Color Models and Color
Applications
Topics :
Color Fundamentals
Chromaticity Diagram
Color Models
What is Color ?
To see color,
three essential
elements must be
present:
light,
an illuminated
object,
and an observer.
Visible Spectrum
We perceive electromagnetic energy having wavelengths
in the range 400-700 nm as visible light.
Visible light is an electromagnetic wave in
the range 400-700 nm
Violet light
Red light
The color spectrum
shows the range of
wavelengths of
energy that are
visible to the human
eye. Variation in
wavelengths alters
the colors we see.
As Isaac Newton
showed (1666) with
his prisms, white light
is a mixture of all the
colors of the visible
spectrum.
Light and Color
The frequency ( or mix of frequencies ) of the light determines the color.
The amount of light(sheer quantity of photons ) is the intensity.
Three independent quantities are used to describe any particular color. :
hue, saturation, and lightness or brightness or intensity.
The hue is determined by the dominant wavelength.(the apparent color
of the light)
When we call an object
"red," we are referring to
its hue. Hue is
determined by the
dominant wavelength.
Light and Color
The saturation of
a color ranges
from neutral to
brilliant. The circle
on the right is a
more vivid red
than the circle on
the left although
both have the
same hue.
The saturation is determined by the excitation purity , and depends
on the amount of white light mixed with the hue. A pure hue is fully
saturated, i.e. no white light mixed in. Hue and saturation together
determine the chromaticity for a given color.
Light and Color
Lightness or
brightness
refers to the
amount of
light the
color
reflects or
transmits.
Finally, the intensity is determined by the actual amount of
light, with more light corresponding to more intense colors
( the total light across all frequencies).
Light that has a dominant frequency or set of frequencies is
called chromatic.
Achromatic light has no color - its only attribute is quantity or
intensity. Greylevel is a measure of intensity. The intensity is
determined by the energy, and is therefore a physical quantity.
On the other hand, brightness is determined by the perception of
the color, and is therefore psychological. Given equally intense
blue and green, the blue is perceived as much darker than the
green. Note also that our perception of intensity is nonlinear,
with changes of normalised intensity from 0.1 to 0.11 and from
0.5 to 0.55 being perceived as equal changes in brightness.
Color depends primarily on the reflectance properties of an object.
We see those rays that are reflected, while others are absorbed.
However, we also must consider the color of the light source, and
the nature of human visual system. For example, an object that
reflects both red and green will appear green when there is green
but no red light illuminating it, and conversely it will appear red in
the absence of green light. In pure white light, it will appear
yellow (= red + green).
Light and Color
When light strikes
an object,
wavelengths may be
reflected, absorbed
or transmitted.
Colorants can be
mixed to control the
wavelengths and
colors we see.
The
photosensitive
part of the eye is
called the retina.
The retina is
largely composed
of two types of
cells, called rods
and cones. Only
the cones are
responsible for
color perception
Light and Our Eyes
The cones are sensitive to colored light and
the rods are sensitive to achromatic light
only.
Light waves that
reach the eye
stimulate a visual
process so complex
it's not yet fully
understood. Within
the retina, cones
respond to color hues
and brightness. Rods
sense only
brightness. Three
types of cones
respond to
wavelengths in ways
that produce all the
colors we see.
The Fovea
Cones are most densely packed within a region of the eye called the
fovea.
Primary colors ( Red, Green,
Blue)
The response of
each type of cone
as a function of the
wavelength of the
incident light is
shown in figure.
The peaks for each
curve are at 440nm
(blue), 545nm
(green) and 580nm
(red). Note that the
last two actually
peak in the yellow
part of the
spectrum.
Figure : Spectral response curves for each cone type. The peaks for
each curve are at 440nm (blue), 545nm (green) and 580nm (red).
Light and Our Eyes
•The color signal to the brain comes from the response of the
3 cones to the spectra being observed. That is, the signal
consists of 3 numbers: R, G, and B
•A color can be specified as the sum of three colors. So colors
form a 3 dimensional vector space.
•These three hues: red, green, and blue are called primary
colors
Standard observer
Based upon psychophysical measurements, standard curves have been
adopted by the CIE (Commission Internationale de l'Eclairage) as the
sensitivity curves for the "typical" observer for the three "pigments" .
