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A Guided Tour of Color Space
Charles Poynton
This article describes the theory of color repro-
duction in video, and some of the engineering
compromises necessary to make practical
cameras and practical coding systems.
Video processing is generally concerned with
color represented in three components derived
from the scene, usually red, green, and blue or
components computed from these. Once red,
green, and blue components of a scene are
obtained, color coding systems transform these
components into other forms suitable for
processing, recording, and transmission. Accu-
rate color reproduction depends on knowledge
of exactly how the physical spectra of the orig-
inal scene are transformed into these compo-
nents and exactly how the color components are
transformed to physical spectra at the display.
I use the term
luminance
and the symbol
Y
to
refer to true, CIE luminance, a linear-light quan-
tity proportional to physical intensity. I use the
term
luma
and the symbol
Y’
to refer to the
signal that is used in video to approximate lumi-
nance. I you are unfamiliar with these terms or
this usage, see page 24 of my book
1
.
Trichromaticity
Color is the perceptual result of light having
wavelength from 400 to 700 nm that is incident
upon the retina.
The human retina has three types of color
photoreceptor
cone
cells, which respond to inci-
1 Charles Poynton,
A Technical Introduction to Digital
Video
(New York: John Wiley & Sons, 1996)
dent radiation with different spectral response
curves. Because there are exactly three types of
color photoreceptors, three components are
necessary and sufficient to describe a color,
providing that appropriate spectral weighting
functions are used: Color vision is inherently
trichromatic
.
A fourth type of photoreceptor cell, the
rod
, is
also present in the retina. Rods are effective only
at extremely low light intensities. Because there
is only one type of rod cell, “night vision” cannot
perceive color. Image reproduction takes place at
light levels sufficiently high that the rod recep-
tors play no role.
Isaac Newton said, “Indeed rays, properly
expressed, are not colored.” Spectral power
distributions (SPDs) exist in the physical world,
but color exists only in the eye and the brain.
Color specification
The Commission Internationale de L’Éclairage
(CIE) has defined a system to compute a triple of
numerical components that can be considered to
be the mathematical coordinates of color space.
Their function is analogous to coordinates on a
map. Cartographers have different map projec-
tions for different functions: Some map projec-
tions preserve areas, others show latitudes and
longitudes as straight lines. No single map
projection fills all the needs of map users. Simi-
larly, no single color system fills all of the needs
of color users.
This is an edited version of a paper first published in New
Foundations for Video Technology (Proceedings of the
SMPTE Advanced Television and Electronic Imaging
Conference, San Francisco, Feb. 1995), 167- 180.
Author’s address: 56A Lawrence Avenue E,
Toronto ON M4N 1S3, Canada.
E-mail poynton@poynton.com,
www.inforamp.net/~poynton
A Guided Tour of Color Space
2
Any system for color specification must be inti-
mately related to the CIE specifications. The
systems useful for color specification are all
based on CIE
XYZ
. Numerical specification of
hue and saturation has been standardized by the
CIE, but is not useful for color specification.
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.
An ink color can be specified by the proportions
of standard or proprietary inks that can be mixed
to make the color. Ink mixture is beyond the
scope of this paper.
The science of colorimetry forms the basis for
describing a color as three numbers. However,
classical colorimetry is intended for the specifica-
tion of color, not for color image coding.
Although an understanding of colorimetry is
necessary to achieve good color performance in
video, strict application of colorimetry is unsuit-
able.
Color image coding
A color image is represented as an array of
pixels, where each pixel contains numerical
components that define a color. Three compo-
nents 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 inti-
mately 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
RGB
, nonlinear
CMY
, nonlinear
CMYK
, and derivatives of nonlinear
RGB
such as
Y’C
B
C
R
. 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. However, 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, consult DeMarsh and
Linear-Light
Tristimulus
(x, y)
Chromaticity
Image Coding Systems
Perceptually
Uniform
Hue-
Oriented
CIE XYZ
CIE xyY
Linear RGB
}
HLS, HSB
Nonlinear
R’G’B’
CIE L*a*b* CIE L* h
ab
c
ab
CIE L* h
uv
c
uv
CIE L*u*v* TekHVC
Nonlinear
Y’C
B
C
R
3
×
3
3
×
3
POLAR/
RECTANGULAR
SCALED POLAR/
RECTANGULAR
POLAR/
RECTANGULAR
NONLINEAR
TRANSFORM
NONLINEAR
TRANSFORM
TRANSFER
FUNCTION
PROJECTIVE
TRANSFORM
NONLINEAR
TRANSFORM
PROJECTIVE
TRANSFORM
Figure 1 Color systems can be classified into four
groups that are related by different kinds of transfor-
mations. Tristumulus systems and perceptually-
uniform systems are useful for image coding.
