Understanding Color 2010

SC076 Understanding Color

Giordano Beretta

HP Labs Palo Alto

Alexandria, someday 2010

http://www.inventoland.net/imaging/uc/slides.pdf

Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 1 / 207

Broad outline

5 Illumination 10 Color image
communication
1 Introduction
6 Measuring color
11 Color appearance
2 Color theories modeling
7 Spectral color
3 Terminology 12 Cognitive color
8 Color reproduction
4 Objective color 13 Conclusions
terms
9 Milestones in color
printing
14 Bibliography


Outline

communication
1 Introduction
6 Measuring color
11 Color appearance
7 Spectral color
terms
printing
14 Bibliography


Course objectives

Develop a systematic understanding of the principles of color
perception and encoding
Understand the differences between the various methods for color
imaging and communication
Gain a more realistic expectation from color reproduction
Develop an intuition for
trade-offs in color reproduction systems
interpreting the result of a color measurement


What is color?

Color is an illusion
Colorimetry: the art to predict an illusion from a physical
measurement
Experience is much more important than knowing facts or theories
The physiology of color vision is understood only to a very small
degree
Physiology: physical stimulus → physiological response
Psychophysics: physical stimulus → behavioral response

What is essential is invisible to the eye
Antoine de Saint-Exupéry (The Little Prince)


Outline

communication
1 Introduction
6 Measuring color
11 Color appearance
7 Spectral color
terms
printing
14 Bibliography


Section Outline

2 Color theories
Chronology
Color vision is not based on a bitmap
Color vision physiology
Limited knowledge


Color theories over the Millennia

Particle theory ca.
945–715 B.C.E.:
sun god Horakthy
emits light as a ﬂux of
colored lilies


Color theories
92,000 B.C.E. — Qafzeh Cave, color symbolism
800 B.C.E. — Indian Upanishads
there are relations among colors
400 B.C.E. — Hellenic philosophers
Democritus: sensations are elicited by atoms
Plato: light or ﬁre rays emanate from the eyes
Epicurus: replicas of objects enter the eyes
100–170 C.E. — Alexandria’s natural philosophers
Claudius Ptolemæus describes additive color based on wheel in
section 96 of the second book of Optics
First Millennium — Arab school, pure science
Abu Ali al-Hasan ibn al-Haytham a.k.a. Alhazen:
invents scientiﬁc process (observation–hypothesis–experiment)
disproves Plato’s emanation theory
image is formed within the eye like in a camera obscura
describes additive color based on top


Opponent colors
15th century — Renaissance, technology
Leonardo da Vinci
color perception
color order system
black & white are colors
3 pairs of opponent colors (black–white, red–green, yellow–blue)
simultaneous contrast
used color ﬁlters to determine color mixtures

Note: rendered with chiaro-scuro technique

Color theories (cont.)

18th century — Enlightenment, physics & chemistry
Isaac Newton:
spectral dispersion, white can be dispersed in a spectrum by a prism
colors of objects relate to their spectral reﬂectance
light is not colored and color perception is elicited in the human visual
system
19th century — scientiﬁc discovery
Thomas Young: trichromatic theory
Hermann von Helmholtz: spectral sensitivity curves
Ewald Hering:
opponent color theory (can explain hues, saturation, and why there is
no reddish green or yellowish blue)
black and dark gray are not produced by the absence of light but by a
lighter surround


Color theories (cont.)

20th century — advanced scientiﬁc instruments
Johannes A. von Kries: chromatic adaptation
why is white balance necessary?
Georg Elias Müller & Erwin Schrödinger: zone theory
physiological evidence for inhibitory mechanisms becomes
available in the 1950s
molecular biology
functional MRI techniques
see http://webvision.med.utah.edu/ for the latest progress


Section Outline

2 Color theories
Chronology
Limited knowledge


Vision is based on contrast
Vision is not hierarchical. The simple model
distal event proximal stimulus brain event
is very questionable. It is believed that feedback loops exist
between all 26 known areas of visual processing
In fact, it has been proved that a necessary condition of some
activity in even the primary visual cortex is input from “higher”
areas
Like the other sensory systems, vision is narcissistic
Many sensory signals are non-correlational — a given signal does
not always indicate the same property or event in the world
The “inner eye’s” function is not to understand what the sensory states
indicate
Example
see Science 17 March 2006: Vol. 311. no. 5767, pp. 1606 – 1609

Cognitive model for color appearance
stimulus detectors early mechanisms pictorial register

color
edges
contour
motion
depth
…
context parameters

chroma
etc.
hue
Color lexicon lightness

chroma internal
etc.
color space
amber hue
lightness

action color name apparent color
representation

Reliable color discrimination: 1 week
Color-opponent channels: 3 months
Color constancy: 4 months
Internal color space
Color names

Memory colors
Vision is not hierarchical
Delk & Fillenbaum experiment (1965)

We tend to see colors of familiar objects as we expect them to be
Surround
10º
Sky
Complexion

2º
Adapting
field
Vegetation


Section Outline

2 Color theories
Chronology
Limited knowledge


The retina has a layer of photoreceptors, which grow like hair
(10µm per day). They are of two kinds: rods and cones
The cones are of three kinds, depending on the pigments they
contain. One pigment absorbs reddish light, one absorbs greenish
light, and one absorbs bluish light
This leads to the method of trichromatic color reproduction, in
which we try to stimulate independently the three kinds of cones
s
ell m
ers nc lls ells
liu
ib lio ls the
ef ng cel ell
s l ce e c nes epi
erv lg
a
ine rc nta con & co ent
tic n ina acr ola orizo d & ds igm
op ret am bip h ro ro p

stimulus


Photoreceptors

Credit: Carlos Rozas (CanalWeb, Chile)
http://webvision.med.utah.edu/movies/3Drod.mov

Photoreceptors
Outer segment

Credit: Helga Kolb
http://webvision.med.utah.edu/movies/discs.mov
http://webvision.med.utah.edu/movies/phago4.mov

The aging retina

Comparative diagrams of 3- and 80-year-old retinal pigment epithelial
(RPE) cells in the eye. As the eye ages, the RPE cells deteriorate,
making it harder for the brain to receive and register light, leading to
blindness. Credit: David Williams, University of Rochester.

