Spectra

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Unrelated vs. Related Color

• Unrelated color color perceived to belong to an
  area in isolation (CIE 17.4)
• Related color color perceived to belong to an
  area seen in relation to other colors (CIE 17.4)

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Illusory contour

• Shape, as well as color, depends on surround
• Most neural processing is about differences

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Illusory contour
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CS 768 Color Science

• Perceiving color
• Describing color
• Modeling color
• Measuring color
• Reproducing color

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Spectral measurement

• Measurement p(l) of the power (or energy, which
  is power x time ) of a light source as a function
  of wavelength l
• Usually relative to p(560nm)
• Visible light 380-780 nm

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Linearity

• additivity of response (superposition)
• r(m1m2)r(m1)r(m2)
• scaling (homogeneity)
• r(am)ar(m)
• r(m1(x,y)m2 (x,y)) r(m1)(x,y)r(m2)(x,y)
  (r(m1)r(m2))(x,y)
• r(am(x,y))ar(m)(x,y)

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Non-linearity
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http//webvision.med.utah.edu/
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Optic nerve
Light
Ganglion
Amacrine
Bipolar
Horizontal
Cone
Rod
Epithelium
Retinal cross section
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Visual pathways

• Three major stages
• Retina
• LGN
• Visual cortex
• Visual cortex is further subdivided

http//webvision.med.utah.edu/Color.html
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Optic nerve

• 130 million photoreceptors feed 1 million
  ganglion cells whose output is the optic nerve.
• Optic nerve feeds the Lateral Geniculate Nucleus
  approximately 1-1
• LGN feeds area V1 of visual cortex in complex
  ways.

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Photoreceptors

• Cones -
• respond in high (photopic) light
• differing wavelength responses (3 types)
• single cones feed retinal ganglion cells so give
  high spatial resolution but low sensitivity
• highest sampling rate at fovea

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Photoreceptors

• Rods
• respond in low (scotopic) light
• none in fovea
• try to foveate a dim starit will disappear
• one type of spectral response
• several hundred feed each ganglion cell so give
  high sensitivity but low spatial resolution

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Luminance

• Light intensity per unit area at the eye
• Measured in candelas/m2 (in cd/m2)
• Typical ambient luminance levels (in cd/m2)
• starlight 10-3
• moonlight 10-1
• indoor lighting 102
• sunlight 105
• max intensity of common CRT monitors 102
• From Wandell, Useful Numbers in Vision Science
  http//white.stanford.edu/brian/numbers/numbers.h
  tml

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Rods and cones

• Rods saturate at 100 cd/m2 so only cones work at
  high (photopic) light levels
• All rods have the same spectral sensitivity
• Low light condition is called scotopic
• Three cone types differ in spectral sensitivity
  and somewhat in spatial distribution.

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Cones

• L (long wave), M (medium), S (short)
• describes sensitivity curves.
• Red, Green, Blue is a misnomer. See
  spectral sensitivity.

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Receptive fields

• Each neuron in the visual pathway sees a specific
  part of visual space, called its receptive field
• Retinal and LGN rfs are circular, with
  opponency Cortical are oriented and sometimes
  shape specific.

On center rf
Red-Green LGN rf
Oriented Cortical rf
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Channels Visual Pathways subdivided

• Channels
• Magno
• Color-blind
• Fast time response
• High contrast sensitivity
• Low spatial resolution
• Parvo
• Color selective
• Slow time response
• Low contrast sensitivity
• High spatial resolution

• Video coding implications
• Magno
• Separate color from bw
• Need fast contrast changes (60Hz)
• Keep fine shading in big areas
• (Definition)
• Parvo
• Separate color from bw
• Slow color changes OK (40 hz)
• Omit fine shading in small areas
• (Definition)
• (Not obvious yet) pattern detail can be all in
  bw channel

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Trichromacy

• Helmholtz thought three separate images went
  forward, R, G, B.
• Wrong because retinal processing combines them in
  opponent channels.
• Hering proposed opponent models, close to right.

