Why is this hard to read

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)

Illusory contour

• Shape, as well as color, depends on surround

• Most neural processing is about differences

Illusory contour

CS 768 Color Science

• Perceiving color

• Describing color

• Modeling color

• Measuring color

• Reproducing color

Spectral measurement

• Measurement p() of the power (or energy, which is power x time ) of a light source as a function of wavelength

• Usually relative to p(560nm)

• Visible light 380-780 nm

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Spectral Distribution of daylight

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leaf

flower

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Spectra of a red flower and a green leaf

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Data from http://www.it.lut.fi/research/color/database/database.html

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Retinal line spread function

retinal position

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Linearity

• additivity of response (superposition)

• r(m1+m2)=r(m1)+r(m2)

• scaling (homogeneity)• r(m)=r(m)• r(m1(x,y)+m2 (x,y))=

r(m1)(x,y)+r(m2)(x,y)= (r(m1)+r(m2))(x,y)

• r(m(x,y))=r(m)(x,y)

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Non-linearity

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adaptive architecture provides more sensitivity over smaller range

http://webvision.med.utah.edu/

Ganglion

Bipolar

Amacrine

Rod Cone

Epithelium

Optic nerve

Retinal cross section

Light

Horizontal

Visual pathways

• Three major stages– Retina

– LGN

– Visual cortex

– Visual cortex is further subdivided

http://webvision.med.utah.edu/Color.html

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.

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

Photoreceptors

• Rods– respond in low (scotopic) light– none in fovea

• try to foveate a dim star—it will disappear

– one type of spectral response– several hundred feed each ganglion cell so give

high sensitivity but low spatial resolution

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 10^2 From Wandell, Useful Numbers in Vision Science

http://white.stanford.edu/~brian/numbers/numbers.html

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.

Cones

• L (long wave), M (medium), S (short)– describes sensitivity curves.

• “Red”, “Green”, “Blue” is a misnomer. See spectral sensitivity.

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Cone Spectral Responses

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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 rf’s are circular, with opponency; Cortical are oriented and sometimes shape specific.

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On center rf Red-Green LGN rf

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Oriented Cortical rf

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 b&w

– Need fast contrast changes (60Hz)

– Keep fine shading in big areas

– (Definition)

• Parvo

– Separate color from b&w

– Slow color changes OK (40 hz)

– Omit fine shading in small areas

– (Definition)

• (Not obvious yet) pattern detail can be all in b&w channel

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V'() V()

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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.

Opponent Models

• Three channels leave the retina:– Red-Green (L-M+S = L-(M-S))– Yellow-Blue(L+M-S)– Achromatic (L+M+S)

• Note that chromatic channels can have negative response (inhibition). This is difficult to model with light.

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RedGreen L-M+S BlueYellow L+M-S

Achromatic L+M+.05*S

Schematic color opponent response

+- +

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Schematic color opponent response

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Color matching

• Grassman laws of linearity:()(((

• Hence for any stimulus s() and response

r(), total response is integral of s() r(), taken over all or approximately s()r()

Primarylights

Test light

Bipartitewhitescreen

Surround field

Test light Primary lights

Subject

Surround light

Color Matching

• Spectra of primary lights s1(), s2(), s3()

• Subject’s task: find c1, c2, c3, such thatc1s1()+c2s2()+c3s3()

matches test light.

• Problems (depending on si())

– [c1,c2,c3] is not unique (“metamer”)

– may require some ci<0 (“negative power”)

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() at find scalars R=R(G=G(B=B(such that

t() = R(rG(gB(b• R(,G(,B(are the color matching

functions based on r,g,b.

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3.5Stiles and Burch 1959 10-degree bipartite field color matching functions

primary lights at 645.2 nm 525.3 nmand 444.4 nm

b10() g10()

r10()

Color matching

• Grassman laws of linearity:()(((

• Hence for any stimulus s() and response

r(), total response is integral of s() r(), taken over all or approximately s()r()

Color matching

• What about three monochromatic lights?• M() = R*R() + G*G() + B*B()• Metamers possible• good: RGB functions are like cone

response• bad: Can’t match all visible lights with any

triple of monochromatic lights. Need to add some of primaries to the matched light

Primarylights

Test light

Bipartitewhitescreen

Surround field

Test light Primary lights

Subject

Surround light

Color matching

• Solution: CIE XYZ basis functions

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CIE 1931 standard colorimetric observer color matching functions

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Color matching

• Note Y is V()

• None of these are lights

• Euclidean distance in RGB and in XYZ is not perceptually useful.

• Nothing about color appearance

XYZ problems

• No correlation to perceptual chromatic differences

• X-Z not related to color names or daylight spectral colors

• One solution: chromaticity

Chromaticity Diagrams

• x=X/(X+Y+Z)y=Y/(X+Y+Z)z=Z/(X+Y+Z)

• Perspective projection on X-Y plane

• z=1-(x-y), so really 2-d

• Can recover X,Y,Z given x,y and on XYZ, usually Y since it is luminance

Chromaticity Diagrams

• No color appearance info since no luminance info.