Evolution
From the difference in the amino-acid sequences for the various
photoreceptor genes it is clear that the human visual system did not evolve
according to a single design

Finding Rod and S Mechanisms L and M Mechanisms
Anatomy Distribution perifoveal foveal

Bipolar circuitry one class (only on) two classes (on and off)

Psychophysics Spatial resolution low high

Temporal resolution low high

Weber fraction high low

Wavelength sensitivity short medium

Electrophysiology Response function saturates does not saturate

Latencies long short

ERG-off-effect negative positive

Ganglion cell response afterpotential no afterpotential

Receptive ﬁeld large small

Vulnerability high low

Genetics autosomal sex-linked

Source: Eberhart Zrenner, 1983


Catching photons

Retinal pigments: rhodopsin, cyanolabe, chlorolabe, erythrolabe
lysine attaches chromophore to a protein backbone
electronic excitation (two-photon catch) initiates a large shift in
electron density in less than 10−15 seconds
shift activates rotation around two double-bonded carbon atoms in
the backbone
entire photocycle lasts less than a picosecond (10−12 sec.)
photoisomerization induces shift in positive charge perpendicular to
membrane sheets containing the protein
this generates a photoelectric signal with a less than 5psec. rise time
forward reaction is completed in ∼ 50µsec.(10−6 sec.)
Quantum efﬁciency: measure of the probability that the reaction
will take place after the absorption of a photon of light
4 pigments sensitized to photons at 4 energy levels (wavelength):
L, M, S, and rods


Phototransduction

Credit: Helga Kolb,
http://webvision.med.utah.edu/movies/trasduc.mov

Catch probabilities
Quantum energy of a photon: hν
For each pigment, there is a probability distribution for a reaction,
depending on the photon’s wavelength
¯
w(λ)dλ
What counts is not the energy of a single photon, but the average
¯
For a spectral power distribution Pλ : S = Pλ w(λ)dλ
absorbance
S-cone
1.0
M-cone
0.8
L-cone

0.6 Rod

0.4

0.2

nm
0.0
400 450 500 550 600 650

Dartnall, H. J. A., Bowmaker, J. K., & Mollon, J. D. (1983). Human visual pigments: microspectrophotometric results from the

eyes of seven persons. Proceedings of the Royal Society of London, B 220, 115–130


Retinal mechanisms
Surround

Center

Surround

Retinal Amacrine Bipolar Horizontal Receptor
ganglion cell cell cell
cell

Receptors in retina are not like pixels in a CCD sensor
Receptive field: area of visual field that activates a retinal ganglion
(H.K. Hartline, 1938)
Center-surround fields allow for adaptive coding (transmit contrast
instead of absolute values)
Horizontal cells presumed to inhibit either its bipolar cell or the
receptors: opponent response in red–green and yellow–blue
potentials (G. Svaetichin, 1956)
Balance of red–green channel might be determined by yellow
Retinal ganglion can be tonic or phasic: pathway may also be
organized by information density or bandwidth

Parvocellular and magnocellular pathways
P– M–
Originating retinal gan- Tonic Phasic
glion cells

Temporal resolution Slow (sustained responses, low conduction Fast (mostly transient responses, some sus-
velocity) tained, high conduction velocity)

Modulation dominance Chromatic Luminance
Adaptation occurs at high frequencies Adaptation occurs at all frequencies

Color Receives mostly opponent type input from Receives mostly combined (broadband) input
cones sensitive to short and long wavelengths from M and L cones, both from the center and
from the surround of receptive fields

Contrast sensitivity Low (threshold > 10%) High (threshold < 2%)

LGN cell saturation Linear up to about 64% contrast At 10%

Spatial resolution High (small cells) Low (large cells)

Spatio-temporal resolu- When fixation is strictly foveal, extraction of Responds to flicker
tion high spatial frequency information (test grat-
ings), reflecting small color receptive fields
Long integration time Short integration time

Relation to channels Could be a site for both a lightness channel Might be a site for achromatic channels be-
as for opponent-color channels. The role de- cause the spectral sensitivity is similar to Vλ ,
pends on the spatio-temporal content of the it is more sensitive to flicker, and has only a
target used in the experiment weak opponent color component

Possible main role in the Sustain the perception of color, texture, shape, Sustain the detection of movement, depth,
visual system and fine stereopsis and flicker; reading of text


Color constancy

Optic
tract Lateral Primary Blob
geniculate visual
Optic cortex
body
radiations

Axons of retinal ganglion cells in optical nerve terminate at LGN
and synapse with neurons radiating to striate cortex
LGN might generate masking effects; combination with saccadic
motion of eye
Blobs in area 17 consist mainly of double opponent cells
May be site for color constancy
Requires input from V4 (Zeki)
Why is white balancing necessary in color reproduction?