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Opponent Models

• Three channels leave the retina
• Red-Green (L-MS L-(M-S))
• Yellow-Blue(LM-S)
• Achromatic (LMS)
• Note that chromatic channels can have negative
  response (inhibition). This is difficult to model
  with light.

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100
Luminance
10
1.0
Contrast Sensitivity
Red-Green
0.1
Blue-Yellow
0.001
-1
0
1
2
Log Spatial Frequency (cpd)
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Color matching

• Grassman laws of linearity (r1 r2)(l) r1(l)
  r2(l) (kr)(l) k(r(l))
• Hence for any stimulus s(l) and response r(l),
  total response is integral of s(l) r(l), taken
  over all l or approximatelyS s(l)r(l)

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Surround light
Primary lights
Surround field
Bipartite white screen
Subject
Test light
Primary lights
Test light
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Color Matching

• Spectra of primary lights s1(l), s2(l), s3(l)
• Subjects task find c1, c2, c3, such
  that c1s1(l)c2s2(l)c3s3(l)matches test light.
• Problems (depending on si(l))
• c1,c2,c3 is not unique (metamer)
• may require some cilt0 (negative power)

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Color Matching

• Suppose three monochromatic primaries r,g,b at
  645.16, 526.32, 444.44 nm and a 10 field (Styles
  and Burch 1959).
• For any monochromatic light t(l) at l, find
  scalars RR(l), GG(l), BB(l) such that t(l)
  R(l)r G(l)g B(l)b
• R(l), G(l), B(l) are the color matching functions
  based on r,g,b.

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Color matching

• Grassman laws of linearity (r1 r2)(l) r1(l)
  r2(l) (kr)(l) k(r(l))
• Hence for any stimulus s(l) and response r(l),
  total response is integral of s(l) r(l), taken
  over all l or approximatelyS s(l)r(l)

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Color matching

• What about three monochromatic lights?
• M(l) RR(l) GG(l) BB(l)
• Metamers possible
• good RGB functions are like cone response
• bad Cant match all visible lights with any
  triple of monochromatic lights. Need to add some
  of primaries to the matched light

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Surround light
Primary lights
Surround field
Bipartite white screen
Subject
Test light
Primary lights
Test light
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Color matching

• Solution CIE XYZ basis functions

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Color matching

• Note Y is V(l)
• None of these are lights
• Euclidean distance in RGB and in XYZ is not
  perceptually useful.
• Nothing about color appearance

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XYZ problems

• No correlation to perceptual chromatic
  differences
• X-Z not related to color names or daylight
  spectral colors
• One solution chromaticity

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Chromaticity Diagrams

• xX/(XYZ)yY/(XYZ)zZ/(XYZ)
• Perspective projection on X-Y plane
• z1-(x-y), so really 2-d
• Can recover X,Y,Z given x,y and on XYZ, usually Y
  since it is luminance

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Chromaticity Diagrams

• No color appearance info since no luminance info.
• No accounting for chromatic adaptation.
• Widely misused, including for color gamuts.

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Some gamuts
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MacAdam Ellipses

• JND of chromaticity
• Bipartite equiluminant color matching to a given
  stimulus.
• Depends on chromaticity both in magnitude and
  direction.

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MacAdam Ellipses

• For each observer, high correlation to variance
  of repeated color matches in direction, shape and
  size
• 2-d normal distributions are ellipses
• neural noise?
• See Wysecki and Styles, Fig 1(5.4.1) p. 307

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MacAdam Ellipses

• JND of chromaticity
• Weak inter-observer correlation in size, shape,
  orientation.
• No explanation in Wysecki and Stiles 1982
• More modern models that can normalize to observer?

