Color vision - Rutgers University School of Engineering

The Eye
The human eye is a camera!
• Iris
I i - colored
l d annulus
l with
ith radial
di l muscles
l
• Pupil - the hole (aperture) whose size is controlled by the iris
• Lens - changes shape by using ciliary muscles (to focus on objects
att different
diff
t distances)
di t
)
• Retina - photoreceptor cells
Slide by Steve Seitz
Rods and cones
cone
pg
pigment
molecules
rod
Rods are responsible for intensity, cones for color perception
Rods and cones are non
non-uniformly
uniformly distributed on the retina
•
Fovea - Small region (1 or 2°) at the center of the visual field containing the highest
density of cones (and no rods)
Slide by Steve Seitz
Rod / Cone sensitivity
Why can’t we read in the dark?
Slide by A. Efros
Electromagnetic spectrum
HumanHuman
Luminance
Sensitivity Function
Luminan
Visible Light
Why do we see light of these wavelengths?
…because that’s where the
Sun radiates EM energy
© Stephen E. Palmer, 2002
Physiology of Color Vision
Three kinds of cones:
RELATIVE A
ABSORBAN
NCE (%)
440
530 560 nm.
100
M
S
L
50
400
450
500
550
600 650
WAVELENGTH (nm.)
• Ratio of L to M to S cones: approx. 10:5:1
• Almost no S cones in the center of the fovea
© Stephen E. Palmer, 2002
Spectra of some real-world surfaces
metamers
The Physics of Light
% Photons Reflected
Some examples of the reflectance spectra of surfaces
Red
400
Yellow
700 400
Blue
700 400
Wavelength (nm)
Purple
700 400
700
© Stephen E. Palmer, 2002
Color spaces
• How can we represent color?
http://en.wikipedia.org/wiki/File:RGB_illumination.jpg
Color spaces: RGB
Default color space
0,1,0
R
(G=0,B=0)
G
1,0,0
(R=0,B=0)
0,0,1
Some drawbacks
B
(R=0,G=0)
• Strongly correlated channels
• Non-perceptual
Image from: http://en.wikipedia.org/wiki/File:RGB_color_solid_cube.png
Linear color space CIE XYZ from RGB
• Primaries are imaginary, but matching
functions are everywhere positive
• The Y parameter corresponds to brightness or
luminance of a color
• 2D visualization: draw (x,y), where
x = X/(X+Y+Z), y = Y/(X+Y+Z)
Matching functions
http://en.wikipedia.org/wiki/CIE_1931_color_space
Forsyth & Ponce
Pure wavelength in chromaticity
diagram
• Blue: big value of Z, therefore x and
y small
x=X/(X+Y+Z)
y=Y/(X+Y+Z)
Pure wavelength in chromaticity
diagram
• Then y increases
x=X/(X+Y+Z)
y=Y/(X+Y+Z)
Pure wavelength in chromaticity
diagram
• Green: y is big
x=X/(X+Y+Z)
y=Y/(X+Y+Z)
Pure wavelength in chromaticity
diagram
• Yellow: x & y are equal
x=X/(X+Y+Z)
y=Y/(X+Y+Z)
Pure wavelength in chromaticity
diagram
• Red: big x, but y is not null
x=X/(X+Y+Z)
y=Y/(X+Y+Z)
Color spaces: L*a*b*
(also L*u*v*)
“Perceptually uniform”* color space
Nonlinear transformations of XYZ space.
L
(a=0,b=0)
a
(L=65,b=0)
b
(L=65,a=0)
distances quasi Euclidean
VI. CIE COLOUR SPACES
A. CIE
CIE, the International Commission on Illumination - abbreviated as CIE from its French title Commission Internationale de
l’Eclairage - is an organization devoted to international cooperation and exchange of information among its member countries
on all matters relating to the science and art of lighting [2].
In 1931 CIE laid down the CIE 1931 standard colorimetric
observer. This is the data on the ideal observer on which all
colorimetry is based [5, page 131].
u0n =
4Xn
Xn + 15Yn + 3Zn
9Y
X + 15Y + 3Z
9Yn
vn0 =
Xn + 15Yn + 3Zn
v0 =
The tristimulus values Xn , Yn , Zn are those of the nominally
white object-colour stimulus.