Section Outline

2 Color theories
Chronology
Limited knowledge


Limited knowledge

Reaction time at rhodopsin level: femtoseconds
Reaction time at perceptual level: seconds
From photon catches to constant color names

We do not know exactly what happens in-between
Example
simultaneous contrast
chromatic induction


1 color appears as 2


Appearance mode

Three ﬂat objects or picture of a white cube illuminated from the top
and right?


Our goal

We would like to be able to predict the color of a sample by
making a measurement
Humans can distinguish about 7 to 10 million different colors —
just name them and build an instrument that identiﬁes them
Task: ﬁnd good correlates to the subjective color terms


Basis for colorimetry

Too many unknowns in physiology and cognitive processes
Cannot yet build accurate color vision model
Unlike auditory system, visual system is not spectral but
integrative
Advantage of integrative system: metamerism
Basis of colorimetry:
1 Instead of a physiological model, build a psychophysical model
Physiology: physical stimulus physiological response
Psychophysics: physical stimulus behavioral response
2 Assume additivity
3 Keep the viewing conditions constant


Outline

communication
1 Introduction
6 Measuring color
11 Color appearance
7 Spectral color
terms
printing
14 Bibliography


Section Outline

3 Terminology
Basics
Subjective color terms
Objective color terms
Color matching
Metamerism
Chromaticity diagrams
CIE 1931 standard colorimetric observer
Tristimulus normalization


The CIE

The International Commission on Illumination — also known as
the CIE from its French title, the Commission Internationale de
l’Éclairage — is devoted to worldwide cooperation and the
exchange of information on all matters relating to the science and
art of light and lighting, colour and vision, and image technology
With strong technical, scientiﬁc and cultural foundations, the CIE
is an independent, non-proﬁt organisation that serves member
countries on a voluntary basis
Since its inception in 1913, the CIE has become a professional
organization and has been accepted as representing the best
authority on the subject and as such is recognized by ISO as an
international standardization body


CIE definition 845-02-18: (perceived) color
Definition (Color)
Attribute of a visual perception consisting of any combination of
chromatic and achromatic content. This attribute can be described
by chromatic color names such as yellow, orange, brown, red,
pink, green, blue, purple, etc., or by achromatic color names such
as white, gray, black, etc., and qualified by bright, dim, light, dark
etc., or by combinations of such names
Perceived color depends on the spectral distribution of the color
stimulus, on the size, shape, structure and surround of the
stimulus area, on the state of adaptation of the observer’s visual
system, and on the observer’s experience of the prevailing and
similar situations of observation
Perceived color may appear in several modes of appearance. The
names for various modes of appearance are intended to
distinguish among qualitative and geometric differences of color
perceptions

Colorimetry

Definition (Colorimetry)
Colorimetry is the branch of color science concerned with specifying
numerically the color of a physically defined visual stimulus in such a
manner that:
1 when viewed by an observer with normal color vision, under the
same observing conditions, stimuli with the same specification
look alike,
2 stimuli that look alike have the same specification, and
3 the numbers comprising the specification are functions of the
physical parameters defining the spectral radiant power
distribution of the stimulus


Grassmann’s laws of additive color mixture

Deﬁnition (Trichromatic generalization)
Over a wide range of conditions of observation, many color stimuli can
be matched in color completely by additive mixtures of three ﬁxed
primary stimuli whose radiant powers have been suitably adjusted
(proportionality)
In addition, the color stimuli combine linearly, symmetrically, and
transitively


Color term categories
Definition (Subjective color term)
A word used to describe a color attribute perceived by a human.
Example: the colorfulness of a flower

Definition (Objective color term)
A word used to describe a physical quantity related to color that can be
measured. Example: the energy radiated by a source


Section Outline

3 Terminology
Basics
Color matching
Metamerism


Subjective color terms — Hue

Deﬁnition (Hue)
The attribute of a color perception denoted by blue, green, yellow, red,
purple, and so on

Deﬁnition (Unique hue)
A hue that cannot be further described by use of the hue names other
than its own. There are four unique hues, each of which shows no
perceptual similarity to any of the others: red, green, yellow, and blue


Brightness

Deﬁnition (Brightness)
The attribute of a visual sensation according to which a given visual
stimulus appears to be more or less intense, or according to which the
visual stimulus appears to emit more or less light

Objective term: luminance (L)

Brightness scales


Lightness

Deﬁnition (Lightness)
The attribute of a visual sensation according to which the area in which
the visual stimulus is presented appears to emit more or less light in
proportion to that emitted by a similarly illuminated area perceived as a
“white” stimulus
Objective terms: luminance factor (β), CIE lightness (L∗ )

Fact
Brightness is absolute, lightness is relative to an area perceived as
white


Colorfulness

Deﬁnition (Chromaticness or Colorfulness)
The attribute of a visual sensation according to which an area appears
to exhibit more or less of its hue. In short: the extent to which a hue is
apparent

Objective term: CIECAM02 M


Colorfulness — Chroma

Deﬁnition (Chroma)
The attribute of a visual sensation which permits a judgement to be
made of the degree to which a chromatic stimulus differs from an
achromatic stimulus of the same brightness

In other words, chroma is an attribute orthogonal to brightness:
absolute colorfulness; we perceive a color correctly independently of
the illumination level
∗ ∗
Objective term: CIE chroma (Cuv , Cab )


Colorfulness — Saturation
Deﬁnition (Saturation)
The attribute of a visual sensation which permits a judgement to be
made of the degree to which a chromatic stimulus differs from an
achromatic stimulus regardless of their brightness

