Theory and principle of colour management application and communication.pptx

The light reaching the eye
called the colour stimulus.
It is characterized by the
spectral function which
describes in physical terms
its composition of radiation
of different wavelengths.

Long before colour vision
has been understood, painters
were able to prepare and to
mix colours to achieve the
desired effects, and to create
magnificent representations !
• For the development of colour photography, colour TV,
three- and four-colour printing, however, colour science
has been essential.
• Colours had to be measured in order to be reproduced.
• Development of measuring methods and apparatus was
paralleled by the investigation of the visual system.
André Derain’s Charing Cross
Bridge, London, (1906)

Colour is a Perception !
Colour is carried by light, electromagnetic waves, but the
sensation of colour is subjected to many other influences.

How do we see colours ?
 The chromatic stimulus is
electromagnetic radiation from
sources and objects that hits
the optic system and triggers
the visual process.
 Perceived colour is a sensation
produced by the chromatic
stimulus that makes it possible
to differentiate that stimulus
from others with the same
area, duration, shape and
texture.

Colour is response to the wavelengths !
Retina
 3 kinds of cone cells
roughly correspond to
the colours red, green
and blue wavelengths.
 Each cone send a distinct
signal to brain.

What, if yellow is shinning on eye
Eye don’t have a cone to detect yellow specifically
but red and green cones activated to a certain
levels and both send signals to brain saying yellow.
Additive mixing of three
primary colours

The Colour Wheel
If the ends of the spectrum are bent around a colour
wheel is formed:

Colour Schemes
Systematic ways of selecting
colours Harmony of colour
• Monochromatic
• Complimentary
• Analogous
• Warm
• Cool
• Achromatic
• Chromatic
Grays

Colour Schemes: Monochromatic
Monochromatic: One
Hue many values

Colour Schemes: Complementary
Complimentary: Colours
that are opposite on the
wheel. High Contrast
Artist: Paul Cezanne
Title: La Montage Saint Victoire
Year: 1886-88

Colour Schemes: Analogous
Analogous: A selection of
colours that are adjacent.
Minimal contrast
Artist: Vincent van Gogh
Title: The Iris
Year: 1889

Colour Schemes: Warm
Warm: First half of the
wheel give warmer colours.
The colours of fire.
Artist: Jan Vermeer
Title: Girl Asleep at a Table
Year: 1657

Colour Schemes: Cool
Artist: Vincent van Gogh
Title: The Starry Night
Year: 1989
Cool: Second half of the
wheel gives cooler colours

Colour Schemes: Achromatic,
Chromatic Grays
Chromatic Grays: Also
called neutral relief. Dull
colours, low contrast.
Achromatic: Black and
white with all the grays
in-between.

Relation between Colour and
Chemical constitution
Electro magnetic radiation
Light is electromagnetic radiation (that is, it has both
electrical and magnetic components) vibrating in transverse
wave packets (quanta, photons).
Color, Chromophore andAuxochromes
Molecules get coloured because they are selectively able to
absorb and reflect incident light Dyes have radicals called
chromophore and auxochrome that produces colours

Chromophores
O.N. Witt observed in 1876 that coloured compounds contain certain
unsaturated groups which he called chromophores and compound
containing a chromophoreis called a chromogen. When certain groups
called auxochrome are present in the chromogen, a dye is obtained.
• Chromophores are unsaturated organic radicals
• Their specific state of unsaturation enables them to absorb and
reflect incident electromagnetic radiation within visible light
• It is the loosely held electrons in the unsaturated bonds that cause
absorption of certain incident light wave

Auxochromes
Auxochrome may be either acidic or basic like ‐OH or
‐NH2. Other auxochromes include ‐COOH, ‐SO3H, ‐NR2
these groups form salts with either acids or alkalies. they
also form hydrogen bonds with certain groups (‐OH of
cellulose or NH2 of wool, silk).
• Auxochromes presence
influence the orbits of the
loosely held electrons of
the unsaturated bonds.
• This causes these electrons
to absorb and reflect
incident light of specific
wavelengths only.

Various causes of colour generation
Fifteen causes and five mechanisms

COLOUR ORDER SYSTEM
A logical scheme for ordering and specifying colours
• A method of denoting the locations
in that arrangement. (named in some
descriptive terms and/or numbered)
• Systematic and rational method of arranging all possible
colours (using material samples) on the basis of some
clearly defined attributes
This allows the communication
of colour precepts over distance
and through time, even where
physical specimens do not exist
or have changed in colour with
age.