A Guided Tour of Color Space
3
Giorgianni
2
. For a terse, complete technical
treatment, read Schreiber
3
.
Definitions
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.
Brightness
is defined by the CIE as “the attribute
of a visual sensation according to which an area
appears to exhibit 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.
Hue
is the attribute of a color perception
denoted by blue, green, yellow, red, and so on.
Roughly speaking, if the dominant wavelength
of an SPD shifts, the hue of the associated color
will shift.
Saturation
, or
purity
, is the degree of colorful-
ness, from neutral gray through pastel to satu-
2 LeRoy E. DeMarsh and Edward J. Giorgianni, “Color
Science for Imaging Systems,” in
Physics Today
,
September 1989, 44-52.
3 W.F. Schreiber,
Fundamentals of Electronic Imaging
Systems,
Third Edition (New York: Springer-Verlag, 1993).
rated colors. Roughly speaking, the more
concentrated an SPD is at one wavelength, the
more saturated the associated color. You can
desaturate a color by adding light that contains
power at all wavelengths.
Spectral Power Distribution (SPD) and
tristimulus
Physical power (or
radiance
) is expressed in a
spectral power distribution
(SPD), often in 31
components each representing power in a
10 nm band from 400 to 700 nm. The SPD of
the CIE standard daylight illuminant CIE D
65
is
sketched at the top of Figure 2 above.
One way to describe a color is to directly repro-
duce its spectral power distribution. This is
sketched in the middle row of Figure 2, where
31 components are transmitted. It is reasonable
to use this method to describe a single color or a
few colors, but using 31 components for each
pixel is an impractical way to code an image.
Based on the trichromatic nature of vision, we
can determine suitable spectral weighting func-
tions to describe a color using just three compo-
nents, indicated at the bottom of Figure 2.
The relationship between SPD and perceived
color is the concern of the science of
colorimetry
.
In 1931, the CIE adopted standard curves for a
hypothetical
Standard Observer
. These curves
specify how an SPD can be transformed into a
triple that specifies a color.
400 500 600 700
Wavelength, nm
Spectral reproduction (31 components)
Tristimulus reproduction (3 components)
Figure 2 Spectral and tristimulus color reproduction.
A color can be described as a spectral power distribution
(SPD) of perhaps 31 numbers, each representing power
over a 10 nm band. However, if appropriate spectral
weighting functions are used, three values are sufficient.
A Guided Tour of Color Space
4
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.
Scanner spectral constraints
The relationship between spectral distributions
and the three components of a color value is
conventionally explained starting from the
famous color matching experiment. I will instead
explain the relationship by illustrating the prac-
tical concerns of engineering the spectral filters
required by a color scanner or camera, as illus-
trated in Figure 3 above.
The top row shows the spectral sensitivity of
three wideband filters having uniform response
across each of the red, green, and blue regions
of the spectrum. In a typical filter, whether for
electrical signals or for optical power, it is gener-
ally desirable to have a response that is as
uniform as possible across the passband, to have
transition zones as narrow as possible, and to
have maximum possible attenuation in the stop-
bands. Entire textbooks are devoted to filter
design; they concentrate on optimizing filters in
that way. The example on the top row of the
illustration shows two monochromatic sources
which are seen as saturated orange and red.
Applying a “textbook” filter to that example
causes these two different wavelength distribu-
tions to report the identical
RGB
triple, [1, 0, 0].
That is a serious problem, because these SPDs
are seen as different colors!
At first sight it may seem that the problem with
the wideband filters is insufficient wavelength
discrimination. The middle row of the example
addresses the apparent lack of spectral discrimi-
nation of the filters of the top row, by using three
narrowband filters. This set solves one problem,
R
G
B
Wideband filter set
Narrowband filter set
CIE-based filter set
400 500 600 700
450
400 500 600 700
ZYX
R
G
B
400 500 600 700 400 500 600 700
400 500 600 700 400 500 600 700
540 620
Figure 3 Scanner spectral constraints. This diagram
shows the spectral constraints associated with scanners
and cameras. The top row shows the spectral sensitivity
of three wideband filters having uniform response across
the shortwave, mediumwave and longwave regions of
the spectrum. The problem with this approach is that two
monochromatic sources seen by the eye to have different
colors – in this case, saturated orange and a saturated
red – cannot be distinguished by the filter set.