In other words, it is the colorfulness of an area judged in proportion to
its brightness: relative colorfulness; we can judge the uniformity of an
object’s color in the presence of shadows and independently of the
incident light’s angle
Objective term: purity (p), CIE saturation (Suv )

Fact
Colorfulness is absolute, chroma is relative to a white area and
absolute w.r.t. brightness, saturation is in proportion to brightness

Section Outline

3 Terminology
Basics
Color matching
Metamerism


Spectral curves
Quantities we can measure

Definition (spectral power curve)
The spectral power curve gives at each wavelength the power (in
watts), i.e., the rate at which energy is received from the light source

Definition (spectral reflectance curve)
The spectral reflectance curve gives at each wavelength the
percentage of incident light that is reflected
0.40
reflectance

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00
400 450 500 550 600 650 700 nm
Human complexion

Spectral color reproduction
Deﬁnition (spectral color reproduction)
By spectral color reproduction we intend the physically correct
reproduction of color, i.e., the duplication of the original object’s
spectrum

The general reproduction methods (micro-dispersion and
Lippmann) are too impractical for normal use
For some special applications like painting restoration or illuminant
reconstruction, the spectrum may be sampled at a small number
of intervals and combined with principal component analysis
Fortunately, spectral color reproduction is required only in rare
cases, such as paint swatches in catalogs, and in this cases it is
often possible to use identical dyes
Our aim is to achieve a close effect for a normal viewer under average
viewing conditions
Mathematically: build a simple model of color vision

Section Outline

3 Terminology
Basics
Color matching
Metamerism


Completing a wardrobe

Some observations:
If you want to buy a skirt or a pair of slacks to match a jacket, you
cannot match the color by memory — you have to take the jacket
with you
Just matching in the store light is insufﬁcient, you have to match
also under the incandescent light in the dressing room and outdoors
You always get the opinion of your companion or the store clerk
Three fundamental components of measuring color:
light sources
samples illuminated by them
observers


Color matching

Colors are assessed by matching them with reference colors on a
small-ﬁeld bipartite screen


Color-matching functions I
Given a monochromatic stimulus Qλ of wavelength λ, it can be written
as

Qλ = Rλ R + Gλ G + Bλ B
where Rλ , Gλ , and Bλ are the spectral tristimulus values of Qλ


Color-matching functions II

Assume an equal-energy stimulus E whose mono-chromatic
constituents are Eλ (equal-energy means Eλ ≡ 1)
The equation for a color match involving a mono-chromatic constituent
Eλ of E is

r ¯ ¯
Eλ = ¯(λ)R + g (λ)G + b(λ)B
r ¯ ¯
where ¯(λ), g (λ), and b(λ), are the spectral tristimulus values of Eλ

Deﬁnition (color-matching functions)
r ¯ ¯
The sets of such values ¯(λ), g (λ), and b(λ) are called color-matching
functions (CMF)


Color-matching functions III
3.0
Stiles-Burch (1955;1959)
2.5
2.0 b(λ)
1.5 g(λ)
1.0 r(λ)
0.5
0.0
nm
-0.5
400 500 600 700


Section Outline

3 Terminology
Basics
Color matching
Metamerism


Metameric stimuli

Consider two color stimuli

Q1 = R1 R + G1 G + B1 B
Q2 = R2 R + G2 G + B2 B

Deﬁnition (metameric stimuli)
If Q1 and Q2 have different spectral radiant power distributions, but
R1 = R2 and G1 = G2 and B1 = B2 , the two stimuli are called
metameric stimuli

Fact
Color reproduction works because of metamerism


Metameric stimuli
Metamerism kit
0.6

0.5 reflectance
D
C
0.4 B
A

0.3

0.2

0.1

nm

0.0
400 500 600 700


Metameric stimuli
Kinds of metamerism

Illuminant metamerism
example: daylight and a D65 simulation ﬂuorescent lamp
Object metamerism
example: metameric inks (see metamerism kit)
Sensor metamerism
example: scanner and human visual system
Observer metamerism
example: you and your neighbor
Complex metamerism
example: two inks metameric under two illuminants


Section Outline

3 Terminology
Basics
Color matching
Metamerism


We can normalize the color-matching functions and thus obtain new
quantities

r r ¯ ¯
r (λ) = ¯(λ)/[¯(λ) + g (λ) + b(λ)]
¯ r ¯ ¯
g(λ) = g (λ)/[¯(λ) + g (λ) + b(λ)]
¯ ¯
b(λ) = b(λ)/[¯(λ) + g (λ) + b(λ)]
r ¯

with r (λ) + g(λ) + b(λ) = 1

Deﬁnition (spectrum locus)
The locus of chromaticity points for monochromatic colors so
determined is called the spectrum locus in the (r , g)-chromaticity
diagram


(r , g)-chromaticity diagram
2.0

g(m)
1.5

1.0 2° pilot group
Stiles-Burch (1955)

0.5

r(m)
0.0
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

-0.5


Imaginary color stimuli

The fact that the color-matching functions and the chromaticity
coordinates can be negative presents a problem when the
tristimulus values are computed from a spectral radiant power
distribution
Because the color-matching space is linear, a linear
transformation can be applied to the primary stimuli to obtain new
imaginary stimuli that lie outside the chromaticity region bounded
by the spectrum locus
This ensures that the chromaticity coordinates are never negative


