Understanding Color

Understanding
Color
Giordano Beretta
Hewlett-Packard Laboratories

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

Alexandria 2008

Course objectives 1

• 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

G.B. Beretta Alexandria, 6 June 2008 SC076 — Understanding Color

What is color? 2
• 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)


1 Terminology 3
CIE deﬁnition 845-02-18: (perceived) 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


1.0.1 Color term categories 4
Subjective color term: A word used to describe a color attribute
perceived by a human. Example: the colorfulness of a flower
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
We use objective color terms as correlates to subjective color terms


1.0.2 Subjective color terms — Hue 5
Hue: The attribute of a color perception denoted by blue, green,
yellow, red, purple, and so on

hue scale

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


1.0.3 Brightness 6

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 scale


1.0.4 Lightness 7

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*)

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


1.0.5 Colorfulness 8

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


1.0.5.1 Colorfulness — Chroma 9

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 (C*uv, C*ab)


1.0.5.2 Colorfulness — Saturation 10
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 terms: purity (p), CIE saturation (Suv)

saturation scale

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


1.1 Our goal 11
• 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
• 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


1.2 Spectral curves 12
quantities we can measure

• 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
• The spectral reﬂectance curve gives at each wavelength the percentage of
incident light that is reﬂected

0.40

reflectance
human complexion
0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00
400 450 500 550 600 650 700 nm


1.2.1 Spectral color reproduction 13
• 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


2 Color theories 14
• 800 B.C.E. — Indian Upanishads
• there are relations among colors

• 400 B.C.E. — Hellenic philosophers
• Plato: light or ﬁre rays emanate from the eyes
• Epicurus: replicas of objects enter the eyes

• First Millennium — Arab school, pure science
• Abu Ali Mohammed Ibn al Hazen: image is formed
within the eye like in a camera obscura

• 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


2.0.1 Opponent colors 15
W
Y
R
G W

B Y

Y
K
G
R
B

W

K
G R

B

Note: rendered with chiaro-scuro technique


2.0.2 Color theories (cont.) 16

• 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


2.0.3 Color theories (cont.) 17

• 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


2.1 Color vision is not based on a bitmap 18
• 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
Science 17 March 2006: Vol. 311. no. 5767, pp. 1606 - 1609


2.1.1 Cognitive model for color appearance 19
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

2.1.2 Memory colors 20
• 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


2.2 Color vision physiology 21
• 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
ls
s cel um
ib er
lio
n
ls ll s ells th eli
rvef ng cel ce lls
ta l ce ne c ones t epi
ne ga ne on & co s & c men
tic in al a cri o lar riz d
op ret am bip ho ro rod pig

stimulus


2.2.1 Photoreceptors 22

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

2.2.1.1 Outer segment 23

http://webvision.med.utah.edu/movies/discs.mov

http://webvision.med.utah.edu/movies/phago4.mov

Credit: Helga Kolb


2.2.2 Evolution 24
• 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

Distribution perifoveal foveal
Anatomy one class two classes
Bipolar circuitry
(only on) (on and off)
Spatial resolution low high
Temporal resolution low high
Psychophysics
Weber fraction high low
Wavelength sensitivity short medium
Response function saturates does not saturate
Latencies long short
ERG-off-effect negative positive
Electrophysiology
Ganglion cell response afterpotential no afterpotential
Receptive ﬁeld large small
Vulnerability high low

Genetics autosomal sex-linked

Source: Eberhart Zrenner, 1983


2.2.3 Catching photons 25
• 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 5 psec. rise time
• forward reaction is completed in ~50 μsec. (10–6 sec.)