The middle row of the illustration shows three narrow
-
band filters. This set solves the problem of the first set,
but creates another: many monochromatic sources “fall
between” the filters, and are seen by the scanner as
black. To see color as the eye does, the three filter
responses must be closely related to the color response of
the eye.
The bottom row shows the spectral response functions
of the CIE Standard Observer.
A Guided Tour of Color Space
5
but creates another: many monochromatic
sources “fall between” the filters, and are seen
by the scanner as black. In the example, the
orange source reports an
RGB
triple of [0, 0, 0],
identical to the result of scanning black.
Although this example is contrived, the problem
is not. Ultimately, the test of whether a camera
or scanner is successful is whether it reports
distinct
RGB
triples if and only if human vision
sees different colors. To see color as the eye
does, the three filter sensitivity curves must be
closely related to the color response of the eye.
A famous experiment, the
color matching
experiment
, was devised during the 1920s to
characterize the relationship between SPD and
color. The experiment measures mixtures of
different spectral distributions that are required
for human observers to match colors. Exploiting
this indirect method, the CIE in 1931 standard-
ized a set of spectral weighting functions that
models the perception of color. These curves,
defined numerically, are referred to as the x, y,
and z
color matching functions
(
CMFs
) for the
CIE Standard Observer
4
. They are illustrated in
the bottom row of Figure 3 opposite, and are
graphed at a larger scale in Figure 4 above.
CIE XYZ tristimulus
The CIE designed their system so that one of the
three tristimulus values – the
Y
value – has a
spectral sensitivity that corresponds to the light-
ness sensitivity of human vision. The
luminance
Y
of a source is obtained as the integral of its
SPD weighted by the
y
color matching function.
When luminance is augmented with two other
components
X
and
Z,
computed using the
x
and
z
color matching functions, the resulting
(
X
,
Y
,
Z
) components are known as
XYZ
tristim-
ulus
values (pronounced
“big-X, big-Y, big-Z”
or
“cap-X, cap-Y, cap-Z”
). These are linear-light
values that embed the spectral properties of
human color vision.
Tristimulus values are computed from contin-
uous SPDs by integrating the SPD using the
x
,
y
,
and
z
color matching functions. In discrete form,
tristimulus values can be computed by a matrix
multiplication, as shown in Figure 5 overleaf.
4 The CIE system is standardized in Publication
CIE No 15.2,
Colorimetry, Second Edition
(Vienna,
Austria: Central Bureau of the Commission Internationale
de L’Éclairage, 1986).
0.0
0.5
1.0
1.5
2.0
z
x
y
400 500 600 700
Wavelength, nm
Response
Figure 4 CIE Color Matching Functions. A camera must
have these spectral response curves, or linear combina-
tions of these, in order to capture all colors. However,
practical considerations make this difficult.
A Guided Tour of Color Space
6
Human color vision follows a principle of super-
position, first elaborated by Grassman and now
known as Grassman’s Law: The tristimulus
values that result after summing a set of SPDs is
identical to the sum of the tristimulus values of
each of the SPDs. Due to this linearity of additive
color mixture, any set of three components that
is a nontrivial linear combination of
X, Y, and Z is
also a set of tristimulus values.
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 power, but their spectral
composition corresponds to the color matching
characteristics of human vision.
CIE x, y chromaticity
It is convenient, for both conceptual under-
standing and computation, to have a represen-
tation of “pure” color in the absence of
luminance. The CIE standardized a procedure for
normalizing XYZ tristimulus values to obtain two
chromaticity values x and y (pronounced
“little-x, little-y”). The relationships are
computed by this projective transformation:
A color plots as a point in an (x, y) chromaticity
diagram, illustrated in Figure 6 opposite. When a
narrowband SPD comprising power at just one
wavelength is swept across the range 400 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 wave-
length: To produce purple requires a mixture of
shortwave and longwave light. The line of
purples joins extreme blue to extreme red. The
chromaticity coordinates of real (physical) SPDs
are bounded by the line of purples and the spec-
tral locus: All colors are contained in this region
of the chromaticity diagram.