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MacAdam Ellipses

• JND of chromaticity
• Extension to varying luminence ellipsoids in XYZ
  space which project appropriately for fixed
  luminence

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MacAdam Ellipses

• JND of chromaticity
• Technology applications
• Bit stealing points inside chromatic JND
  ellipsoid are not distinguishable chromatically
  but may be above luminance JND. Using those
  points in RGB space can thus increase the
  luminance resolution. In turn, this has
  appearance of increased spatial resolution
  (anti-aliasing)
• Microsoft ClearType. See http//www.grc.com/freean
  dclear.htm and http//www.ductus.com/cleartype/cle
  artype.html

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CIELab

• L 116 f(Y/Yn)-16
• a 500f(X/Xn) f(Y/Yn)
• b 200f(Y/Yn) f(Z/Zn)
• where
• Xn,Yn,Zn are the CIE XYZ coordinates of the
  reference white point.
• f(z) z1/3 if zgt0.008856
• f(z)7.787z16/116 otherwise

• L is relative achromatic value, i.e. lightness
• a is relative greenness-redness
• b is relative blueness-yellowness

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CIELab

• L 116 f(Y/Yn)-16
• a 500f(X/Xn) f(Y/Yn)
• b 200f(Y/Yn) f(Z/Zn)
• where
• Xn,Yn,Zn are the CIE XYZ coordinates of the
  reference white point.
• f(z) z1/3 if zgt0.008856
• f(z)7.787z16/116 otherwise

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CIELab

• L 116 f(Y/Yn)-16
• a 500f(X/Xn) f(Y/Yn)
• b 200f(Y/Yn) f(Z/Zn)
• where
• Xn,Yn,Zn are the CIE XYZ coordinates of the
  reference white point.
• f(z) z1/3 if zgt0.008856
• f(z)7.787z16/116 otherwise

• Cab sqrt(a2b2) corresponds to perception of
  chroma (colorfulness).
• hue angle habtan-1(b/a) corresponds to hue
  perception.
• L corresponds to lightness perception
• Euclidean distance in Lab space is fairly
  correlated to color matching and color distance
  judgements under many conditions. Good
  correspondence to Munsell distances.

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lightness
chroma hue
bgt0 yellower
alt0 greener
agt0 redder
blt0 bluer
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Complementary Colors

• c1 and c2 are complementary hues if they sum to
  the whitepoint.
• Not all spectral (i.e. monochromatic) colors have
  complements. See chromaticity diagram.
• See Photoshop Lab interface.

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CIELab defects

• Perceptual lines of constant hue are curved in
  a-b plane, especially for red and blue hues
  (Fairchiled Fig 10.5)
• Doesnt predict chromatic adaptation well without
  modification
• Axes are not exactly perceptual unique r,y,g,b
  hues. Under D65, these are approx 24,
  90,162,246 rather than 0, 90, 180, 270
  (Fairchild)

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CIELab color difference model

• DEsqrt(DL2 Da 2 Db 2)
• May be in the same Lab space or to different
  white points (but both wps normalized to same
  max Y, usually Y100).
• Typical observer reports match for DE in range
  2.5 20, but for simple patches, 2.5 is
  perceptible difference (Fairchild)

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Viewing Conditions

• Illuminant matters. Fairchild Table 7-1 shows DE
  using two different illuminants.
• Consider a source under an illuminant with SPD
  T(l). If color at a pixel p has spectral
  distribution p(l) and reflectance factor of
  screen is r(l) then SPD at retina is
  r(l)T(l)p(l).
• Typically r(l) is constant, near 1, and diffuse.

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Color ordering systems

• Want system in which finite set of colors vary
  along several (usually three) axes in a
  perceptually uniform way.
• Several candidates, with varying success
• Munsell
• Spectra available at Finnish site
• NCS
• OSA Uniform Color Scales System

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Color ordering systems

• CIE Lab still not faithful model, e.g.
  contours of constant Munsell chroma are not
  perfect circles in Lab space. See Fairchild
  Fig 10-4, Berns p. 69.