Suppose a person with
normal colour vision and no
experience of dealing with
colours is idling on a desert
island, surrounded by a large
number of pebbles of similar
texture but having a wide
variety of colours. Suppose
he wanted to organise these
pebbles in some orderly way,
according to their colour.
The Desert Island Experiment
(Judd, 1975)

Definitions
 Hue: Attribute of visual perception according to which an
area appears to be similar to one of the colours, red, yellow,
green and blue, or to a combination of adjacent pairs of
these colours considered in a closed ring (CIE 17.4).
 Lightness: Attribute by which a perceived colour is judged
to be equivalent to one of a series of greys ranging from
black to white (ASTM E 284).
 Chroma: Attribute of colour used to indicate the degree of
departure of the colour from a grey of the same lightness
(ASTM E 284).

Chroma
Lightness
Industry Terminology
Textile dyers use the terms “brighter”, “duller”, “weaker”
and “stronger” to represent specific changes in lightness
and chroma. Changes in dye concentration relate to
stronger or weaker colours, and one may need to change
the choice of dyestuff to increase a colour’s “brightness”.

Colour Space
Three dimensional colour space.
 Firstly, we need a coordinate system to specify
which colour lies at which point in the colour space.
 Secondly, we need a notation system to describe
colours with reference to other colours within the
colour space.

Popular Colour Notation Systems
1. Munsell – Hue, Value and Chroma
2. Natural Colour System – Hue, Blackness and
Chromaticness
3. Ostwald system – Hue, Lightness and Saturation
4. DIN system – Hue, Saturation degree and Darkness degree
5. OSA-UCS - no separate scaling of three attributes
6. Coloroid System – Hue, Saturation and Lightness

The Munsell Colour Notation System
In 1905 Albert Munsell invented a complete colour
description system.
This system consists of:-
 A set of master physical samples whose colours are
the basic reference colours. These are carefully
spaced out as to cover colourspace evenly and as
completely as possible.
 A colour notation by which each colour can be
described and located.
 Commercially available colour atlases, which
contain carefully made copies of the original
master reference colours.

Munsell Three Attributes of Colour
A. Hue
B. Value
C. Chroma
Coordinate system to specify which colour

Primary Hues: Spectral colours
Hue is that attribute of a colour by which we distinguish
redfrom green, bluefrom yellow, and so on. There is a
natural order of hues: red, yellow, green, blue, purple.
One can mix paints of adjacent colours in this series to
obtain a continuous variation from one colour to the other.

For example, red and yellow may be mixed in any
proportion to obtain all the hues from red through orange
to yellow. The same may be said of yellow and green,
green and blue, blue and purple, and purple and red.

Value indicates the lightness
of a colour. The scale of
value ranges from 0 for pure
black to 10 for pure white.
Black, white and the grays
between them are called
"neutral colours." They have
no hue. Colours that have a
hue are called "chromatic
colours." The value scale
applies to chromatic as well
as neutral colour.
Achromatic Chromatic

Weak
Strong
• Colours of low chroma are sometimes called
"weak," while those of high chroma are said
to be "highly saturated," "strong" or "vivid”.
• Chroma is the degree of departure of a colour
from the neutral colour of the same value.
• Chroma is generally on a variable length
scale of equal perceptual steps ranging from
zero to 20.
If you started with gray and gradually added
increasing proportions of purple until the
original vivid purple colour was obtained,
you would develop a series of gradually
changing colours that increase in chroma, as
shown in Figure.

Munsell Colour Ordering
Munsell established numerical scales with visually
uniform steps for each of three attributes, i.e. Hue,
Value and Chroma.
In Munsell notation, each colour has a logical
relationship to all other colours. This opens up endless
creative possibilities in colour choices, as well as the
ability to communicate those colour choices precisely.
Munsell called red, yellow, green, blue and purple
"principal hues" and placed them at equal intervals
around this circle. He inserted five intermediate hues:
yellow-red, green-yellow, blue-green, purple-blue and
red-purple, making ten hues in all.