These are not the actual pigment absorption characteristics found in
the "standard" human retina but rather sensitivity curves derived from
actual data .
This function of wavelength is called
the luminance-efficiency function of
the eye.
For an arbitrary homogeneous region in an image that has an intensity
as a function of wavelength (color) given by I(), the three responses are
called the tristimulus values:
Color Matching
In order to define the perceptual 3D space in a "standard" way, a set
of experiments can (and have been) carried by having observers try
and match color of a given wavelength, lambda, by mixing three other
pure wavelengths, such as R=700nm, G=546nm, and B=436nm in the
following example. Note that the phosphorus of color TVs and other
CRTs do not emit pure red, green, or blue light of a single
wavelength, as is the case for this experiment.
We commonly
see colors
arrayed in two
dimensions.
This is a
useful, but
incomplete
representation.
Colors actually
occupy a threedimensional
space.
•
L*a*b Color Model
Lightness is the third
dimension that is not
shown in color wheels
often used in image
editing software
•A refined CIE model,
named CIE L*a*b in 1976
•Luminance: L
Chrominance: a -- ranges
from green to red, b -ranges from blue to yellow
Used by Photoshop
CIE Chromaticity Diagram
To measure and predict
the appearance of a
particular color, we need
a way to link perception
to numbers and
formulas.
Scientific color values
were established earlier
this century by the CIE
group. CIE models for
defining color space all
rely on the same basic
numbers.
CIE Chromaticity Diagram
In 1931, the CIE defined three standard primaries (X, Y, Z).
The Y primary was intentionally chosen to be identical to the
luminous-efficiency function of human eyes.
C  XX  YY  ZZ
•The above figure shows the amounts of X, Y, Z needed to
exactly reproduce any visible color.
CIE Color Space
In order to achieve a representation which uses only positive mixing
coefficients, the CIE ("Commission Internationale d'Eclairage") defined
three new hypothetical light sources, x, y, and z, which yield positive
matching curves:
If we are given a spectrum and wish to find the corresponding X, Y, and
Z quantities, we can do so by integrating the product of the spectral
power and each of the three matching curves over all wavelengths. The
weights X,Y,Z form the three-dimensional CIE XYZ space, as shown
below.
CIE chromaticity coordinates
In 1931, the Commission Internationale de l'Éclairage (CIE)
defined three standard primaries, called X, Y and Z, that can be
added to form all visible colors. The primary Y was chosen so that
its color matching function exactly matches the luminous-efficiency
function for the human eye, given by the sum of the three curves2.
The chromaticity coordinates which describe the perceived
color information are defined as:
The red chromaticity coordinate is given by x and the green
chromaticity coordinate by y. The tristimulus values are linear in I()
and thus the absolute intensity information has been lost in the
calculation of the chromaticity coordinates {x,y}. All color
distributions, I(), that appear to an observer as having the same color
will have the same chromaticity coordinates.
Figure : The CIE Chromaticity Diagram showing all visible colors. x and
y are the normalized amounts of the X and Y primaries present, and
hence z = 1 - x - y gives the amount of the Z primary required.
CIE Chromaticity Diagram
Often it is convenient to work in a
2D color space. This is commonly
done by projecting the 3D color
space onto the plane X+Y+Z=1,
yielding a CIE chromaticity
diagram. The projection is defined
as:
Giving the chromaticity diagram shown on the right.
CIE Chromaticity Diagram
A complete
description of a color
is typically given
with the three values
x, y, and Y. The
remaining CIE
amounts are then
calculated as :
x
X  Y;
y
z
Z Y
y
Figure : Mixing colors on the chromaticity diagram. All colors on the
line IJ can be obtained by mixing colors I and J, and all colors in the
triangle IJK can be obtained by mixing colors I, J and K.
The formulas for converting from the tristimulus values
(X,Y,Z) to the well-known CRT colors (R,G,B) and back are
given by:
As long as the position of a desired color (X,Y,Z) is inside
the phosphor triangle in Figure , the values of R, G, and B
as computed by eq. will be positive and can therefore be
used to drive a CRT monitor.
