1

• Light and the EM spectrum• The H.V.S. and Color Perception

2

What is an ImageWhat is an Image? ? • An image is a projection of a 3D scene into a 2D

projection plane.• An image can be defined as a 2 variable function I(x,y) ,

where for each position (x,y) in the projection plane, I(x,y) defines the light intensity at this point.

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Camera trial #1

scene film

Put a piece of film in front of an object.

source: Yung-Yu Chuang

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Pinhole cameraPinhole camera

scene film

Add a barrier to block off most of the rays.• It reduces blurring• The pinhole is known as the aperture• The image is inverted

barrier

pinhole camera

source: Yung-Yu Chuang

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6

X

Y

(x,y,z)

(x,y)

center of projection(pinhole)

d

d – focal length

The Pinhole Camera Model (where)The Pinhole Camera Model (where)

Z

10/100

0010

0001

Z

Y

X

dw

y

x

d

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The Shading Model (what)The Shading Model (what)

Shading Model: Given the illumination incident at a point on a surface, what is reflected?

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Shading Model ParametersShading Model Parameters

• The factors determining the shading effects are:

– The light source properties:• Positions, Electromagnetic Spectrum, Shape.

– The surface properties:• Position, orientation, Reflectance properties.

– The eye (camera) properties:• Position, orientation, Sensor spectrum sensitivities.

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Newton’s Experiment, 1665 Cambridge.Discovering the fundamental spectral components of light.(from Foundations of Vision: Brian Wandell, 1995.

The Light PropertiesThe Light Properties

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A prism

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Electromagnetic Radiation - SpectrumElectromagnetic Radiation - Spectrum

Wavelength in nanometers (nm)

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Electromagnetic WaveElectromagnetic Wave

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MonochromatorsMonochromators

Monochromators measure the power or energy at different wavelengths

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The Spectral Power Distribution (SPD) of a light is a function e() which defines the relative energy at each wavelength.

Wavelength ()

400 500 600 7000

0.5

1R

ela

tive

Pow

er

Spectral Power Distribution (SPD)Spectral Power Distribution (SPD)

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Examples of Spectral Power Distributions

Blue Skylight Tungsten bulb

Red monitor phosphor Monochromatic light

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0.5

1

400 500 600 7000

0.5

1

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0.5

1

400 500 600 7000

0.5

1

• Interactions between light and matter depends on the physical characteristics of light as well as the matter.

• Three types of interactions:

– Reflection

– Absorption

– Transmittance

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The Surface PropertiesThe Surface PropertiesIncoming Light

Transmitted Light

Reflected Light

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The Bidirectional Reflectance The Bidirectional Reflectance Distribution Function (BRDF)Distribution Function (BRDF)

• A BRDF describes how much light is reflected when light makes contact with a certain material

),,(

),,(

ii

ee

E

LBRDF

Spectral radiance: quantity of light reflected in direction (e,e)

Spectral irradiance: quantity of light arriving from direction (i,i)

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Specular reflection mirror like reflection at the surface

Diffuse (lambertian) reflection Reflected randomly between color particlesreflection is equal in all directions.

Incident light Specular reflection

Diffuse reflection

normal

Simplified ModelSimplified Model

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Different Types of Surfaces

Simplified rendering models: reflectanceSimplified rendering models: reflectance

Often are more interested in relative spectral composition than in overall intensity, so the spectral BRDF computation simplifies a wavelength-by-wavelength multiplication of relative energies.

.* =

B. Freeman, and Foundations of Vision, by Brian Wandell,

21

400 500 600 700

0.2

0.4

0.6

0.8

1

400 500 600 700

0.2

0.4

0.6

0.8

1

400 500 600 700

0.2

0.4

0.6

0.8

1

400 500 600 700

0.2

0.4

0.6

0.8

1

Surface Body Reflectances (albedo)

Yellow Red

Blue Gray

Wavelength (nm)