(x, y )-chromaticity diagram

spectrum locus

2.0

A: ~2856˚K

1.5 Planckian locus
D65: ~6504˚K

∞
1.0

0.5 z2(λ)
y2(λ)
x2(λ)
nm
0.0
400 500 600 700 800


Section Outline

3 Terminology
Basics
Color matching
Metamerism


We want to build an instrument delivering results valid for the group of
normal trichromats (95% of population); since

R=k Pλ¯(λ)dλ
r

G=k ¯
Pλ g (λ)dλ

B=k ¯
Pλ b(λ)dλ

an ideal observer can be deﬁned by specifying values for the
color-matching functions

Deﬁnition (CIE 1931 standard colorimetric observer)
The Commission Internationale de l’Éclairage (CIE) has recommended
¯ ¯ ¯
such tables containing x (λ), y (λ), z (λ) for λ ∈ [360nm, 830nm] in 1nm
steps


CIE 1931 Observer (cont.)

In addition to the color-matching properties, the CIE 1931
Standard Observer is such that it has also the heterochromatic
brightness-matching properties. The latter is achieved by
¯
choosing y (λ) to coincide with the photopic luminous efﬁciency
function
X and Z are on the alychne, which in the chromaticity diagram is a
straight line on which are located the chromaticity points of all
stimuli having zero luminance
The data is based averaging the results
1 on color matching in a 2◦ ﬁeld of 17 observers and
2 the relative luminances of the colors of the spectrum, averaged for
about 100 observers


Section Outline

3 Terminology
Basics
Color matching
Metamerism


X , Y , and Z are defined up to a common normalization factor.
This factor is different for objects and for emissive sources
The perfect reflecting diffuser is an ideal isotropic diffuser with a
reflectance equal to unity
The perfect reflecting diffuser is completely matt and is entirely
free from any gloss or sheen. The reflectance is equal to unity at
all wavelengths
When the tristimulus values are measured with an instrument, YL
represents a photometric measure, such as luminance. For object
surfaces it is customary to scale X , Y , Z , so that Y = 100 for the
perfect diffuser
In practice a working standard such as a BaSO4 plate or a ceramic
tile is used in lieu of the perfect diffuser
For emissive sources there is no illuminant and therefore the
perfect diffuser is not relevant. So it is customary to use the
photometric measures

Outline

communication
1 Introduction
6 Measuring color
11 Color appearance
7 Spectral color
terms
printing
14 Bibliography


Quantities we can measure

Deﬁnition (Dominant wavelength)
Wavelength of the monochromatic stimulus that, when additively mixed
in suitable proportions with a speciﬁed achromatic stimulus, matches
the color stimulus considered
[In disuse, replaced by chromaticity]
y
520
530
0.8
540
510
550

560
0.6
570
500
580

590
0.4
Planckian locus A: ~2856˚K 600
610
620
490 630
D65: ~6504˚K 700

0.2 ∞
480

470
0

460 x
45

0 0.2 0.4 0.6


Luminance

Definition (Luminance)
The luminous intensity in a given direction per unit projected area

Lv = Km Le,λ V (λ)dλ
λ

where Km is the maximum photopic luminous efficacy (683lm · W−1 ),
Le,λ the radiance, and V (λ) the photopic efficiency

Definition (Luminance factor)
The ratio of the luminance of a color to that of a perfectly reflecting or
transmitting diffuser identically illuminated
Symbol: β


Section Outline

4 Objective color terms
Y and chromaticity
Uniformity
Color spaces sliced and diced


Y

Definition (Y stimulus)
In the XYZ system the luminance depends entirely on the Y stimulus.
The Y values of any two colors are proportional to their luminances.
Therefore, Y gives the percentage reflection or transmission directly,
where a perfectly reflecting diffuser or transmitting color has a value of
Y = 100

Y =V
where V is the luminance of the stimulus computed in accordance with
the luminous efficiency function V (λ)

Called luminosity in some literature
Application: conversion of a color image to black and white


Excitation purity
Deﬁnition (Excitation purity)
A measure of the proportions of the amounts of the monochromatic
stimulus and of the speciﬁed achromatic stimulus that, when additively
mixed, match the color stimulus considered

x − xw y − yw
pc = or pc =
xb − xw yb − yw
where w denotes the achromatic stimulus and b the boundary color
stimulus
In disuse, replaced by chromaticity
y
520
530
0.8
540
510
550

560
0.6
570
500
580

590
0.4
Planckian locus A: ~2856˚K 600
610
620
490 630
D65: ~6504˚K 700

0.2 ∞
480

470
0

460 x
45

0 0.2 0.4 0.6


Chromaticity

Deﬁnition (Chromaticity)
Proportions of the amounts of three color-matching stimuli needed to
match a color
Relationship between chromaticity coordinates r (λ), g(λ), b(λ) and
x(λ), y (λ), z(λ) of a given spectral stimulus of wavelength λ are
expressed by the projective transformation

0.49000r (λ) + 0.31000g(λ) + 0.20000b(λ)
x(λ) =
0.66697r (λ) + 1.32240g(λ) + 1.20063b(λ)
0.17697r (λ) + 0.81240g(λ) + 0.01063b(λ)
y (λ) =
0.66697r (λ) + 1.32240g(λ) + 1.20063b(λ)
0.00000r (λ) + 0.01000g(λ) + 0.99000b(λ)
z(λ) =
0.66697r (λ) + 1.32240g(λ) + 1.20063b(λ)