Munsell divided the hue circle into 100 steps of equal
visual change in hue and identified 10 hue sectors. For
simplicity, he used the initials as symbols to designate the
ten hue sectors: R, YR, Y, GY, G, BG, B, PB, P and RP.
Example: Middle of the
red sector is called "five
red," and is written "5R."
(The zero step is not used)

Munsell Notation
The complete Munsell notation for a chromatic colour is
written symbolically: HV/C. For a vivid red having a hue
of 5R, a value of 6 and a chroma of 14, the complete
notation is 5R 6/14. When a finer division is needed for
any of the attributes, decimals are used. For example, 5.3R
6.1/14.4.
The notation for a neutral colour is written: NV/. The
chroma of a neutral colour is zero, but it is customary to
omit the zero in the notation. The notation N 1/ denotes a
black, a very dark neutral, while N 9/ denotes a white, a
very light neutral. This notation for a middle gray is N 5/.

Example
A paint panel of colour represented by 10Y 6/6 changes on
weathering to 7.5Y 8/4. Describe:
• The original colour of the panel.
• The nature of change on weathering.
Answer
• With a hue coordinate of 10Y, the panel is very much
greener than ‘pure’ yellow and will be yellow green. It is
fairly light, with a value of 6 but only ‘moderate’ chroma.
• On weathering, the panel moves away from the green
towards the pure yellow. It also becomes lighter, but loses
chroma. Thus it becomes yellower, lighter, and paler.

Pantone Matching System (PMS)
• A color standardization system that helps in color identification
and matching.
• The Pantone color numbers consist of a three- or four-digit
number followed by the letter C, U or M, which stands for
"coated," "uncoated" and "matte," respectively.
• The color palette in
the PMS consists of
about 1,114 colors.
• Very helpful in
avoiding color
inconsistencies
between the various
types of print and
digital media.

1) The system is rigid, so it is very difficult to specify
colours lying between those that are shown in the
swatch books.
2) It is arbitrary in its description and numbering.
3) It is not organized around any apparent scientific or
psychophysical basis.
4) It includes many colours that cannot be achieved
accurately in ordinary process inks.
Despite these problems, and because of its universal
availability, the new generation of designers, artists,
electronic publishers, printers, suppliers and editors take
for granted that Pantone is the standard.
However, the Pantone Matching System has
Several basic problems:

Natural Colour System (NCS)
Invented by German psychologist Ewald Herring in 1875.
Herring proposed that, despite the trichromatic nature of
vision, there are four unique hues: red, yellow, green and
blue, as illustrated below:
Any achromatic colour can
therefore be represented as a
combination of two (or less)
of these hues. Hues such as
red and green or yellow and
blue cannot be perceived
together in the same colour
and are known as opponent.

The Natural Colour System
The NCS system is based on single hue triangles with
white, black and a pure colour at the corners.
NCS describes colours in terms of their
redness(r), yellowness(y), greenness(g),
blueness(b), whiteness(w) and
blackness(s) using a percentage scale.
Blackness and whiteness describe the
resemblance of a stimulus to a perfect
black or white respectively.
Another scale, chromaticnessis simply
the sum r + y + g + b and describes the
resemblance of a test colour to a colour
of the same hue having the maximum
possible chromatic content.

Advantages of colour order systems
 They are easy to understand because they usually have
actual samples that can be seen.
 They are easy to use. In most circumstances side by
side comparisons are made without the need for
instrumentation.
 The number and spacing of the samples can be adapted
for different applications, and different arrangements of
the samples can be used for different purposes.

Disadvantages of colour-order systems
 There are many different colour-order systems in use and
there is no simple means of transferring the results from
one system into another.
 There are gaps between the samples which means
interpolation often needs to be used.
 The visual spacing of the samples is valid only if standard
illuminating and viewing conditions are maintained.
 Different observers may make slightly different matches
on the same colour (observer metamerism).

Additive Color Mixing
• The mixing of “light”
• Primary: Red, Green, Blue
• “White” means…
COLOR MIXING
Subtractive Color Mixing
• The mixing of “pigment”
• Primary: Cyan, Magenta, Yellow
• Why black?

Subtractive Color Mixing
• Why?
 Pigments absorb light
• Thinking:
 the Color Filters
Each filter (or pigment)
absorbs its complementary
color and transmits (diffusely
reflects) the others
• Question:
 Yellow + Cyan=?