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Effect of viewing conditions

• Impact of measurement geometry on Lab
• Need illumination and viewing angle standards
• Need reflection descriptions for opaque material,
  transmission descriptions for translucent

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Reflection geometry
specular
diffuse
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Reflection geometry
Semi-glossy
glossy
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Reflection geometry
Semi-glossy
glossy
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Some standard measurement geometries

• d/8i diffuse illumination, 8 view, specular
  component included
• d/8e as above, specular component excluded
• d/di diffuse illumination and viewing, specular
  component included
• 45/0 45 illumination, 0 view

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Viewing comparison
L C h DE
d/8i 51.1 41.5 269
45/0 44.8 46.9 268 8.3
d/8e 47.5 44.6 268 4.7
Measurement differences of a semi-gloss tile
under different viewing conditions (Berns, p.
86). DE is vs. d/8i. Data are for Lab.
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Luv

• CIE u' v' chromaticity coordinates
• u'4X/(X15Y3Z) 4x/(-212y3)
• v'9Y/(X15Y3Z)9y/(-212y3)
• Gives straighter lines of constant Munsell chroma
  (See figures on p. 64 of Berns).
• L 116(Y/Yn)1/3 16
• u 13L(u' un')
• v 13L(v'-vn')

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Luv

• L 116(Y/Yn)1/3 16
• u 13L(u' un')
• v 13L(v'-vn')
• un', vn' values for whitepoint

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Models for color differences

• Euclidean metric in CIELab (or CIELuv) space not
  very predictive. Need some weighting
• DV (1/kE))(DL)/kLSL)2(DCa/kCSC)2(DHa/kHSH)
  21/2
• a uv or ab according to whether using Lab or
  Luv
• The k's are parameters fit to the data.
• The S's are functions of the underlying variable,
  estimated from data.

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Models for color differences

• DE94
• kL kC kH 1
• SL 1
• SC1.0.045Cab
• SH 10.015Cab
• Fitting with one more parameter for scaling gives
  good predictions. Berns p 125.

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Color constancy

• Color difference models such as previous have
  been used to predict color inconstancy under
  change of illumination. Berns p. 214.

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Other color appearance phenomena

• Models still under investigation to account for
• Colorfulness (perceptual attribute of chroma)
  increases with luminance ("Hunt effect")
• Brightness contrast (perceptual attribute of
  lightness difference) increases with luminance
• Chromatic adaptation

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Color Gamuts

• Gamut the range of colors that are viewable
  under stated conditions
• Usually given on chromaticity diagram
• This is bad because it normalizes for lightness,
  but the gamut may depend on lightness.
• Should really be given in a 3d color space
• Lab is usual, but has some defects to be
  discussed later

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Color Gamut Limitations

• CIE XYZ underlies everything
• this permits unrealizable colors, but usually
  "gamut" means restricted to the visible spectrum
  locus in chromaticity diagram
• Gamut can depend on luminance
• usually on illuminant relative luminance, i.e.
  Y/Yn

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Color Gamut Limitations

• Surface colors
• reflectance varies with gloss. Generally high
  gloss increases lightness and generally lightness
  reduces gamut (see figures in Berns, p. 145 ff)
• Stricter performance requirements often reduce
  gamut
• e.g. require long term fade resistance

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Color Gamut Limitations

• Physical limitations of colorants and illuminants
• Specific set of colorants and illuminants are
  available. For surface coloring we can not
  realize arbitrary XYZ values even within the
  chromaticity spectral locus
• Economic factors
• Color may be available but expense not justified

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Color mixing

• Suppose a system of colorants (lights, inks,).
  Given two colors with spectra c1(l) and c2(l).
  This may be reflectance spectra, transmittance
  spectra, emission spectra,Let d be a mix of
  c1and c2. The system is additive if d(l)
  c1(l) c2(l)no matter what c1 and c2 are.

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Scalability

• Suppose the system has some way of scaling the
  intensity of the color by a scalar k.
• Examples
• CRT increase intensity by k.
• halftone printing make dots k times bigger
• colored translucent materials make k times as
  thick
• If c is a color, denote the scaled color as d. If
  the spectrum d (l) is k(c(l)) for each l, the
  system is scalable

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Scalability

• Consider a color production system and a colors
  c1,c2 with c2kc1. Let mimax(ci(l))and
  di(1/mi)ci. Highschool algebra shows that the
  system is scalable if and only if d1(l )d2 (l)
  for all l, no matter what c1 and k.