• Quantum efﬁciency: measure of the probability S harpe et al. ∑Human R ed, G reen, and R ed-G reen Hybrid C one P igments

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


2.2.4 Phototransduction 26

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


2.2.5 Catch probabilities 27
• 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


2.2.6 Retinal mechanisms 28
Surround

Center

Surround

Retinal Amacrine Bipolar Horizontal Receptor
ganglion cell cell cell
cell

• Receptors in retina are not like pixels in a CCD
• 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


2.2.7 Parvocellular and magnocellular pathways 29
P– M–

Originating retinal ganglion cells Tonic Phasic

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

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

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

When fixation is strictly foveal, extraction of high
spatial frequency information (test gratings), Responds to flicker
Spatio-temporal resolution reflecting small color receptive fields
Short integration time
Long integration time
Could be a site for both a lightness channel as for Might be a site for achromatic channels because
opponent-color channels. The role depends on the the spectral sensitivity is similar to Vλ, it is more
Relation to channels
spatio-temporal content of the target used in the sensitive to flicker, and has only a weak opponent
experiment color component

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


2.2.8 Color constancy 30

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?


2.3 Limited knowledge 31

• 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
• Examples: simultaneous contrast, chromatic induction


2.3.1 1 color appears as 2 32

Appearance mode

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

2.4 Basis for colorimetry 33
• 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


3 Colorimetry 34
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
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
Grassmann’s laws of additive color mixture

3.1 Color matching 35
Colors are assessed by matching them with reference colors on a
small-field bipartite screen:


3.1.1 Color-matching functions 36
Given a monochromatic stimulus Qλ of wavelength λ, it can be written as
Qλ = RλR + GλG + BλB,
where Rλ, Gλ, and Bλ are the spectral tristimulus values of Qλ
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
Eλ = r(λ)R + g(λ)G + b(λ)B,
where r(λ), g(λ), and b(λ), are the spectral tristimulus values of Eλ. The sets
of such values are called color-matching functions
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


3.1.2 Metameric stimuli 37
Consider two color stimuli
Q1 = R1R + G1G + B1B
Q2 = R2R + G2G + B2B
0.6

reflectance
If Q1 and Q2 have
different spectral radiant 0.5
D
power distributions, but C
R1 = R2 and G1 = G2 and B1 0.4 B

= B2, the two stimuli are A

called metameric stimuli 0.3

• Color reproduction 0.2
works because of
metamerism 0.1

nm

0.0
400 500 600 700


3.1.2.1 Kinds of metamerism 38

• 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

• Complex metamerism
• example: two inks metameric under two illuminants


3.2 Chromaticity diagrams 39
We can normalize the color-matching functions and thus obtain new
quantities
r (λ) = r (λ) / [r (λ) + g(λ) + b(λ)]
g(λ) = g(λ) / [r (λ) + g(λ) + b(λ)]
b(λ) = b(λ) / [r (λ) + g(λ) + b(λ)]

with r(λ) + g(λ) + b(λ) = 1 2.0

g(m)
The locus of chromaticity points 1.5

for monochromatic colors so
determined is called the spectrum 1.0 2° pilot group
Stiles-Burch (1955)
locus in the (r, g)-chromaticity
diagram 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


3.2.1 Imaginary color stimuli 40
• 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 spectrum locus
linear, a linear
transformation can 2.0
be applied to the
primary stimuli to A: ~2856˚K
obtain new 1.5 Planckian locus
imaginary stimuli D65: ~6504˚K

that lie outside the ∞
chromaticity region 1.0
bounded by the
spectrum locus. This
ensures that the
0.5 z2(λ)
chromaticity y2(λ)
coordinates are x2(λ)
never negative nm
0.0
400 500 600 700 800


3.3 CIE 1931 standard colorimetric 41
observer
We want to obtain results valid for the group of normal trichromats
(95% of population)

Because
R = ∫ P λ r (λ ) d λ , G = ∫ Pλ g(λ) dλ, B = ∫ Pλ b(λ) dλ,

an ideal observer can be defined by specifying values for the color-
matching functions
The Commission Internationale de l'Éclairage (CIE) has
recommended such tables containing x(λ), y(λ), z(λ)
for λ ∈ [360 nm, 830 nm] in 1 nm steps