It is common to specify a color by its chroma-
ticity and luminance, in the form of an xyY triple.
(A third chromaticity value, z, can be computed
similarly. However, z is redundant if x and y are
known, due to the identity x + y + z = 1.)
=•
82.75
91.49
93.43
86.68
104.86
117.01
117.81
114.86
115.92
108.81
109.35
107.80
104.79
107.69
104.41
104.05
100.00
96.33
95.79
88.69
90.01
89.60
87.70
83.29
83.70
80.03
80.21
82.28
78.28
69.72
71.61
400 nm
450 nm
500 nm
550 nm
600 nm
650 nm
700 nm
0.0143
0.0435
0.1344
0.2839
0.3483
0.3362
0.2908
0.1954
0.0956
0.0320
0.0049
0.0093
0.0633
0.1655
0.2904
0.4334
0.5945
0.7621
0.9163
1.0263
1.0622
1.0026
0.8544
0.6424
0.4479
0.2835
0.1649
0.0874
0.0468
0.0227
0.0114
0.0004
0.0012
0.0040
0.0116
0.0230
0.0380
0.0600
0.0910
0.1390
0.2080
0.3230
0.5030
0.7100
0.8620
0.9540
0.9950
0.9950
0.9520
0.8700
0.7570
0.6310
0.5030
0.3810
0.2650
0.1750
0.1070
0.0610
0.0320
0.0170
0.0082
0.0041
0.0679
0.2074
0.6456
1.3856
1.7471
1.7721
1.6692
1.2876
0.8130
0.4652
0.2720
0.1582
0.0782
0.0422
0.0203
0.0087
0.0039
0.0021
0.0017
0.0011
0.0008
0.0003
0.0002
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
X
Y
Z
T
Figure 5 Calculation of tristimulus values by matrix
multiplication. The column vector at the right is a
discrete version of CIE Illuminant D65. The 31-by-3
matrix is a discrete version of the set of CIE x, y and z
color matching functions, here represented in 31 wave-
lengths at 10 nm intervals across the spectrum. The result
of performing the matrix multiplication is a set of XYZ
tristimulus values.
xX
XYZ yY
XYZ
=++ =++
Eq 1
A Guided Tour of Color Space
7
To recover X and Z tristimulus values from chro-
maticities and luminance, use the inverse of Eq 1:
The projective transformation used to compute x
and y is such that any linear combination or two
spectra, or two tristimulus values, plots on a
straight line in the (x, y) plane. However, the
transformation does not preserve distances, so
chromaticity values do not combine linearly.
There is no unique physical or perceptual defini-
tion of white. An SPD that is considered white
will have CIE (x, y) coordinates roughly in the
central area of the chromaticity diagram, in the
region of (1⁄3, 1⁄3).
Additive mixture (RGB)
The simplest way to reproduce a wide range of
colors is to mix light from three lights of different
colors, usually red, green, and blue. Figure 7
overleaf illustrates additive reproduction. In
physical terms, the spectra from each of the
lights add together wavelength by wavelength
to form the spectrum of the mixture.
As a consequence of the principle of superposi-
tion, the color of an additive mixture is a strict
function of the colors of the primaries and the
fraction of each primary that is mixed.
Additive reproduction is employed directly in a
video projector, where the spectra from a red
beam, a green beam, and a blue beam are phys-
ically summed at the surface of the projection
screen.
Additive reproduction is also employed in a
direct-view color CRT, but through slightly indi-
rect means. The screen of a CRT comprises small
dots that produce red, green, and blue light.
When the screen is viewed from a sufficient
distance, the spectra of these dots add at the
observer’s retina.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
x
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
y
Comparison of SMPTE 240M,
EBU Tech. 3213-E
and ITU-R Rec. BT.709 Primaries
400
440
460
480
500
520
540
580
600
620
640 700
560
SMPTE
GREEN
RED
BLUE
CIE D65
EBU
Rec. 709
Figure 6 The (x, y) chromaticity
diagram. The spectral locus, an
inverted U-shaped path, is swept out as
a monochromatic source runs from 400
to 700 nm. The locus of all colors is
closed by the line of purples, which
traces SPDs that combine longwave
and shortwave power but have no
mediumwave contribution.
On this chromaticity diagram, I plot
the chromaticity of the D65 white point,
and the chromaticities of the red, green,
and blue primaries of contemporary
SMPTE, EBU, and ITU-R standards for
video primaries. See A Technical Intro-
duction to Digital Video for details.