CIE Chromaticity Diagram
•All visible colors are in a "horseshoe" shaped cone in the X-Y-Z
space. Consider the plane X+Y+Z=1 and project it onto the X-Y
plane, we get the CIE chromaticity diagram as below.
Definitions:
•Spectrophotometer :A device to
measure the spectral energy
distribution. It can therefore also
provide the CIE xyz tristimulus
values.
•Illuminant C : The point C is
plotted for a white-light source
known as illuminant C
•Complementary colors : If the two
color sources combine to produce
white light, they are referred to as
complementary colors ( blue and
yellow; red and cyan. For example,
colors on segment CD are
complementary to the colors on
segment CB.
Definitions:
*dominant wavelength : The
spectral color which can be mixed
with white light in order to
reproduce the desired color. color
B in the above figure is the
dominant wavelength for color A.
* non-spectral colors : colors not
having a dominant wavelength.
For example, color E in the above
figure.
A color can be
specified by its
colorimetric
values. A
colorimeter is
an instrument
that measures
color using
numbers
derived from
CIE values.
A
spectrophotom
eter is another
instrument for
measuring
color. It
samples
wavelengths
across the color
spectrum
•The gamut of colors is all colors that can be reproduced
using the three primaries
Measuring color
allows us to compare
the color gamut, or
range of colors
produced by different
methods.
We find that color
transparency film
produces a wide range
of colors including
some a monitor
cannot display.
Digital color printers and
printing presses have
different color gamuts.
They can never capture
all the colors in an
original transparency,
but they can simulate
the appearance very
successfully if color
reproduction is
understood and
controlled. Color
management software,
described later, helps
transform color from one
gamut to another.
Color Models
Color models provide a standard way to specify a
particular color, by defining a 3D coordinate
system, and a subspace that contains all
constructible colors within a particular model. Any
color that can be specified using a model will
correspond to a single point within the subspace it
defines. Each color model is oriented towards either
specific hardware (RGB,CMY,YIQ), or image
processing applications (HSI).
The RGB Color Cube
The additive color model used for computer graphics is represented by
the RGB color cube, where R, G, and B represent the colors produced by
red, green and blue phosphorus, respectively.
The RGB Model
This is an additive model, i.e. the colors present in the light add to form
new colors, and is appropriate for the mixing of colored light for
example. The image on the left of figure shows the additive mixing of
red, green and blue primaries to form the three secondary colors yellow
(red + green), cyan (blue + green) and magenta (red + blue), and white
((red + green + blue).
The RGB model is used for color monitors and most video cameras.
The figure on the left shows the additive mixing of red, green and blue
primaries to form the three secondary colors yellow (red + green),
cyan (blue + green) and magenta (red + blue), and white ((red + green
+ blue). The figure on the right shows the three subtractive primaries,
and their pairwise combinations to form red, green and blue, and
finally black by subtracting all three primaries from white.
The RGB Color Cube
The color cube sits within the CIE XYZ color space as
follows.
RGB Color Model for CRT Displays
•CRT displays have three phosphors (RGB) which produce
a combination of wavelengths when excited with electrons.
CMY Color Model
•Cyan, Magenta, and Yellow (CMY) are complementary colors of
RGB. They can be used as Subtractive Primaries.
•CMY model is mostly used in printing devices where the color
pigments on the paper absorb certain colors (e.g., no red light reflected
from cyan ink).
Conversion between RGB and CMY
•Convert White from (1, 1, 1) in RGB to (0, 0, 0) in CMY:
•Sometimes, an alternative CMYK model (K stands for Black) is
used in color printing (e.g., to produce darker black than simply
mixing CMY).
K := min (C, M, Y), C := C - K, M := M - K, Y := Y - K.
Color Gamuts
The chromaticity diagram can be used to compare the "gamuts" of
various possible output devices (i.e., monitors and printers). Note
that a color printer cannot reproduce all the colors visible on a
color monitor
Color Printing
Green paper is green because it reflects green and absorbs other
wavelengths. The following table summarizes the properties of
the four primary types of printing ink. dye color absorbs reflects
cyan
red
blue and green
magenta
green
blue and red
yellow
blue
red and green
black
all
none
To produce blue, one would mix cyan and magenta inks, as they
both reflect blue while each absorbing one of green and red.
