by 0.877283 to get V. The factors are chosen to limit
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. >>


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
decreasing luma: white, yellow, cyan, green, magenta, red, blue and black.

  [ 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%.


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:
rotating the knob ten degrees produces approximately the same perceptual
increment in volume anywhere across the range of the control. If the
control were physically linear, the logarithmic nature of human loudness
perception would place all of the perceptual "action" of the control at the
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
space consumed a decade or more at the CIE and in the end no single system
could be agreed. So the CIE standardized two systems, L*u*v* and L*a*b*,
sometimes written CIELUV and CIELAB. (The u and v are unrelated to video U
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,
where the prime denotes the successor to the obsolete 1960 CIE u and v
system:

  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
pixels. Although it was not specifically optimized for this purpose, the
nonlinear R'G'B' coding used in video is quite perceptually uniform,
and has the advantage of being fast enough for interactive applications.


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
specify colors numerically. The usual formulations of HSB and HLS are
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
PANTONE), or use perceptually-based systems like L*u*v* and L*a*b*, HSB and
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
half as bright as a lightness of 100. But the usual formulations of HSB and
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
properties of color vision, as it computes yellow to be about six times
more intense than blue with the same "lightness" value (say L=50).

HSB and HSL are not useful for image computation because of the
discontinuity of hue at 360 degrees. You cannot perform arithmetic mixtures
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.

If you really need to specify hue and saturation by numerical values,
rather than HSB and HSL you should use polar coordinate version of u* and
v*: h*uv for hue angle and c*uv  for chroma.


37.  WHAT IS TRUE COLOR?

True color is the provision of three separate components for additive red,
green and blue reproduction. True color systems often provide eight bits
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
possible to use a true color system with either linear or nonlinear
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.


38.  WHAT IS INDEXED COLOR?

Indexed color (or pseudocolor), is the provision of a relatively small
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,
green and blue components that are then sent to the display.

The colors in the map may be fixed systematically at the design of a
system. As an example, 216 index entries an eight-bit indexed color system
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
is straightforward. For an arbitrary colormap, the colormap has to be
searched looking for entries that are "close" to the requested color.
"Closeness" should be determined according to the perceptibility of color
differences. Using color systems such as CIE L*u*v* or L*a*b* is
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
image-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.

If your system accommodates arbitrary colormaps, when the map associated
with the image in a particular window is loaded into the hardware colormap,
the maps associated with other windows may be disturbed. In window system
such as the X Window System(tm) running on a multitasking operating system
such as UNIX, even moving the cursor between two windows with different
maps can cause annoying colormap flashing.

An eight-bit indexed color system requires less data to represent a
picture than a twenty-four bit truecolor system. But this data reduction
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
resizing the image. In indexed color these operations introduce severe
artifacts because the underlying representation lacks the properties of a
continuous representation, even if converted back to RGB.

In graphic file formats such as GIF of TIFF, an indexed color image is
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
directly to a CRT, without further gamma correction.


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.
Instead, some bands appear quite narrow, and others are quite broad.
Perceptibility of hue variation near 540 nm is half that of either 500 nm
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.

If you are using color to aid in the visual detection of patterns, you
should use colors chosen according to the principles of perceptual
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.


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
sufficiently distant from the display, the value of neighboring pixels can
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
reproduced.

Computer displays are generally viewed from distances where the device
pixels subtend a rather large angle at the viewer's eye, relative to his
visual acuity. Applying dither to a conventional computer display often
introduces objectionable artifacts. However, careful application of dither
can be effective. For example, human vision has poor acuity for blue
spatial detail but good color discrimination capability in blue. Blue can
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.


41.  HOW DOES HALFTONING RELATE TO COLOR?

The processes of offset printing and conventional laser printing are
intrinsically bilevel: a particular location on the page is either covered
with ink or not. However, each of these devices can reproduce
closely-spaced dots of variable size. An array of small dots produces the
perception of light gray, and an array of large dots produces dark gray.
This process is called halftoning or screening. In a sense this is
dithering, but with device dots so small that acceptable pictures can be
produced at reasonable viewing distances.

Halftone dots are usually placed in a regular grid, although stochastic
screening has recently been introduced that modulates the spacing of the
dots rather than their size.

In color printing it is conventional to use cyan, magenta, yellow and
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
registration requirements are more stringent than conventional offset
printing.

Agfa's booklet [17] is an excellent introduction to practical concerns of
printing. And it's in color! The standard reference to halftoning
algorithms is Ulichney [18], but that work does not detail the
nonlinearities found in practical printing systems. For details about
screening for color reproduction, consult Fink [19]. Consult Frequently
Asked Questions about Gamma for an introduction to the transfer function of
offset printing.


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
desktop computing. These solutions deal with specific pairs of devices but
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
insufficient 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
perform the color transformations necessary to exchange accurate color
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
requests that the color manager perform a mathematical transform from one
space to another. The color spaces involved can be device-independent
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
state of the particular instance of the device.

Sophisticated color management systems are commercially available from
Kodak, Electronics for Imaging (EFI) and Agfa. Apple's ColorSync(tm)
provides an interface between a Mac application program and color
management capabilities either built-in to ColorSync or provided by a
plug-in. Sun has announced that Kodak's CMS will be shipped with the next
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
such as in prepress. All of the announced systems have provisions for
plug-in color management modules (CMMs) that can provide sophisticated
transform machinery. Advanced color management modules will be
commercially available from third parties. 


43.  HOW DOES A CMS KNOW ABOUT PARTICULAR DEVICES?

A CMS needs access to information that characterizes the color
reproduction capabilities of particular devices. The set of
characterization data for a device is called a device profile. Industry
agreement has been reached on the format of device profiles, although
details have not yet been publicly disseminated. Apple has announced that
the forthcoming ColorSync version 2.0 will adhere to this agreement.
Vendors of color peripherals will soon provide industry-standard profiles
with their devices, and they will have to make, buy or rent
characterization services.

If you have a device that has not been characterized by its manufacturer,
Agfa's FotoTune(tm) software - part of Agfa's FotoFlow(tm) color manager -
can create device profiles.


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
specification systems such as pantone(tm) and colorcurve(tm). These vendors
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
will no longer need to pay to license these systems individually.


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
performance, and is the basis for HDTV development so it's future-proof.

If you need to operate in linear light, so be it. Otherwise, for best
perceptual performance and maximum ease of interchange with digital video,
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
performance. Raise tristimulus values to the 1/1.8-power before presenting
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!

PhotoCD uses all of the preceding measures. PhotoCD codes color
differences asymmetrically, according to film gamut. Unless you have a
requirement for film gamut, you should code into color differences using
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
defined for these parameters. This will enable intelligent readers, today
or in the future, to determine the parameters of your coded image and give
you the best possible results.


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
Industry, Third Edition (New York: John Wiley & Sons, 1975).

[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,
1992). This supersedes the Second Edition.

[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,
1992, p. 305.

[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 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
60056-7917. 800-395-7007.

[18] Robert Ulichney, Digital Halftoning (Cambridge, Mass.: MIT Press,
1988).

[19] Peter Fink, PostScript Screening: Adobe Accurate Screens (Mountain
View, Calif.: Adobe Press, 1992).


47.  CONTRIBUTORS

Thanks to Norbert Gerfelder, Alan Roberts and Fred Remley for their
proofreading and editing. I learned about color from LeRoy DeMarsh, Ed
Giorgianni, Junji Kumada and Bill Cowan. Thanks!

I welcome corrections, and suggestions for additions and improvements.


Charles Poynton
colorfaq@poynton.com
<http://www.poynton.com/colorfaq/>