Xx
yYZ
xy
yY==
−−1
Eq 2
A Guided Tour of Color Space
8
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.
It is often convenient for purposes of calculation
to define white as a uniform SPD. This white
reference is known as the equal-power illumi-
nant, 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 repre-
sent compromises between the conditions of
indoor (tungsten) and daylight viewing.
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.
However, 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.
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.
A typical source of illumination has a heated
object at its core, so it is often useful to charac-
terize an illuminant by specifying the tempera-
ture (in units of kelvin, K) of a black body
radiator that appears to have the same color.
Although an illuminant can be specified infor-
mally by its color temperature, a more complete
specification is provided by the chromaticity
coordinates of the SPD of the source. Figure 8
shows the SPDs of several standard illuminants.
Camera white reference
There is an implicit assumption in television that
the camera operates as if the scene were illumi-
nated by a source having the chromaticity of
CIE D65. In practice, the scene illumination is
often deficient in the shortwave (blue) region of
the spectrum. Television studio lighting is often
accomplished by tungsten lamps, which are very
yellow. This situation is accommodated by white
balancing, that is, by adjusting the gain of the
red, green, and blue components of the scene so
that a white object reports the values that would
be reported if the scene were illuminated by D65.
R
G
B
400
Wavelength, nm
500 600 700
Figure 7 Additive mixture. This diagram illustrates the
physical process underlying additive color mixture, as is
used in color television. Each colorant has an indepen-
dent, direct path to the image. The spectral power of the
image is, at each wavelength, the sum of the spectra of
the colorants. The colors (chromaticities) of the mixtures
are completely determined by the colors of the primaries,
and analysis and prediction of mixtures is reasonably
simple. The spectral curves shown here are those of an
actual Sony Trinitron™ monitor.
A Guided Tour of Color Space
9
Monitor white reference
In an additive mixture the illumination of the
reproduced image is generated entirely by the
display device. In particular, reproduced white is
determined by the characteristics of the display,
and is not dependent on the environment in
which the display is viewed. In a completely dark
viewing environment such as a cinema theater,
this is desirable. However, in an environment
where the viewer’s field of view encompasses
objects other than the display, the viewer’s
notion of “white” is likely to be influenced or
even dominated by what he perceives as
“white” in the ambient. To avoid subjective
mismatches, the chromaticity of white repro-
duced by the display and the chromaticity of
white in the ambient should be reasonably close.
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. This
situation can be corrected by calibrating the
monitor to a white reference with a lower color
temperature.
Characterization of RGB primaries
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. Subtrac-
tive reproduction is much more complicated: the
colors of mixtures are determined by the prima-
ries and by the colors of their combinations.
An additive RGB system is specified by the chro-
maticities 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
and there is no standard white point. If you have
an RGB image but have no information about its
450400350 500 550 600 650 700 750 800
0.5
1
1.5
2
2.5
D
75
D
65
D
55
D
50
C
A
Figure 8 CIE illuminants are graphed here. Illuminant A
is now obsolete; it is representative of tungsten illumina-
tion. Illuminant C was an early standard for daylight; it
too is obsolete. The family of D Illuminants represent
daylight at several color temperatures.
A Guided Tour of Color Space
10
chromaticities, you cannot accurately determine
the colors represented by the image data.
The NTSC in 1953 specified a set of primaries
that were representative of phosphors used in
color CRTs of that era. However, phosphors
changed over the years, primarily in response to
market pressures for brighter receivers, and by
the time of the first 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 practical use today.
Contemporary studio monitors have slightly
different standards in North America, Europe,
and Japan. However, international agreement5
has been obtained on primaries for high-defini-
tion television (HDTV), and these primaries are
closely representative of contemporary monitors
in studio video, computing, and computer
graphics. The standard is formally denoted
ITU-R Recommendation BT.709 (formerly CCIR
Rec. 709). I’ll call it Rec. 709. The Rec. 709
primaries and its D65 white point are these:
For a discussion of nonlinear RGB in computer
graphics, read Lindbloom’s SIGGRAPH paper6.
For technical details on monitor calibration,
consult Cowan7.
Video standards specify abstract R’G’B’ systems
that are closely matched to the characteristics of
5 Basic Parameter Values for the HDTV Standard for the
Studio and for International Programme Exchange
(Geneva, Switzerland: ITU, 1990).