Combining two of subtractive primaries filters
obtains an additive primary color !

Absorption, transmission, reflection and scattering
Absorption, transmission and reflection
Interaction of Radiation with Matter

Specular reflection on a
polished, reflective surface
Diffuse reflection
(scattering) on a
rough, corroded
metal plate

• Absorption refers to the taking up of radiant energy by an
irradiated object!
• Transmission refers to the penetration of an object with
radiation!
• Reflection refers to the throwing back of radiation by a
“mirroring” object!
• A reflection is called “specular” (mirror-like) when the
incident light rays of a light beam are reflected in a
common direction! (The law of reflection)
• A reflection is called
diffused or scattered if
the incident light rays
of a light beam are
reflected in different
directions!

The Beer-Lambert law
• Dyes inside fibres usually behave as they are dissolved in the fibre and their
absorption behavior is similar to that of solutions.
• The absorption of light in dyed fibres is governed by two laws.
• The first is Lambert's law (also known as Bouguer's law) which states that
layers of equal thickness of the same substance transmit the same fraction of
incident light, at any given wavelength.
• The second is Beer’s Law which states that the absorption of light is
proportional to the number of absorbing molecules in its path (i.e. the
concentration of the absorbing solution).
• These laws can be combined to form the Beer-Lambert law, which can be
expressed mathematically thus: I = I0 10-εcl where I is the intensity of the
transmitted radiation, I0 is the intensity of the incident radiation, ε is the molar
extinction coefficient (l mol-1 cm -1), c is the concentration of the absorbing
substance (mol l-1) and l is the path length through which the radiation passes
(cm).
• When the percentage of incident light transmitted (T) is measured, the above
expression can be written: A = log (100/T) = εcl where A is the absorbance.
• Deviations from the Beer-Lambert law can occur if the dye is aggregated,
rather than dissolved as monomolecular species within a fibre.

The Kubelka-Munk function
The Kubelka Munk equation gives the relationship
between absorption, scattering and reflectance of a
sample at a particular wavelength as follows:
where K is the absorption coefficient, S is the scattering
coefficient, R∞ is the reflectance of the surface having
such a thickness that there is no further change in the
reflectance by increasing the thickness.
𝑲
𝑺 =
𝟏 − 𝑹∞
𝟐
𝟐𝑹∞
𝑹∞ = 𝑲/𝑺 + 𝟏 − 𝑲 ∕ 𝑺 + 𝟏 𝟐 − 𝟏
and

Light Source Versus Illuminant
 The terms light source and illuminant have precise and
different meanings.
 A light source is a physical emitter of radiation such as a
candle, a tungsten bulb, and natural daylight.
 An illuminant is the specification for a potential light
source.
 All light sources can be specified as an illuminant, but not
all illuminants can be physically realized as a light source.

Color Temperature
The color temperature of a
light source is the temperature
of an ideal black-body
radiator that radiates light of a
color comparable to that of
the light source.
The color temperature chart
illustrates the range of colors
generated by both artificial
and natural sunlight lighting.

Standard Illuminants
Illuminants are tables of spectral energy distributions
intended to represent real light source

Colour Rendering
Index
A color rendering index
(CRI) is a quantitative
measure of the ability of a
light source to reveal the
colors of various objects
faithfully in comparison
with an ideal or natural light
source. Light sources with a
high CRI are desirable in
color-critical applications
such as neonatal care and art
restoration.

 The color rendering index (CRI) is measured as a number
between 0 and 100. At zero (0), all colors look the same. A CRI
of 100 shows the true colors of the object. Incandescent and
halogen light sources have a CRI of 100.
 CRI is independent of color temperature. These are two different
things. For example, a 5000K (daylight color temperature)
fluorescent light source could have a CRI of 75, but another
5000K fluorescent light source can have a CRI of 90.
 Bellow chart is a good depiction of differing CRIs, with each
image having the same warm color temperature (2700K).