The transformation from CIE XYZ to CIE Lab is performed
with the following equations
¶1
Y 3
− 16
Yn
"µ
¶ 1 µ ¶ 31 #
Y
X 3
∗
−
a = 500
Xn
Yn
"µ ¶ 1 µ ¶ 1 #
Z 3
Y 3
−
b∗ = 200
Yn
Zn
µ
B. CIE XYZ
CIE standardized the XY Z values as tristimulus values that
can describe any colour that can be percepted by an average
human observer (the CIE 1931 standard colorimetric observer).
These primaries are nonreal, i.e. they cannot be realized by actual colour stimuli [5, page 138]. This colour space is chosen
in such a way that every perceptible visual stimulus is described
with positive XY Z values.
A very important attribute of the CIE XYZ colour space is that
it is device independent. Every colour space that has a transformation from the CIE XYZ colour space (RGB709 , CIELab,
CIELuv) can also be regarded as being device independent. The
CIE XYZ colour space is usually used as a reference colour space
and is as such an intermediate device-independent colour space.
C. CIE Luv and CIE Lab colour spaces
In 1976 the CIE proposed two colour spaces (CIELuv and
CIELab) whose main goal was to provide a perceptually equal
space. This means that the Euclidian distance between two
colours in the CIELuv/CIELab colour space is strongly correlated with the human visual perception. To achieve this property
there were two main constraints to take into account:
• chromatic adaptation
• non-linear visual response
The main difference between the two colour spaces is in the
chromatic adaptation model implemented. The CIE Lab colour
space normalizes its values by the division with the white point
while the CIELuv colour space normalizes its values by the subtraction of the white point.
The transformation from CIE XYZ to CIE Luv is performed
with the following equations
µ
∗
L = 116
Y
Yn
¶ 31
− 16
L∗ = 116
The perceptually linear colour difference formulaes between
two colours are
p
∗
∆Eab
= (∆L∗ )2 + (∆a∗ )2 + (∆b∗ )2
p
∗
∆Euv
= (∆L∗ )2 + (∆u∗ )2 + (∆v ∗ )2
VII. C ONCLUSION
In this paper we have presented an overview of colour spaces
used in image processing. We have tried to stress the importance
of the historical and perceptual background that has led to the
introduction of these colour spaces.
R EFERENCES
[1] Symon D’O. Cotton, Colour, colour spaces and the human visual system,
School of Computer Science, University of Birmingham, England, Technical Report, B15-2TT, May 1996.
[2] CIE home page http://members.eunet.at/cie/ .
[3] Charles Poynton, A Guided Tour of Color Space, New Foundations for
Video Technology (Proceedings of the SMTPE Advanced Television and
Electronic Imaging Conference), 1995, pages 167-180.
[4] Charles Poynton,
Frequently Asked Questions about Color,
http://www.inforamp.net/ poynton, 1999.
[5] Gunter Wyszecki, W.S. Stiles, Color Science Concepts and Methods, Quantitative Data and Formulae, John Wiley and Sons, Inc, 2000.
[6] Mark D. Fairchild, Color Appearance Models, Addison Wesley, 1998.
[7] Henryk Palus, Colour spaces, Chapmann and Hall, 1998.
[8] Adrian Ford and Alan Roberts, Colour space conversions, Westminster
University, London, 1998.
u∗ = 13L∗ (u0 − u0n )
v ∗ = 13L∗ (v 0 − vn0 )
for
Y
Yn
> 0.01, otherwise the following L∗ formulae is used
L∗ = 903.3
Y
Yn
The quantities u0 , v 0 and u0n , vn0 are calculated from
u0 =
4X
X + 15Y + 3Z
L between 0 and 100
u* between -134 and 200
v* between -140 and 122
L*u*v* the
inner solid
If you chose only chrominance (say, a and b)...
Only color shown – constant intensity
... if you chose only luminance (say, L).
Only intensity shown – constant color
Most information in intensity.
Original image