6 Bruce Lindbloom, “Accurate Color Reproduction for
Computer Graphics Applications,” in Computer
Graphics, Vol. 23, No. 3 (July 1989), 117-126.
7 William B. Cowan, “An Inexpensive Scheme for Cali-
bration of a Colour Monitor in terms of CIE Standard
Coordinates,” in Computer Graphics, Vol. 17, No. 3
(July 1983), 315-321.
real monitors. Physical devices that produce
additive color involve tolerances and uncertain-
ties, 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 Rec. 709 as an interchange
standard in studio video, broadcast television,
and high definition television, and the percep-
tual basis of the standard, assures that its param-
eters will be used even by devices such as flat-
panel displays that do not have the same physics
as CRTs.
Non-realizable spectra
In the x, y, and z functions, the contribution of
each weighting function to each tristimulus
value is positive at every wavelength. Light
cannot convey negative power; if a color
matching function had a negative excursion, its
filter could not be physically realized.
If you examine the x, y, and z functions, you will
see that – except for the trivial case of an identi-
cally zero spectrum – it is not possible to have a
physical spectrum that produces zero luminance:
Every wavelength has some positive contribu-
tion to Y. There is no way to generate nonzero X
or Z values without also generating nonzero Y.
Thus, a “pure” X tristimulus triple [1, 0, 0] can
never be obtained from a physical (all-positive)
spectral distribution. However, setting aside for
the moment the physical constraint, a pure X
tristimulus value would correspond mathemati-
cally to a spectrum that has negative power at
some wavelengths, in order to generate unity X
and zero luminance Y.
The SPDs corresponding to the CIE x, y, and z
color matching functions correspond to physi-
cally realizable spectra, SPDs having these
shapes could in theory be used as the primaries
in a display device such as a CRT. However, using
XYZ tristimulus values to drive a display having
x, y, and z primaries would not correctly repro-
duce color. This is fundamentally because the
analysis of the source SPD into X, Y, and Z
components proceeds independently during
scanning, but in an additive display device, the
SPDs of the primaries interact when they
Table 1 Rec. 709 primaries and white reference
RGBwhite
x0.640 0.300 0.150 0.3127
y0.330 0.600 0.060 0.3290
z0.030 0.100 0.790 0.3582
A Guided Tour of Color Space
11
combine at the display. If power from the source
could be “steered” into three components at the
source – if power contributing to one compo-
nent could be subtracted from the other two –
then the component values at the scanner could
be directly used at the display.
Unfortunately this “steering” operation involves
subtraction, which in the case of the x, y, and z
functions leads to spectral sensitivity functions
that are negative at some wavelengths, and
therefore not realizable in practice.
Alternatively, the display could be arranged so
that the X tristimulus component produced a
contribution having a spectral power distribution
x-- y -- z (and similarly for Y and Z). Unfortunately
this proposal suffers from nonrealizable prima-
ries at the display. So we have a dilemma: to
utilize XYZ tristimulus components directly to
achieve color reproduction, we must have either
a nonrealizable scanner or a nonrealizable
display!
The solution to this dilemma involves trans-
forming the tristimulus components into a math-
ematical domain where physical realizability is
not a constraint. The transformation depends on
the fact that the principle of superposition
applies to human color vision. We process the
XYZ components through a 3×3 linear (matrix)
multiplication, to produce a new set of compo-
nents appropriate for physical RGB display
primaries.
Transformations between CIE XYZ and RGB
RGB values in a particular set of primaries can be
transformed to and from CIE XYZ by a 3×3
matrix transform. These transforms involve
tristimulus values, that is, sets of three linear-
light components that conform to the CIE color
matching functions. SMPTE has published
details on how to compute these transforma-
tions8. CIE XYZ is a special case of tristimulus
values. In XYZ, any color is represented by a
positive set of values.
8 SMPTE RP 177-1993, Derivation of Basic Television
Color Equations.
To transform from CIE XYZ into Rec. 709 RGB
(with its D65 white point), use this transform:
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 transform. Because white is
normalized to unity, the middle row sums to
unity:
To recover primary chromaticities from such a
matrix, compute little x and y for each RGB
column vector. To recover the white point, trans-
form RGB = [1, 1, 1] to XYZ, then compute x
and y.
Transforms among RGB systems
RGB tristimulus values in a system employing
one set of primaries can be transformed into
another set by a 3×3 matrix multiplication.