3.3.0.1 CIE 1931 Observer (cont.) 42
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 a) on color matching in a 2°
field of 17 observers and b) the relative luminances of the colors of
the spectrum, averaged for about 100 observers


3.4 Tristimulus normalization 43

• 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


4 Objective color terms 44
quantities we can measure

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)

Luminance: The luminous intensity in a given direction per unit projected
area
L v = K m ∫ L e, λ V ( λ ) dλ
λ

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

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


4.1 Y 45

Y stimulus (luminosity in some literature): 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)

Application: conversion of a color image to black and white


4.1.1 Excitation purity 46

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
(In disuse, replaced by chromaticity)
x – xw y – yw
p c = ------------------ or p c = ------------------
xb – xw yb – yw
where w denotes the achromatic stimulus and b the boundary color
stimulus


4.1.2 Chromaticity 47

Chromaticity: Proportions of the amounts of three color-matching stimuli
needed to match a color (see p. 39).
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 ) + 1.13240g ( λ ) + 1.20063b ( λ )
0.17697r ( λ ) + 0.81240g ( λ ) + 0.01063b ( λ )
y ( λ ) = ----------------------------------------------------------------------------------------------------------
-
0.66697r ( λ ) + 1.13240g ( λ ) + 1.20063b ( λ )
0.00000r ( λ ) + 0.01000g ( λ ) + 0.99000b ( λ )
z ( λ ) = ----------------------------------------------------------------------------------------------------------
-
0.66697r ( λ ) + 1.13240g ( λ ) + 1.20063b ( λ )


4.2 Uniformity 48
• The X, Y, Z tristimulus
coordinates allow us to
decide if two colors match in
y
a given context. If there is 520

no match, it does not tell us 0.8
530

540
how large the perceptual 510
550
Stiles Line Element
mismatch is Ellipses plotted 3 x
560
0.6
• Consequently, the CIE 1931 500
570

chromaticity diagram is not 580

a perceptually uniform 0.4
590

600
chromaticity space from 610
620
which the perception of 490 630
700

chromaticity can be derived 0.2
x = X ⁄ (X + Y + Z), 480

y = Y ⁄ (X + Y + Z), 470
x+y+z = 1
0

460 x
45

0 0.2 0.4 0.6


4.2.1 Uniform chromaticity diagram 49
• 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'

0.5

0.4

0.3

0.2

0.1

u'
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8


4.2.2 CIELAB 50
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 the Munsell Value scale

L* = 116 ⋅ 3 Y ⁄ Y n – 16
• Tangential near origin
• Two color opponent channels a*, b*

a* = 500 ⋅ { 3 X ⁄ X n – 3 Y ⁄ Y n }
b* = 200 ⋅ { 3 Y ⁄ Y n – 3 Z ⁄ Z n }
• Xn, Yn, Zn: reference white
• D50: 96.422, 100, 82.521; D65: 95.047, 100, 108.883
• von Kries type adaptation

4.2.3 Color difference formulæ 51
• 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
C* ab = a* + b*
h ab = atan ( b* ⁄ a* )
ΔC* ab 2 ΔH* ab 2
⎛ ----------------⎞ 2 + ⎛ ---------------- ⎞ + ⎛ -----------------⎞
ΔL*
ΔE* 94 = -
⎝k ⋅ S ⎠ ⎝k ⋅ S ⎠ ⎝k ⋅ S ⎠
L L C C H H

SL = 1
S C = 1 + 0.045 ⋅ C* ab
S H = 1 + 0.015 ⋅ C* ab
kL = kC = kH = 1

4.3 Color spaces 52
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


4.3.1 Colorimetric spaces 53
XYZ + basis for all other CIE color spaces
– non-uniform
RGB + can be produced by additive devices
+ linear transformation of XYZ
– non-uniform

R 0.019710 – 0.005494 – 0.002974 X
e.g., 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
CIELAB + most uniform CIE space
+ widely used in the printing industry
– cubic transformation