Unfortunately, inks also interact in non-linear ways. This makes the
process of converting a given monitor color to an equivalent printer
color a challenging problem.
Black ink is used to ensure that a high quality black can always be
printed, and is often referred to as to K. Printers thus use a CMYK
color model.
Color Conversion
To convert from one color gamut to another is a simple procedure. Each phosphor color
can be represented by a combination of the CIE XYZ primaries, yielding the following
transformation from RGB to CIE XYZ:
The transformation
yields the color on monitor 2 which is
equivalent to a given color on monitor 1. Conversion to-and-from printer gamuts is
difficult. A first approximation is as follows:
C=1-R
M=1-G
Y=1–B
The fourth color, K, can be used to replace equal amounts of CMY:
K = min(C,M,Y) C' = C - K
M' = M - K
Y' = Y - K
The YIQ (luminance-inphase-quadrature) model is a recoding of RGB
for color television, and is a very important model for color image
processing. The importance of luminance was discussed .
The conversion from RGB to YIQ is given by:
The luminance (Y) component contains all the information required for
black and white television, and captures our perception of the relative
brightness of particular colors. That we perceive green as much lighter
than red, and red lighter than blue, is indicated by their respective
weights of 0.587, 0.299 and 0.114 in the first row of the conversion
matrix above. These weights should be used when converting a color
image to greyscale if you want the perception of brightness to remain
the same.
The YIQ Model
Figure: Image (a) shows a
color test pattern, consisting
of horizontal stripes of
black, blue, green, cyan,
red, magenta and yellow, a
color ramp with constant
intensity, maximal
saturation, and hue
changing linearly from red
through green to blue, and a
greyscale ramp from black
to white. Image (b) shows
the intensity for image (a).
Note how much detail is
lost. Image (c) shows the
luminance. This third image
accurately reflects the
brightness variations
perceived in the original
image
The HSI Model
As mentioned above, color may be specified by the three
quantities hue, saturation and intensity. This is the HSI model,
and the entire space of colors that may be specified in this way is
shown in figure .
The HSI Model
Figure : The HSI model, showing the HSI solid on the left, and the
HSI triangle on the right, formed by taking a horizontal slice through
the HSI solid at a particular intensity. Hue is measured from red, and
saturation is given by distance from the axis. Colors on the surface
of the solid are fully saturated, i.e. pure colors, and the greyscale
spectrum is on the axis of the solid. For these colors, hue is
undefined.
Conversion between the RGB model and the HSI model is quite
complicated.
See HSICalc.java
See ShowColors2.java
Comparison of Three Color Gamuts
•The gamut of colors is all colors that can be reproduced using the three
primaries
•The Lab gamut covers all colors in visible spectrum
•The RGB gamut is smaller, hence certain visible colors (e.g. pure yellow, pure
cyan) cannot be seen on monitors
•The CMYK gamut is the smallest (but not a straight subset of the RGB gamut)
True-Color Frame Buffers
•Each pixel requires at least 3 bytes. One byte for each primary
color.
•Sometimes combined with a look-up table per primary
•Each pixel can be one of 2^24 colors
Indexed-Color Frame Buffers
•Each pixel uses one byte
•Each byte is an index into a color map
•If the color map is not updated synchronously then Color-map flashing
may occurs.
•Color-map Animations
•Each pixel may be one of 2^24 colors, but only 256 color be displayed
at a time
High-Color Frame Buffers
•Popular PC/(SVGA) standard
•Each pixel can be one of 2^15 colors
•Can exhibit worse quantization effects than Indexed-color
Specialty Frame Buffers
•Non-RGB color models (YUV) or 4-2-2
•True color plus an Overlay
•Older 4-bit per pixel models [I,R,G,B]
•True-color with a lookup-per-color component
Conclusions
color - in computer graphics we use an additive color model
* colors are represented using Red, Green, and Blue
components
* the CRT has a mechanism for displaying these three
components
* a 24-bit RGB color model uses 8 bits for each of red, green,
and blue
* the human eye processes color similarly - there are three
kinds of cones
* RGB color model combines color and intensity information
in each component
* HSI color model separates intensity from color information
* java.awt.Color provides a method to do conversion
* HSICalc.java
* documentation for RGBtoHSB( ) is online