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Control in color mixing systems

• Normally we control some variable to control
  intensity
• CRT
• voltage on electron gun
• integer 0...255
• Translucent materials (liquids, plastics...)
• thickness
• Halftone printing
• dot size

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Linearity

• A color production system is linear if it is
  additive and scalable.
• Linearity is good it means that model
  computations involving only linear algebra make
  good predictions.
• Interesting systems are typically additive over
  some range, but rarely scalable.
• A simple compensation can restore often restore
  linearity by considering a related mixing system.

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Scalability in subtractive systems
n
0ltklt1
kL0
L0
kkL0
knL0
d
d
d
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Scalability in subtractive systems
n
0ltklt1
L0
knL0
Tl tlb where Tl is total transmittance at
wavelength l, tl transmittance of unit thickness
and b is thickness
L(nd) knL0 n integer L(bd) kbL0 b
arbitrary L(b) kbL0 when d 1 L(b)/L0
kb
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Linearity in subtractive systems

• Absorbance
• Al -log(Tl) defn
• -log(tlb)
• -blog(tl)
• -bal where alabsorbance of unit
  thickness
• so absorbance is scalable when thickness b is the
  control variable
• By same argument as for scalability, the
  transmittance of the "sum" of colors Tl and Sl
  will be their product and so the absorbance of
  the sum will be the sum of the absorbances.
• Thus absorbance as a function of thickness is a
  linear mixture system

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Tristimulus Linearity

• Xmix Ymix Zmix X1 Y1 Z1 X2 Y2 Z2
• c X Y Z cX cY cZ
• This is true because
• r(l) g(l) b(l) are the basis of a 3-d linear
  space (of functions on wavelength) describing
  lights
• Grassman's laws are precisely the linearity of
  light when described in that space.
• X Y Z is a linear transformation from this
  space to R3

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Monitor (non)Linearity
L1(A,B,C)
L2(A,B,C)
f2(L1, L2, L3)
L3(A,B,C)
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Monitor (non)Linearity

• In A,B,C --gt L L1, L2, L3 --gt Out
  O1 O2 O3 f1(L1, L2, L3) f2(L1, L2, L3)
  f3(L1, L2, L3)
• Interesting monitor cases to consider
• In dr dg db where dr, dg, db are integers
  0255 or numbers 01 describing the programming
  API for red, green, blue channels
• Out X Y Z tristimulus coords or monitor
  intensities in each channel
• Typically
• fi depends only on Li
• fi are all the same
• fi(u) ug for some g characteristic of the
  monitor

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Monitor (non)Linearity

• Warning
• LCD non-linearity is logistic, not exponential
  but flat panel displays are usually built to
  mimic CRT because much software is
  gamma-corrected (with typical g2.4-2.7)
• Somewhat related Most LCDdisplays are built
  with analoginstead of digital inputs, in
  orderto function as SVGA monitors.This is
  changing.

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Monitor (non)Linearity

• (CRT Colorimetry example of Berns, p. 168-169)
• Non-linearity is f(u)ug , g 2.7, same for all
  output channels.
• Linearity is diagonal

a 0 00 a 00 0 a
b 0 00 b 00 0 b


where a1.02/255, b -.02
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RGB vs. gray, LCD projector
120
100
80
60
40
20
0
0
50
100
150
200
250
300
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More depth on Gamma

• Poynton, Gamma and its disguises The nonlinear
  mappings of intensity in perception, CRTs, film
  and video. SMPTE Journal, 1993, 1099-1108

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Halftoning

• The problem with ink its opaque
• Screening luminance range is accomplished by
  printing with dots of varying size. Collections
  of big dots appear dark, small dots appear light.
• of area covered gives darkness.

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Halftoning references

• A commercial but good set of tutorials
• Digital Halftoning, by Robert Ulichney, MIT
  Press, 1987
• Stochastic halftoning

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Color halftoning

• Needs screens at different angles to avoid moire
• Needs differential color weighting due to
  nonlinear visual color response and spatial
  frequency dependencies.

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Halftone ink

• May not always be opaque
• Three inks can give 238 distinct colors
• Visual system gives more since dot size, spacing,
  yields intensity, gives somewhat additive system
• Highly nonlinear. See Berns et al. The Spectral
  Modeling of Large Format Ink Jet Printers

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From http//www.matrixcolor.com/
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