4.3.1.1 Colorimetric spaces (cont.) 54
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
L*C*hab + has perceptual correlates
+ good for gamut mapping
+ perceptually uniform
– cylindrical
– not uniform for compression


4.3.2 Uniform color spaces 55
• Munsell
• perceptually uniform
• based on atlas

• CIELAB
• colorimetric

• CIELUV
• colorimetric

• OSA
• based on atlas

• Coloroid
• æstetically uniform
• based on atlas


4.3.3 Visually scaled color spaces 56

• Munsell
• based on atlas

• OSA
• based on atlas

• Coloroid
• æstetically uniform
• based on atlas

• NCS
• atlas with uniform coordinates
• not perceptually uniform


4.3.4 Color spaces deﬁned by an atlas 57

• 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


4.4 Uniform discretization errors 58
Cartesian coordinates (e.g.,
CIELAB):

Cylindrical coordinates (e.g., L*C*hab):


5 Color imaging 59
Application
Protocol
Format
Compression
Color image

Requirement for digital color imaging
• The total size of a page should be such it can be transferred quickly
• Therefore, the color space must compress well


5.1 Luma-chroma spaces 60
L fR ( R )
C1 = A ⋅ f ( G )
G
C2 fB ( B )

YIQ YUV YC1C2

NTSC EBU SMPTE CCIR sRGB
XYZ RGB RGB RGB 709

Photo
CIELAB YES YCC


5.2 RGB separations 61

R

G B

• Allow quick display — no processing necessary
• Unsuitable for color image communication — separations not decorrelated


5.3 CIELAB separations 62

L*

a* b*


5.4 Chroma subsampling 63

L*

b* a*


6 Illumination 64
• 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


6.1 Light sources of interest 65

• 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


6.2 CIE standard illuminants 66

• CIE standard illuminant A 300

represents light from a full
(or blackbody) radiator at 250

relative radiant power
2854°K
200 D65
• CIE standard illuminant D65
A
represents a phase of natural
150
daylight with a correlated
color temperature of 6504°K
100
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 50
being dropped because they are seriously deﬁcient
in the UV region (important for ﬂuorescent
materials) wavelength [nm]
0
300 350 400 450 500 550 600 650 700 750 800


6.3 CIE standard sources 67

• Illuminant refers to a specific spectral radiant power distribution
incident to the object viewed by the observer
• 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.communities.hp.com/online/blogs/mostly_color/archive/2007/06/22/
HPPost3682.aspx


7 Measuring color 68

• 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
• see drawing on page 64 (Illumination)
• Because they are a closed system, spectrophotometers are very reliable


7.1 Trusting your instrument 69

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


7.2 Calibration 70
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 ΔE units) from the absolute color of the tile
• important for agreement between laboratories

Relative certiﬁcation: verifies if the measured color of the tile is within
the tolerance (e.g. 0.3 ΔE 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/


7.3 Effect of variability 71

• 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, 100 Barr Harbor Drive, West Conshohoken, PA 19428, 610-832-9585,
http://www.astm.org
• Improve all process aspects to minimize the required number of measurements
• ISO 9001


7.4 Geometries of illumination and 72
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


8 Color reproduction 73
In most cases, color reproduction is simple and inexpensive because
of metamerism
Spectral color reproduction: equality of spectral reflectance or SPD
• rarely needed
• paint samples, metamerism assessment
Colorimetric reproduction: equality of chromaticities and relative
luminances
• useful when viewing conditions are the same and light source is
the same
Exact reproduction: equality of chromaticities, absolute & relative
luminances
• useful when viewing conditions are identical


8.0.1 Reproduction modes (cont.) 74

Equivalent reproduction: same appearance of chromaticities,
absolute & relative luminances
• useful when the luminance level is the same
Corresponding reproduction: same appearance of chromaticities
and relative luminances when the luminance levels are the same
• current focus of research in color reproduction; CIECAM
Preferred reproduction: achieve more pleasing reproduction of
memory colors by departing from equality of appearance