Commission Internationale de l'Eclairage (CIE)
It is an organization devoted to international cooperation
and exchange of information among its member countries
on all matters relating to the science and art of lighting
MATHEMATICALLY DEFINED
COLOR SPACE
INTERNATIONAL COMMISSION ON ILLUMINATION

 Primary Colours
 Source
 Observer
Standardization

 The trichromatic theory was postulated by Young and later
by Helmholtz and was based upon colour matching
experiments carried out by Maxwell.
 Maxwell's experiments demonstrated that most colours can
be matched by superimposing three separate light sources
known as primaries; a process known as additive mixing.
 The Young-Helmholtz theory of colour vision was built
around the assumption of there being three classes of
receptors although direct proof for this was not obtained
until 1964 when micro spectrophotopic recordings of
single cone cells were obtained. The roots of trichromacy
are firmly understood to be in the receptoral stage of
colour vision.
Trichromatic Theory

The match can be written C
≡ aR + bG + cB, where C is
the colour to be matched,
R, G, B are the chosen
primaries and a, b, c, record
the amount of each primary
Maxwell triangle (1850)

Maxwell triangle (1850)
Negative value !

Spectrum locus of spectral colours
Spectrum
Locus

The mathematics of 'colour space'
is used to generate 3 primaries that
don't correspond to actual colours
but allow all real colours to be
expressed as positive mixtures of
them. In the CIE system all real
colours have positive coordinates.
The 'colour triangle' now becomes
a distorted shape with rounded
sides of the CIE chromaticity
diagram but the concept behind it
is just the one Maxwell laid down
in the late 1850s.
CIE primaries – X, Y, Z

The C.I.E Primaries
This new set of primaries, called X, Y, and Z, have the
following properties:
 They always produce positive tristmulus value.
 It is possible to represent any colour in terms of these
primaries.
 They were derived so that equal values of X, Y, and Z
produce white.
 They were arranged so that a single parameter Y
determines the luminance of the colour.
 They are related to the sensitivity of the human eye by
the use of colour matching functions which match to
the C.I.E. 1931 Standard Observer.

Chromaticity Coordinates
In terms of the
tristimulus values
X, Y and Z:
x = X / (X + Y + Z)
y = Y / (X + Y + Z)
z = Z / (X + Y + Z)
x + y + z = 1

The need for a uniform colour space led to a number of
non- linear transformations of the CIE 1931 XYZspace
and finally resulted in the specification of one of these
transformations as the CIE 1976 (L* a* b*) colour space.
There are perhaps two problems with the specification of
colours in terms of tristimulus values and chromaticity
space. Firstly, this specification is not easily interpreted in
terms of the psychophysical dimensions of colour
perception namely, hue, value and chroma.
Secondly, the XYZ system and the associated chromaticity
diagrams are not perceptually uniform. The second of
these points is a problem if we wish to estimate the
magnitude of the difference between two colour stimuli.

The opponent-colours theory of colour vision, proposed
by Hering, seemingly contradicts the Young-Helmholtz
trichromatic theory. It was advanced to explain various
phenomena that could not be adequately accounted for by
trichromacy. Examples of such phenomena are the after-
image effect (if the eye is adapted to a yellow stimulus the
removal of the stimulus leaves a blue sensation or after-
effect) and the non-intuitive fact that an additive mixture of
red and green light gives yellow and not a reddish-green.
Hering proposed that yellow-blue and red-green represent
opponent signals; this also went some way towards
explaining why there were four psychophysical colour
primaries red, green, yellow, and blue and not just three.
Hering also proposed a white-black opponency.

CIELAB allows the sepcification of colour perceptions in terms of a
three-dimensional space. The L*-axis is known as the lightness and
extends from 0 (black) to 100 (white). The other two coordinates a* and
b* represent redness-greeness and yellowness-blueness respectively.
Samples for which a* = b* = 0 are achromatic and thus the L*-axis
represents the achromatic scale of greys from black to white.
CIE 1976 (L* a* b*) colour space or CIELAB

𝐂𝐡𝐫𝐨𝐦𝐚 𝐂∗
= 𝐚∗ 𝟐 + 𝐛∗ 𝟐
𝐇𝐮𝐞 𝐚𝐧𝐠𝐥𝐞 𝐡 = 𝐭𝐚𝐧−𝟏
𝐛∗
𝐚∗
The L*c*h colour space uses the same
diagram as the L*a*b* color space, but uses
cylindrical coordinates instead of
rectangular coordinates. In this color space,
L*indicates lightness and is the same as the
L* of the L*a*b* color space, C* is chroma,
and h is the hue angle. The value of chroma
C* is 0 at the center and increases according
to the distance from the center. Hue angle h
is defined as starting at the +a* axis and is
expressed in degrees: 0 would be +a* (red),
90 would be +b* (yellow), 180 would be -
a* (green), and 270 would be -b* (blue). If
we measure the apple using the L*C*h color
space, we get the results shown below. If we
plot these values on Figure 1, we obtain
point (A).