Section Outline

Y and chromaticity
Uniformity


Uniformity
The X , Y , Z tristimulus
coordinates allow us to decide
if two colors match in a given y
context. If there is no match, it 0.8
520
530

does not tell us how large the 510
540
Stiles Line Element
550
Ellipses plotted 3 x
perceptual mismatch is. 560
0.6
Consequently, the CIE 1931 500
570

580
chromaticity diagram is not a 590
0.4
perceptually uniform 600
610
620
chromaticity space from which 490 630
700

the perception of chromaticity 0.2
480
can be derived.
470

0
460 x

45
0 0.2 0.4 0.6
x = X /(X + Y + Z )
y = Y /(X + Y + Z )
1=x +y +z

Uniform chromaticity diagram
The CIE 1976 UCS (Uniform Chromaticity Scale) chromaticity diagram
is perceptually uniform
u = 4X /(X + 15Y + 3Z ) = 4x/(−2x + 12y + 3)
v = 9Y /(X + 15Y + 3Z ) = 9y /(−2x + 12y + 3)

0.6 v'
y

0.8

0.7

0.5 0.6

0.5

0.4

0.3

0.4 0.2

0.1

x
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.5 v

0.3
0.4

0.3

0.2 0.2

0.1

u
0.1 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

u' Original MacAdam data, 10×
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8


CIELAB
1976 CIE L a b color space

CIE 1976 lightness L
A non-linear function to provide a measure that correlates with
lightness more uniformly
Similar lightness distribution to Munsell Value scale
3
L = 116 · Y /Yn − 16

Tangential near origin — when Y /Yn < 0.001:

Y Y
Lm = 903.3 for 0.008856
Yn Yn


CIELAB (cont.)
1976 CIE L a b color space

Two color opponent channels a , b

3 3
a = 500 · X /Xn − Y /Yn
3 3
b = 200 · Y /Yn − Z /Zn

Tangential near origin — when X /Xn , Y /Yn , Z /Zn < 0.001
Xn , Yn , Zn : reference white

D50 : (96.422, 100.000, 82.521)
D65 : (95.047, 100.000, 108.883)

von Kries type adaptation


Color difference formulæ
The CIE has deﬁned two uniform color spaces, 1976 CIE L u v
and 1976 CIE L a b in which the difference of two color stimuli
can be measured
u and v (but not a and b ) are coordinates on a uniform
chromaticity diagram. The third dimension is the psychometric
lightness

2 2
Cab = a +b hab = arctan(b /a )
2 2 2
∆L ∆Cab ∆Hab
∆E94 = + +
kL · SL kC · SC kH · S H

SL = 1
SC = 1 + 0.045 · Cab
SH = 1 + 0.015 · Cab
kL = kC = kH = 1

Section Outline

Y and chromaticity
Uniformity


Color spaces
color model operators

Device dependent spaces
counts received from or sent to a device
typically RGB counts or CMYK percentages
Device independent spaces
human visual system related
counts for an idealized device
Colorimetric spaces
analytically derived from the CIE colorimetry system
Uniform spaces
Euclidean, with a distance metric
Visually scaled spaces
Spaces deﬁned by an atlas


Colorimetric spaces

XYZ + basis for all other CIE color spaces
– non-uniform
RGB + can be produced by additive devices
+ linear transformation of XYZ
– non-uniform
example:
    
R 0.019710 −0.005494 −0.002974 X
G = −0.009537 0.019363 −0.000274 Y 
B 0.000638 −0.001295 0.009816 Z

matrix elements are the primary colors
sRGB + contains non-linearity typical for PC CRTs
+ easy to implement
– non-uniform and non-linear


Colorimetric spaces (cont.)
CIELAB + most uniform CIE space
+ widely used in the printing industry
– cubic transformation
CIELUV + simple transformation of XYZ
+ uniform
+ related to YUV (PAL, SECAM)
– less uniform than CIELAB
YIQ + used for NTSC encoding
+ black and white compatible
– contains gamma correction
– non-uniform
YES, YCC + linear transformations of XYZ
+ black and white compatible
+ opponent color models
– less uniform than CIELAB and CIELUV
– YCC contains gamma correction
– private standards

Colorimetric spaces (cont.)
L C hab + has perceptual correlates
+ good for gamut mapping
+ perceptually uniform
– cylindrical
– not uniform for compression
xvYCC + large gamut for HDTV with LED BLU (backlight unit)
+ backwards compatible to sRGB
Luma Gamut of xvYCC
Y
254
Over White
1.0 235
1< R’,G’,B’ 1< R’,G’,B’ BT.709-5
(sRGB)
sYCC

Extended Region
Extended Region

0 < R’,G’,B’ < 1 xvYCC

(Gamut of BT.709-5)
(sRGB)

R’,G’,B’< 0 R’,G’,B’< 0
0.0 16
-0.57 - 0.5 Black +0.5 +0.56
1
128
Cb, Cr
1 16 240 254
Extended Extended Chroma


Uniform color spaces

Munsell
perceptually uniform
based on atlas
CIELAB
colorimetric
CIELUV
colorimetric
OSA
based on atlas
Coloroid
æstetically uniform
based on atlas


Visually scaled color spaces

Munsell
based on atlas
OSA
based on atlas
Coloroid
æstetically uniform
based on atlas
NCS
atlas with uniform coordinates
not perceptually uniform


Color spaces deﬁned by an atlas

Munsell
OSA
Coloroid
NCS
Scandinavian, popular in Europe
RAL
German, popular in Europe
Pantone
popular in the U.S.A.
Many atlases deﬁned by government agencies, industrial
associations, companies