8.1 Additive and substractive color 75
Mixing of colored lights vs. mixing of colorants

• Additive color: start with black and add primaries
• red green blue

• Substractive color: start with white and substract complements
of primaries
• cyan magenta yellow


8.1.1 The additive method 76

• Probable sensitivity absorbance
S-cone
1.0
curves of the human eye
M-cone
and the three best lights 0.8
for additive color L-cone

reproduction 0.6 Rod
• Note the strong overlap
0.4
in the orange-yellow
interval 0.2
• This means that correct
color reproduction 0.0 nm
400 450 500 550 600 650
cannot be achieved with
simple trichromatic methods, because there are always unwanted stimulations
• Hence, the trivial idea of stimulating the cones independently does not work
with a simple approach


8.1.2 The subtractive method 77
• The additive method has two major disadvantages when the set-up is not
light-emissive:
• the required ﬁlters signiﬁcantly reduce the brightness of the image
• the reproduction of a mosaic can be tricky
• It is easier to generate colors from a beam of white light and varying the
proportions of reddish, green, and bluish parts
• On top to the unwanted stimulations, there is a problem with unwanted
absorptions, making the subtractive method even harder to master than the
additive method
1.0

0.8

0.6

0.4 10%
50%
0.2
100%
0.0
400 450 500 550 600 650 700

1.2
1.0
0.8
0.6 10%
0.4 50%
0.2 100%
0.0
400 450 500 550 600 650 700

1.0

0.8

0.6 10%
0.4 50%
100%
0.2

0.0
400 450 500 550 600 650 700


8.1.3 Dithering 78
• Color is a usually represented with at least 8 bits per channel,
for 256 levels
• Some devices can display less levels
• mobile LCD displays often have only 6 bits per channel
• most printers have only 1 bit per channel

• Displays: temporal dithering
• Printers: spatial dithering, a.k.a. halftoning


8.2 Scan — think — print 79

• Because of the unwanted stimulations and absorptions, it is
practically impossible to engineer a color reproduction system
based on light and lenses producing satisfactory image quality
• Because of the large amount of data and lengthy computations,
digital systems are possible only slowly
• Initially, closed proprietary solutions
• Later, open solutions based on standards and a color
management system
• SWOP inks
• ICC proﬁles


8.2.1 Managed color reproduction 80

sRGB
profile maker

spectro- business
negative
YCC
photometer TIJ printer
PhotoCD CMYK
scanner
graphic arts
CIELAB
TIJ printer
RGB
ICC profile
RGB
graphic arts workstation
scanner and archive digital
positive
proof printer
AdobeRGB RGB
CMYK

Inte
ICC profile
digital

rne
camera display and platemaker or

t
softcopy direct press
CIELAB+sRGB any
ICC profile color rendering dictionary

repository raster image
(database) processor


9 Milestones in color printing 81
30,000 BCE: hand is commonly used as a stencil by holding it against
a cave wall and blowing powder on it
1457: Fust and Schöffer use colored metal plates
to print the Psalterium with colored initial
letters. They had to discover and solve the
problems of color trapping and registration
Breakthrough: mass-production of illuminated
books
1580–1644: during the Ming dynasty, techniques are perfected for
the mass-production of multicolored book illustrations
~1700: invention of the katagami stencil. The stencil’s loose
elements are connected with silk wires fine enough that ink
can flow around them, enabling the mass-production of fine
illustrations. Ukiyo-e — pictures of the floating world


9.0.1 Color printing milestones (cont.) 82
1719: Le Blon receives British patent 423 for inventing the
trichromatic printing principle. Yellow, red, blue plus black for
better gray balance and clean blacks
1797: Senefelder invents lithography, enabling the inclusion of a
large number of illustrations in very long run books like the
Encyclopédie
1816: Engelmann invents chromolithography; 6 to 19 partial colors,
sometimes even 24 and 30
1816: Young invents color filters, which will allow to separate color
images
1852: Fox Talbot invents concept of halftone screening
1879: Swan invents line screen
1888: Meisenbach invents crossline screen