Generally these matrices are normalized for a
white point luminance of unity. For details, see
Television Engineering Handbook9.
As an example, here is the transform from
SMPTE 240M (or SMPTE RP-145) RGB to
Rec. 709:
This matrix is very close to the identity matrix. 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.
9 Television Engineering Handbook, Featuring HDTV
Systems, Revised Edition by K. Blair Benson, revised by
Jerry C. Whitaker (New York: McGraw-Hill, 1992). This
supersedes the Second Edition.
R
G
B
X
Y
Z
709
709
709
3 240479 1 537150 0 498535
0 969256 1 875992 0 041556
0 055648 0 204043 1 057311
=−−
−−
•
...
...
...
X
Y
Z
R
G
B
=
•
0 412453 0 357580 0 180423
0 212671 0 715160 0 072169
0 019334 0 119193 0 950227
709
709
709
...
...
...
R
G
B
R
G
B
709
709
709
145
145
145
0 939555 0 050173 0 010272
0 017775 0 965795 0 016430
0 001622 0 004371 1 005993
=−−
•
...
...
...
A Guided Tour of Color Space
12
Here’s another example. To transform EBU 3213
RGB to Rec. 709:
Transforming among RGB systems may lead to
an out of gamut result where one or more RGB
components is negative or greater than unity.
Scanning colored media
The previous section discusses the analysis filters
necessary to obtain three tristimulus values from
incident light from a colored object. However, if
the incident light has itself been formed by an
imaging system based on three components, the
spectral composition of light from the original
scene has already been analyzed. To perform a
spectral analysis based on the CIE color
matching functions is unnecessary at best, and is
likely to introduce degraded color information.
A much more direct, practical, and accurate
approach is to perform an analysis using filters
tuned to the spectrum of the colorants of the
reproduced image, and thereby extract the three
color “records” present in the reproduction
being scanned.
In practical terms, if an image to be scanned has
already been recorded on color film, or printed
by color photography or offset printing, then
better results will be obtained by using three
narrowband filters designed to extract the color
components that have already been recorded on
the media. A densitometer is an instrument that
performs this task (but reporting logarithmic
density values instead of linear-light tristimulus
values). Several spectral sensitivity functions
have been standardized for densitometers for
use in different applications.
Practical camera spectral response
The previous section explained how the CIE x, y,
and z functions are representative of the spectral
response of the three color photoreceptor cells
of human vision, and explained how XYZ tristim-
ulus components from such a scanner are trans-
formed for use by a display device having
realizable primaries. Although an ideal scanner
or a camera would use these spectral functions,
many practical difficulties preclude their use in
real cameras and scanners.
The CIE x, y, and z functions capture all colors.
However, the range of colors commonly
encountered in the natural or man-made world
is a fraction of total color space. Although it is
useful for an instrument such as a colorimeter to
measure all colors, in an imaging system we are
generally concerned with the subset of colors
that occur frequently. If a scanner is designed to
capture all colors, its complexity is necessarily
higher and its performance is necessarily worse
than a camera designed to capture a smaller
range of colors.
Furthermore, in a system that reproduces
images, such as television, any economical
display device will be limited in the range of
colors that it can reproduce. There are usually
good engineering reasons to capture a range of
colors that is not excessively larger than the
range of colors that can be reproduced. For
much of the history of color television, cameras
were designed to incorporate assumptions about
the color reproduction capabilities of color CRTs.
However, nowadays, video production equip-
ment is being used to originate images for a
wider range of applications than just television
broadcast. The desire to make video cameras
suitable for originating images for these wider
applications has led to cameras with increased
color range.
“Subtractive” mixture (CMY)
In contrast to additive mixture described earlier,
another way to produce a range of color
mixtures is to selectively remove portions of the
spectrum from a relatively broadband illuminant.
This is illustrated in Figure 9 opposite.
The illuminant at the left of the sketch produces
light over most or all of the visible spectrum, and
each successive filter transmits some portion of
the band and attenuates other portions. The
overall attenuation of each filter is controlled: In
the case of color photography, this is accom-
plished by varying the thickness of each dye
R
G
B
R
G
B
EBU
EBU
EBU
709
709
709
1 044036 0 044036 0
010
0 0 011797 0 988203
=−
•
...
...
...
A Guided Tour of Color Space
13
layer that functions as a filter, the shape of each
curve remaining constant.