• No accounting for chromatic adaptation.

• Widely misused, including for color gamuts.

Some gamuts

SWOP

ENCAD GA ink

MacAdam Ellipses

• JND of chromaticity

• Bipartite equiluminant color matching to a given stimulus.

• Depends on chromaticity both in magnitude and direction.

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

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?

MacAdam Ellipses

• JND of chromaticity – Extension to varying luminence: ellipsoids in

XYZ space which project appropriately for fixed luminence

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/freeandclear.htm and http://www.ductus.com/cleartype/cleartype.html

CIELab

• L* = 116 f(Y/Yn)-16

• a* = 500[f(X/Xn) – f(Y/Yn)]

• b* = 200[f(Y/Yn) –f(Z/Zn)]

where

Xn,Yn,Zn are the CIE XYZ coordinates of the reference white point.

f(z) = z1/3 if z>0.008856

f(z)=7.787z+16/116 otherwise

L* is relative achromatic value, i.e. lightness

a* is relative greenness-redness

b* is relative blueness-yellowness

CIELab

• L* = 116 f(Y/Yn)-16

• a* = 500[f(X/Xn) – f(Y/Yn)]

• b* = 200[f(Y/Yn) –f(Z/Zn)]

where

Xn,Yn,Zn are the CIE XYZ coordinates of the reference white point.

f(z) = z1/3 if z>0.008856

f(z)=7.787z+16/116 otherwise350 400 450 500 550 600 650 700 7500

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CIELab

• L* = 116 f(Y/Yn)-16

• a* = 500[f(X/Xn) – f(Y/Yn)]

• b* = 200[f(Y/Yn) –f(Z/Zn)]

where

Xn,Yn,Zn are the CIE XYZ coordinates of the reference white point.

f(z) = z1/3 if z>0.008856

f(z)=7.787z+16/116 otherwise

C*ab = sqrt(a*2+b*2) corresponds to perception of chroma (colorfulness).

hue angle hab=tan-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.

a*>0

redder

a*<0

greener

b*>0

yellower

b*<0

bluer

chroma

hue

lightness

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.

CIELab defects

Perceptual lines of constant hue are curved in a*-b* plane, especially for red and blue hues (Fairchiled Fig 10.5)

Doesn’t 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)

CIELab color difference model

E*=sqrt(L*2 + a* 2 + b* 2)– May be in the same L*a*b* space or to

different white points (but both wp’s normalized to same max Y, usually Y=100).

– Typical observer reports match for E* in range 2.5 – 20, but for simple patches, 2.5 is perceptible difference (Fairchild)

Viewing Conditions

• Illuminant matters. Fairchild Table 7-1 shows E* using two different illuminants.

• Consider a source under an illuminant with SPD T(). If color at a pixel p has spectral distribution p(and reflectance factor of screen is r(then SPD at retina is r()T()+p().

• Typically r(is constant, near 1, and diffuse.

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

– …

Color ordering systems

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

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

Reflection geometry

diffuse

specular

Reflection geometry

Semi-glossy

glossy

Reflection geometry

Semi-glossy

glossy

Some standard measurement geometries

• d/8:i diffuse illumination, 8° view, specular component included

• d/8:e as above, specular component excluded

• d/d:i diffuse illumination and viewing, specular component included

• 45/0 45° illumination, 0° view

Viewing comparison

L* C* h E

d/8:i 51.1 41.5 269

45/0 44.8 46.9 268 8.3

d/8:e 47.5 44.6 268 4.7

Measurement differences of a semi-gloss tile under different viewing conditions (Berns, p. 86). E is vs. d/8:i. Data are for Lab.

L*u*v*

• CIE u' v' chromaticity coordinates:u'=4X/(X+15Y+3Z)= 4x/(-2+12y+3)v'=9Y/(X+15Y+3Z)=9y/(-2+12y+3)

• 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')

L*u*v*

• L* = 116(Y/Yn)1/3 –16

• u* = 13L*(u' – un')

• v* = 13L*(v'-vn')

• un', vn' values for whitepoint

Models for color differences

• Euclidean metric in CIELab (or CIELuv) space not very predictive. Need some weighting

V = (1/kE))[(L*)/kLSL)2+(C*/kCSC)2+(H*/kHSH)2]1/2

= uv or ab according to whether using L*a*b* or L*u*v*

• The k's are parameters fit to the data.• The S's are functions of the underlying variable, estimated

from data.

Models for color differences

E*94

kL = kC = kH = 1

SL = 1

SC=1+.0.045C*ab

SH = 1+0.015C*ab

Fitting with one more parameter for scaling gives good predictions. Berns p 125.

Color constancy

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

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

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– L*a*b* is usual, but has some defects to be

discussed later

Color Gamut Limitations

1. CIE XYZ underlies everything– this permits unrealizable colors, but usually

"gamut" means restricted to the visible spectrum locus in chromaticity diagram

2. Gamut can depend on luminance– usually on illuminant relative luminance, i.e.

Y/Yn

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

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