9.0.2 Color printing milestones (cont.) 83
1910: invention of the panchromatic film emulsion, allowing the
use of Maxwell’s filters
From here on all effort goes into color correction (masking)
1937: Neugebauer proposes an eight-color analytical method based
on colorimetry
1948: Hardy and Wurzburg invent the scanner — electronic circuitry
is used to determine the color correction in one single step.
The 1941 Murray and Morse scanner just tried to simulate masking
Hardy and Wurzburg’s solved the Neugebauer equations

1957: Patent 2,790,844 — early effort towards gamut mapping
1977: Ichiro Endo receives U.S. patent 4,723,129 for thermal ink jet
technology
1987: Canon launches CLC-1 color copier

10 Color image communication 84
Application
Protocol
Format
Compression
Color image


10.1 Lossless coding 85
• Huffman coding
• Arithmetic coding
• LZ coding
• LZW coding (USP 4,558,302)
• Flate and deﬂate (IETF RFC 1951)
• Binary image compression
• Group 3 1-d (MH) and 2-d (MR)
• ITU-T Rec. T.4
• Group 4 (MMR)
• ITU-T Rec. T.6
• JBIG — progressive bi-level image compression
• ISO 11544 / ITU-T Rec. T.82
• ITU-T Rec. T.85 — application proﬁle for fax
• ITU-T Rec. T.43 — bit-plane coding for color fax images using JBIG
• JBIG2 — lossy/lossless coding for bi-level images
• ISO 14492 / ITU-T Rec. T.88
• text halftone, and generic modes
• lossless JPEG
• lossless JPEG 2000


10.2 Palette color 86
Counting colors

• 24-bit pixels can represent 16 million colors

• Humans can distinguish 10 million colors

• A 2×3K image contains
6 million pixels

• A 512×512 image contains
250 thousand pixels

• A “typical” 5122 image has
26 thousand colors

• One byte can represent 256 colors


10.2.1 Color palettes (mapped color) 87
• Represent original colors by indices into a map with reduced set
of colors (paint by numbers)
• choose N colors (palette)
• image dependent (adaptive) or image independent (ﬁxed)
• e.g., median cut
• quantize (map) original to palette colors
• use look-up table to map index to palette color
• may use dither in palettized image

quantize
original index
Q


10.3 JPEG 88
• No color space speciﬁcation
• Baseline JPEG: 4 or less color components
• Colorimetric color representation is possible
• Full JPEG: 256 or less color components
• Discrete spectral color representation is possible
• Compression can be improved with chroma subsampling

JPEG 2000

• Wavelet-based follow-on to JPEG
• same committee, different contributors
• Single compression architecture
• continuous-tone and binary compression
• lossy, lossless, and lossy-to-lossless coding
• progressive rendering
• 1–256 color (spectral) components


10.4 Mixed Raster Content — background 89
T.6 T.4
black-and-white black-and-white
MMR text and line text and line MH
diagrams diagrams

T.85 in1
out
in1
out
in2 in2
JBIG
black-and-white
text, halftones,
stipples, line art, PSTN
and so on

Multiple, independent
compression methods—
T.42 T.43 each optimized for one
JPEG JBIG kind of image content
CIELAB CIELAB


10.4.1 Mixed Raster Content — solution 90
black-and-white
T.44
text & digrams
as before, Mixed
colored Raster
text Content
too

interchange
black-and-white
text and line
diagrams
black-and-white
text, halftones,
stipples, line art,
color text and
in1 and so graphics
on
in2 out

MRC is a method for using
multiple compression methods
in raster documents that contain
multiple kinds of content


10.4.2 Mixed Raster Content — overview 91

• MRC = Mixed Raster Content
• multi-layer model for representing compound images
• described in ITU-T Recommendation T.44
• originally proposed in joint Xerox/HP contribution
• efﬁcient processing, interchange and archiving of raster-oriented pages
with a mixture of multilevel and bilevel images