Outline

communication
1 Introduction
6 Measuring color
11 Color appearance
7 Spectral color
terms
printing
14 Bibliography


Illumination
The spectral power distribution of the light reﬂected to the eye by an
object is the product, at each wavelength, of the object’s spectral
reﬂectance value by the spectral power distribution of the light source
CWF Complexion

400 500 600 700 400 500 600 700 400 500 600 700

Incident SPD x Reflectance curve = Reflected SPD

Deluxe Complexion
CWF

400 500 600 700 400 500 600 700 400 500 600 700


Light sources of interest

At the beginning of color perception there is radiant energy
Treatment in color science is slightly different from what we
learned in high school physics — it can be limited to the visible
domain
The spectral power distribution of a tungsten filament lamp
depends primarily on the temperature at which the filament is
operated
Typical average daylight has a color temperature of 6504◦ K, which
can be achieved also by Artificial Daylight fluorescent lamps,
a.k.a. North-light or Color Matching lamps


CIE standard illuminants
300

Definition (Illuminant A)
250
CIE standard illuminant A

relative radiant power
represents light from a full (or 200 D65
blackbody) radiator at 2854◦ K A

150

Definition (Illuminant D65 )
100
CIE standard illuminant D65
represents a phase of natural 50

daylight with a correlated color
wavelength [nm]
temperature of 6504◦ K 0
300 350 400 450 500 550 600 650 700 750 800

Fact (Illuminants B, C)
CIE standard illuminants B and C were intended to represent direct
sunlight with a correlated color temperature of 4874◦ K resp. 6774◦ K.
They are being dropped because they are seriously deficient in the UV
region (important for fluorescent materials)

CIE standard sources
Definition (Illuminant)
Illuminant refers to a specific spectral radiant power distribution
incident to the object viewed by the observer

Definition (Source)
Source refers to a physical emitter of radiant power, such as a lamp or
the sun and sky

CIE illuminant A is realized by a gas-filled coiled-tungsten filament
lamp operating at a correlated color temperature of 2856◦ K
There are no artificial sources for illuminant D65 , due to the jagged
spectral power distribution. However, some sources qualify as
daylight simulators for colorimetry
For more information see
http://www.mostlycolor.ch/2007/06/
hot-body-excited-particles-and-north.html

Outline

communication
1 Introduction
6 Measuring color
11 Color appearance
7 Spectral color
terms
printing
14 Bibliography


Measuring color
There are no filters that approximate well the color matching
functions
There are no artificial sources for the popular illuminants D65 and
D50
Today’s hardware situation has changed dramatically
Embedded processors are inexpensive
Holographic gratings are inexpensive
Light sources are highly efficient
CCD sensors have much less dark noise
It is better to perform spectral measurements and let the
instrument do the colorimetry
Spectroradiometer: determine the reflected SPD
Spectrophotometer: determine the reflectance curve
Because they are a closed system, spectrophotometers are very
reliable


Trusting your instrument
Sooner or later all users enter a deep trust crisis in their instruments.
Some survival tips:
Illuminate your work area with a source simulating your target
illuminant
see what the instrument “sees”
Compact spectrophotometers have a very small geometry;
perpendicularity between optical axis and sample, as well as
distance to the sample are critical
maintain an uncluttered work space
The instrument’s light source generates heat, which increases
dark current noise in the CCD and causes geometric deformations
in the grating
wait between measurements
recalibrate
at each session start
after each pause
after a long series of measurements,
when the ambient temperature has changed by more than 5◦ C

Calibration
White calibration: adjusts computational parameters so the calculated
tile’s reflectance curve is the same as the absolute reflectance curve
do it often
Absolute certification: verifies that the measured color of the tile is
within the tolerance (e.g. 0.6∆E units) from the tile’s absolute color
important for agreement between laboratories
Relative certification: verifies if the measured color of the tile is within
the tolerance (e.g. 0.3∆E units) from the initial color of the tile with the
same instruments
important for reproducibility
Collaborative testing: verifies that the entire color measurement
procedure is in agreement with outside laboratories
Collaborative Testing Services Inc, 21331 Gentry Drive, Sterling,
VA 20166, 571–434–1925
http://www.collaborativetesting.com/

Effect of variability
A measurement is never perfect
The effect of variability of color measurement is reduced by using
multiple measurements
How many measurements should I make and average?
Rule of thumb: 10× for each variability parameter
instrument’s variability: measure each spot — 10×
sample uniformity: repeat at several locations — 100×
sample variability: repeat for several samples — 1000×
...
Follow ASTM standard practice E 1345 – 90 to determine how
many measurements are necessary in each case
ASTM International, 100 Barr Harbor Drive, West Conshohocken,
PA 19428-2959, 610–832–9585, http://www.astm.org
Improve all process aspects to minimize the required number of
measurements
ISO 9001

Geometries of illumination and viewing
On a glossy surface there are mirror-like (specular) reflections
There are more reflections in the case of diffuse light sources
Since the color of the illuminant is white, specular reflections add
white, with the effect of desaturating the color
Non-metallic glossy surfaces look more saturated in directional
than in diffuse illumination
Matte surfaces scatter the light diffusely — matte surfaces usually
look less saturated than glossy surfaces
Most surfaces are between glossy and matte
Diffuse illumination is provided by integrating spheres
usually they are provided with gloss traps
Instruments with 45◦ /0◦ and 0◦ /45◦ geometry are less critical
ASTM recommendation for partly glossy samples:
use the geometry that minimizes surface effects (usually the one
that gives lowest Y and highest excitation purity)
45◦ /0◦ geometry gives rise to polarization problems