L* a* b* c* h0 Colour
A1 56.70 37.10 46.90
A2 57.25 36.50 47.40
B1 61.70 -37.23 -20.15
B2 61.10 -38.40 -21.95
Calculate Chroma, Hue angle
and describe the Colour

COLOR DIFFERENCE
CIELAB
Colour Space Diagram

1
2
3
4
Give these colours approximate
L* a* b* C* and h0 values

Give these colours approximate
L* a* b* C* and h0 values
1
2
3
4

Colour Difference
One measure of the difference in colour between two
stimuli is the Euclidean distance ΔE between the two
points in the three-dimensional space.
ΔE = { (ΔX)2 + (ΔY)2 + (ΔZ)2 }1/2
The term ΔE is derived from the German word for
sensation Empfindung. ΔE therefore literally means
difference in sensation.

MacAdam ellipses plotted on a CIE 1931 chromaticity diagram;
the axes oftted ellipses are ten times their actual lengths

CIELAB Space colour Differences
in L* a* b*
Standard (S0) Sample (E1)
𝐿0
∗
= 52,15
𝑎0
∗
= +51,72
𝑏0
∗
= +19,29
𝐿1
∗
= 55,55
𝑎1
∗
= +54,32
𝑏1
∗
= +21,09
𝛥𝐿∗ = +3,40
𝛥𝑎∗ = +2,60
𝛥𝑏∗
= +1,80
𝛥𝐸∗ = 𝛥𝐿∗2 + 𝛥𝑎∗2 + 𝛥𝑏∗2 = 3,42 + 2,62 + 1,82 = 4,64

Differences in Rectangular
Co-ordinates L* a* b*
Standard (S0)
Sample (E1)

CIELAB Space Colour Differences
in L* C* h*
Standard (S0) Sample (E)
𝐿0
∗
= 52,15
𝐶0
∗
= 55,20
ℎ0 = 20,45ᵒ
𝐿1
∗
= 55,55
𝐶1
∗
= 58,26
ℎ1ᵒ = 21,22ᵒ
𝛥𝐿∗
= +3,40
𝛥𝐶∗ = +3,40
𝛥𝐻∗= 0,78
Δh= 0,77ᵒ
𝛥𝐸∗
= 𝛥𝐿∗2 + 𝛥𝐶∗2 + 𝛥𝐻∗2 = 3,402 + 3,062 + 0,782 = 4,64
∆H* = 2(C0* C1*)1/2 sin [(h1 – h0)/2]
∆H* = (∆E*2 - ∆L*2 - ∆C*2)1/2

Towards Single Number Shade Passing
Depending on the position of the standard in colour
space the Lightness, Chroma and Hue tolerances limits
could be different.
Tolerance ellipsoid may be created, where the semi-axes
Lt units for Lightness, Ct units for Chroma and Ht units
for Hue may be assessed and used.

JPC79 Equation
It was found that the Chroma tolerance increased rapidly as
the Chroma of standard increased; the Hue tolerance also
increase in a similar fashion to Chroma tolerance, but Hue
tolerance (Ht) was about half the Chroma tolerance (Ct).
The lightness tolerance (Lt) increased only as the Lightness
of the standard increased.
𝜟𝑬 =
𝜟𝑳
𝑳𝒕
𝟐
+
𝜟𝑪
𝑪𝒕
𝟐
+
𝜟𝑯
𝑯𝒕
𝟐
𝟏
𝟐

JPC79 Equation
ΔE = [(ΔL/Lt)2 + (ΔC/Ct)2 + (ΔH/Ht)2]1/2
Where Lt = 0.08195 L1 / (1+0.01765 L1)
Ct = 0.0638 C1 / (1+0.0131C1) + 0.638
Ht = TCt
T = 1 if C1 <0.638, Otherwise
T = 0.36 + │ 0.4 cos (θ1 + 35) │
Unless θ1 is between 1640 and 3450 when
T = 0.56 + │0.2 cos (θ1 + 168)│
L1, C1 and θ1 refer to standard