In physical terms, the spectrum of the mixture is
the wavelength by wavelength product of the
spectrum of the illuminant and the spectral
transmission curves of each of the colorants. The
spectral transmission curves of the colorants
multiply, so this method of color reproduction
should really be called “multiplicative.” Photo-
graphers and printers have for decades
measured transmission in base-10 logarithmic
density units, where transmission of unity corre-
sponds 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). Figure 9 illustrates
the situation of a transmissive display such as in
the projection of color photographic film.
RGB information can be used as the basis for
subtractive image reproduction. If the color to be
reproduced has a blue component of zero, then
the yellow filter must attenuate the shortwave
components of the spectrum as much as
possible. As the amount of blue to be repro-
duced increases, the attenuation of the yellow
filter should decrease. This reasoning leads to the
“one-minus-RGB” relationships:
Cyan in tandem with magenta produces blue,
cyan with yellow produces green, and magenta
with yellow produces red. Here is a memory aid:
Additive primaries are at the top, subtractive at
the bottom. On the left, magenta and yellow
filters combine subtractively to produce red. On
the right, red and green sources combine addi-
tively to produce yellow.
Subtractive details
Although the “one-minus-RGB” relationships
are a good starting point, they are not useful in
practice. One problem is that the relationships
assume RGB to represent linear-light tristimulus
values and CMY to represent linear-light trans-
400
Wavelength, nm
500 600 700
Yl
Illuminant
Mg
Cy
Figure 9 Subtractive mixture as employed in color
photography and color offset printing, is illustrated in this
diagram. The colorants act in succession to remove spec-
tral power from the illuminant. In physical terms, the
spectral power of the mixture is, at each wavelength, the
product of the spectrum of the illuminant and the trans-
mission of the colorants: the mixture could be called
multiplicative. If the amount of each colorant is repre-
sented in the form of density – the negative of the
base-10 logarithm of transmission – then color mixtures
can be determined by subtraction.
Color mixtures in subtractive systems are complex
because the colorants have absorption not only in the
intended region of the spectrum but also unwanted
absorptions in other regions. The unwanted absorptions
cause interaction among the channels, and therefore
nonlinearity in the mixtures. The illuminant shown here is
CIE D65; the colorant absorption curves are those of the
dyes of a commercial color photographic print film.
RGB RGB
Cy Mg Yl Cy Mg Yl
Cy 1R–=
Mg 1 G–=
Yl 1B–=
A Guided Tour of Color Space
14
mission values. In computing and in offset
printing, neither the RGB nor the CMY quanti-
ties are directly proportional to intensity.
Another problem is that the “one-minus-RGB”
relationships do not incorporate any about infor-
mation about tristimulus values of the assumed
RGB primaries or the assumed CMY colorants!
Obviously the spectra of the colorants has some
influence over reproduced color, but the model
embeds no information about the spectra!
The most serious practical problem with
“subtractive” color mixture is that any overlap
among the absorption spectra of the colorants
results in “unwanted absorption” in the mixture.
For example, the magenta dye is intended to
absorb only medium wavelengths, roughly
between 500 and 600 nm. However, for the
photographic film dyes shown in Figure 9, the
magenta dye also has substantial absorption in
the shortwave region of the spectrum. Conse-
quently, the amount of shortwave light that
contributes to any mixture is not only a function
of the amount of attenuation introduced by the
yellow filter, but also the incidental attenuation
introduced by the magenta filter. There is no
simple way to compensate these interactions,
because the multiplication of spectra is not
mathematically a linear operation.
In practice, the conversion from RGB to CMY is
accomplished using either fairly complicated
polynomial arithmetic, or by three-dimensional
interpolation of lookup tables.
In a subtractive mixture, reproduced white is
determined by characteristics of the colorants
and by the spectrum of the illuminant used at
the display. In a reproduction such as a color
photograph that is illuminated by the ambient
light in the viewer’s environment, mismatch
between the white reference in the scene and
the white reference in the viewing environment
is eliminated. In a subtractive reproduction using
a device that generates its own illumination, the
subjective effect of white mismatch may need to
be considered.
Image synthesis
Once light is on its way to the eye, any tristim-
ulus-based system can accurately represent
color. However, the interaction of light and
objects involves SPDs and spectral absorbtion
curves, 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 Hall10.
10 Roy Hall, Illumination and Color in Computer Gener-
ated Imagery (New York: Springer-Verlag, 1989)