Outline

communication
1 Introduction
6 Measuring color
11 Color appearance
7 Spectral color
terms
printing
14 Bibliography


Section Outline

7 Spectral color
Computational color
Metamerism and Matrix R
The LabPQR interim connection space


Motivation

Examples when spectral color methods are required:
Metamerism
Fluorescence
Media and ink characterization
Reproduction across illuminants
Mapping from one device to another
More than 3 colorant hues (e.g., CMYKOGV)
Scanner and camera characterization


Repetition of Standard Observer

R=k Pλ · ¯(λ)dλ
r

means that the red color coordinate is obtained by integrating the SPD
using the red CMF for the measure, where

Pλ = E(λ) · S(λ)

is the product of the SPD of an illuminant E with the object spectrum S.
Usually we are interested in the coordinates of various objects under a
ﬁxed illuminant for a standard observer, so we reorder to

R=k ¯(λ)E(λ) · S(λ)dλ
r


Discretization
In practice, the CMF are given as a table with 1nm steps, and
instruments measure at steps of 1, 4, 10, 20nm etc., so in reality this is
a summation [for red R]:

R=k ¯(λ)E(λ)S(λ)dλ ≈ k
r ¯(λi )E(λi )S(λi )∆λ
r

The integration resp. summation is over the visible range [380, 780]nm,
but in practice it is often over [380, 730]nm for n = 36 samples
Instead of doing color science with measure theory, we can do it
with simple linear algebra
In 1991 H. Joel Trussell has made available a comprehensive
MatLab library and several key papers for color scientists
Since then, spectral color science is mostly done with linear
algebra


Formalism
We use the vector-space notation
WLOG, let k = 1
¯ ¯
R = (R E)S, G = (G E)S, ¯
B = (B E)S
Instead of doing this for each of R, G, B or X , Y , Z , using linear
algebra we can write it as a single equation by combining the CMF
in an n × 3 matrix A with the CMFs data in the columns:
Υ = (A E)S

Sometimes we are interested in the color of a ﬁxed object under
different illuminants, then we write
Υ = A (ES) = A η

η corresponds to the Pλ from earlier


Matlab, etc.

a
b
c
d


Section Outline

7 Spectral color
Computational color


Fundamental and residual

How can we reconcile metamerism and color reproduction
technology?
In 1953 Günter Wyszecki pointed out that the SPD of stimuli
consists of a fundamental color-stimulus function η (λ) intrinsically
´
associated with the tristimulus values, and a residual called the
metameric black function κ(λ)
κ(λ) is orthogonal to the space of the CMF


Matrix R theory

How does this translate to the discrete case?
In 1982 Jozef Cohen with William Kappauf developed the matrix R
theory
Use an orthogonal projector to decompose stimuli in fundamental
and residual
The fundamental is a linear combination of the CMF A
The metameric black is the difference between the stimulus and
the fundamental
For a set of metamers η1 (λ), η2 (λ), . . . , ηm (λ):

A η1 = A η2 = · · · = A ηm = Υ


Development of matrix R

R is deﬁned as the symmetric n × n matrix

Deﬁnition (matrix R)
R := A(A A)−1 A

Matrix R is an orthogonal projection
A(A A)−1 =: Mf , so R = Mf A (remember: Υ = A η)
Because A has 3 independent columns, R has rank 3
It decomposes the stimulus spectrum into fundamental η (λ) and
´
the metameric black κ:

η = Rηi
´
κ = ηi − η = ηi − Rηi = (I − R)ηi
´


Corollaries

Metameric black has tristimulus value zero

A κ = [0, 0, 0]

η = Rηi means that any group of metamers has a common
´
fundamental η , but different residuals κ
´
Inversely, a stimulus spectrum can be expressed as

ηi = η + κ = Rηi + (I − R)ηi
´

i.e., the stimulus spectrum can be reconstructed if the
fundamental metamer and metameric black are known
Why is this useful?


Section Outline

7 Spectral color
Computational color


Reducing the data

Storing a multidimensional vector for each pixel is expensive
Can we project on a lower-dimensional vector space?
Yes, because the spectra are relatively smooth
Popular technique: principal component analysis
Due to the usually smooth spectra, the dimension can be quite
low: between 5 and 8
We have known how to deal with this for decades, it just requires
linearly more processing


The hard problem
We would like to use an ICC type workflow also for spectral
imaging
Colorimetric workflow:
profile connection
image 3-hue printer
space

The killer is the LUT used in the PCS:
bands in bands out levels per band size [bytes]
3 6 17 30K
6 6 17 145M
9 6 17 700G
31 6 17 8 · 1027 G


Interim Connection Space

Proposal by Mitchell Rosen et al. at RIT
Introduce a lower-dimensional Interim Connection Space ICS

PCS to ICS

scene multi-hue printer

ICS to counts via
low-dim. LUT


Choosing the basis vectors

Can we deviate from the usual PCA method of choosing the
largest eigenvectors and build on some other useful basis?
When deﬁning the basis vectors for XYZ, the new basis was
chosen so that one vector coincides with luminous efﬁciency V (λ)
compatibility of colorimetry with photometry
1995 proposal by Bernhard Hill et al. at RWTH Aachen:
incorporate three colorimetric dimensions
compatibility of spectral technology with colorimetry
http://www.ite.rwth-aachen.de/Inhalt/Documents/
Hill/AachenMultispecHistory.pdf


Understanding Color 2010

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