CMC
𝜟𝑬∗ =
𝜟𝑳∗
𝑰𝑺𝑳
𝟐
+
𝜟𝑪∗
𝒄𝑺𝑪
𝟐
+
𝜟𝑯∗
𝑺𝑯
𝟐
I and c are acceptability / perceptibility terms
I=1, C=1; perceptibility
I-2, C=1; acceptability
SL = 0.040975L / (1 + 0.01765L)
unless L < 16 when SL= 0.511
SC = 0.0638C / (1 + 0.0131C) + 0.638
SH = Sc (Tf +1- f) where f = [C4/(C4 + 1900)]1/2
and T = 0.36 +│0.4 cos (H + 35)│
or T = 0.56 +│0.2 cos (H + 168)│ if (H>164 and H <345)

CMC tolerances = ellipsoid
𝑺𝑳 = lightness semi-axis
𝑺𝑪 = Saturation semi-axis
𝑺𝑯 = Hue semi-axis
I and C = Acceptability
and perceptibility factors
DECMC=
𝑫𝑳∗
𝑰𝑺𝑳
𝟐
+
𝑫𝑪∗
𝒄𝑺𝑪
𝟐
+
𝑫𝑯∗
𝑺𝑯
𝟐 𝟏/𝟐
CMC Acceptability Formula

References
1. R. McDonald, Colour Physics for Industry, Society of Dyers and Colourists, Bradford,
UK , 1997
2. A.K. Roy Choudhury, " Modern Concept of Color and Appearance" published jointly by
Science Publishers, Inc., Enfield, NH 03748, USA, and Oxford & IBH Publishing Co.
Pvt. Ltd.New Delhi, 2000.
3. M L Gulrajani, Colour Measurement: Principles, advances and industrial applications.
Edited by Woodhead Publishing Series in Textiles No. 103, ISBN 1 84569 559 3, 2010.
4. A.K. Roy Choudhury, Principles of colour and appearance measurement, Volume1.
Object Appearance, Colour Perception and Instrumental Measurement (Woodhead, UK).
Released on 27 Jan 2014.
5. A.K. Roy Choudhury, Principles of colour and appearance measurement ,Volume 2:
Visual Measurement of Colour, Colour Comparison and Management, released on 13
Oct., 2014.
6. Committee on Colorimetry of the Optical Society of America, The science of color,
Thomas Y. Cromwell, New York, 1953.
7. K McLaren, The Colour Science of Dyes and Pigments, Adam-Hilger, Bristol (U.K.),
1983.
8. Kurt Nassau, The Physics and Chemistry of Colour, Wiley-Interscience, New York, 1983.
9. H. S. Shah and R. S. Gandhi, Instrumental colour measurements and computer aided
colour matching for textiles, Mahajan, India, 1990.
10. R W G Hunt, Measuring Colour, Ellis Horwood, Chichester (U.K.), 1987.

References
11. D. B. Judd and G. Wyszecki,Color in business, science and industry, 2nd.Ed., John
Wiley & sons, New York, 1963.
12. M. R. Pointer and G. G. Attridge. The number of discernible colours. Color Research
and Application, 23:52–54, 1998. See also page 337 of the same volume.
13. Colorimetry, volume 15.2 of CIE Publications. Central Bureau of the CIE, Vienna,
Austria, 2 edition, 1986.
14. G unter Wyszecki and W. S. Stiles. Color Science: Concepts and Methods, Quantitative
Data and Formulae. John Wiley & Sons, New York, 2 edition, 1982.
15. Kurt Nassau. The Physics and Chemistry of Color. The Fifteen Causes of Color. John
Wiley & sons, 1983.
16. Henry R. Kang. Color Technology for Electronic Imaging Devices. SPIE Optical
Engineering Press, 1997.
17. J´an Morovic. To Develop a Universal Gamut Mapping Algorithm. PhD thesis, Colour &
Imaging Institute, University of Derby, October 1998.
18. Gaurav Sharma and H. Joel Trussell. Digital color imaging. IEEE Transactions on Image
Processing, 6(7):901–932, July 1997.
19. Edward J. Giorgianni and Thomas E. Madden. Digital color management: encoding
solutions. Addison-Wesley, 1997.

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