• Technical approach
• segmentation of an image into multiple layers (planes), by image content
• use spatial resolution, color representation and compression method
matched to the content of each layer

• Compound image architecture
• framework for using compression methods

• Performance
• can achieve compression ratios of several 100 to 1 on typical documents


10.4.3 Mixed Raster Content — model 92
Image

3-layer model
black-and-white
text & digrams
colored text • Foreground
• multilevel, e.g., text color
bla • JBIG @ 12 bpp, 100 dpi
ck
red
• Mask
• bilevel, e.g., text shape
bla
tex ck-a
• MMR @ 1 bpp, 400 dpi
t n
co & dig d-wh
lor i
ed rams te
tex
• Background
t • multilevel, e.g., contone im.
• JPEG @ 24 bpp, 200 dpi

Image = M • FG + M’ • BG


10.4.4 Internet fax 93
What is it?

• Store-and-forward Internet fax
• scanned document transmission using e-mail attachments
• ITU-T standards and IETF protocols
• uses ESMTP with delivery confirmation and capabilities exchange

• ITU-T Recommendation T.37 — approved September 1999
• references IETF standards
• requires use of TIFF-FX
• Simple Mode — TIFF-FX Profile S: April 1999
• minimal b&w with no delivery confirmation or capability exchange
• Full Mode — TIFF-FX all profiles: September 1999
• range of b&w and color with delivery confirmation and capability
exchange


10.4.4.1 Internet fax — conﬁgurations 94

Internet
all-in-one

workstation

PSTN

on/off ramp fax


10.4.5 IPP — Internet Printing Protocol 95
What is it?

• Firewall problem
• IETF standard developed with help from the Printer Working
Group
• Client-server protocol for distributed printing on the Internet
• intended to replace LPR/LPD

• Uses HTTP 1.1 POST application protocol
• Internet media type: application/ipp


10.4.5.1 IPP — Internet Printing Protocol 96
Sample conﬁgurations

Client to printer

IPP

client IPP object

Client to server

IPP

client IPP object


10.5 Document ecosystems 97
Seamless ofﬁce imaging

• Scanners, copiers, connected to Ethernet instead of computer
• Documents distributed via e-mail, fax servers, remote printers,
or ISV applications

HP 9100C Imaging
Service Application
write read
TCP/IP

image +
metadata

NOTIFY.DAT

HP 9100C Windows Shared Application
Digital Sender Server Disk Server

11 Color appearance modeling 98

• Recommended model: CIECAM02
• Do not use an appearance model when
• stimulus speciﬁcation is simple (CIELAB, sRGB, …)
• simple color tolerances (CIE94)
• only one viewing condition
• it is not clear it will help

• What they allow you to do
• map from measurements to color names
• predict color matches across viewing conditions
• render color across media
• gain a deeper understanding of color
• no metric for color differences


11.1 Cognitive context 99

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


11.2 CIECAM02 100
• Conditions modeled
• adaptation
• discounting the illuminant
• surround effects

• Predictions missing from the model
• rod contributions
• color difference metric
• constant hue lines
• Helson-Judd effect
• Helmholtz-Kohlrausch effect

• Graphical representation
• CIECAM02 is represented in cylindrical coordinates
• lightness J
• chroma C
• hue h
• trigonometric transformation necessary for plots

• Includes the 5 years of revisions since CIECAM97s


11.3 The color selection problem 101

Surround
10º
Background
Color
considered

2º

Adapting
field Proximal field

• This user interface problem cannot be solved without color appearance model
• Currently users converge towards their intended rendering by trial and error


11.4 The gamut mapping problem 102
b*
Printer

a*

Measure original Monitor

Compute appearance

CG Image
Gamut compression

Modify appearance (L*C*hab)

Compute colorant quantities


Understanding Color

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