Spectral Property of Lambertian SurfacesSpectral Property of Lambertian Surfaces

Forsyth, 2002

Some reflectance spectraSome reflectance spectra

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Optic NerveFovea

Vitreous

Optic Disc

Lens

Pupil

Cornea

Ocular Muscle

Retina

Humor

Iris

The Eye PropertiesThe Eye Properties

Cornea - קרנית Pupil - אישון Iris - קשתית Retina - רשתית

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25

The Visual PathwayThe Visual Pathway

Retina

Optic Nerve

Optic Chiasm

LateralGeniculateNucleus (LGN)

Visual Cortex

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Eye v.s. CameraEye v.s. Camera

Yaho Wang’s slides

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light

rods cones

horizontal

amacrine

bipolar

ganglion

The Human RetinaThe Human Retina

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• Retina contains 2 types of photo-receptors– Cones:

• Day vision, can perceive color tone

– Rods: • Night vision, perceive brightness only

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Cones:• High illumination levels (Photopic vision)• Sensitive to color (there are three cone types: L,M,S)• Produces high-resolution vision• 6-7 million cone receptors, located primarily in the central

portion of the retina

Wavelength (nm)

Re

lativ

e s

en

sitiv

ity

Cone Spectral Sensitivity

400 500 600 7000

0.25

0.5

0.75

1ML

SM

A side note:• Humans and some monkeys have three types of cones (trichromatic vision); most other mammals have two types of cones (dichromatic vision).• Marine mammals have one type of cone.• Most birds and fish have four types. •Lacking one or more type of cones result in color blindness.

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Rods:• Low illumination levels (Scotopic vision).• Highly sensitive (respond to a single photon).• Produces lower-resolution vision• 100 million rods in each eye.• No rods in fovea.

Wavelength (nm)

Re

lativ

e s

en

sitiv

ity

400 500 600 7000

0.25

0.5

0.75

1

Rod Spectral Sensitivity

31rods

S - Cones

L/M - Cones

Foveal Periphery photoreceptors

Photoreceptor DistributionPhotoreceptor Distribution

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Cone Receptor Mosaic(Roorda and Williams, 1999)

L-cones M-cones S-cones

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Distribution of rod and cone photoreceptors

Degrees of Visual Angle

Rec

epto

rs p

er s

quar

e m

m

-60 -40 -20 0 20 40 60

2

6

10

14

18x 104

rodscones

Cone’s Distribution:• L-cones (Red) occur at about ~65% of the cones throughout the retina.

• M-cones (green) occur at about ~30% of the cones.

• S-cones (blue) occur at about ~2-5% of the cones (Why so few?).

fovea

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The Cone ResponsesThe Cone Responses

Assuming Lambertian Surfaces

IlluminantSensors Surface

e() – Fixed, point source illuminantk() –surface’s reflectancel(),m(),s() – Cone responsivities

Output

)()()( kelL

)()()( kemM

)()()( kesS

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Metamer - two lights that appear the same visually. They might have different SPDs (spectral power distributions).

400 500 600 7000

400

800

400 500 600 7000

100

200

Wavelength (nm)

Pow

er

The phosphors of the monitor were set to match the tungsten light.

Tungsten light Monitor emission

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The Trichromatic Color TheoryThe Trichromatic Color Theory

Thomas Young (1773-1829) - A few different retinal receptors operating with different wavelength sensitivities will allow humans to perceive the number of colors that they do. Suggested 3 receptors.

Helmholtz & Maxwell (1850) - Color matching with 3 primaries.

Trichromatic: “tri”=three “chroma”=color color vision is based on three primaries (i.e., it is 3D).

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Color Matching ExperimentColor Matching Experiment

+ -

+ -

+ -

test match

Primaries

• Given a set of 3 primaries, one can determine for every spectral distribution, the intensity of the guns required to match the color of that spectral distribution.

• The 3 numbers can serve as a color representation.

bBgGrRT

R()

G()

B()

T()

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Color matching experiment 1

from: Bill Freeman

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Color matching experiment 1

p1 p2 p3 from: Bill Freeman

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Color matching experiment 1

p1 p2 p3 from: Bill Freeman

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Color matching experiment 1

p1 p2 p3

The primary color amounts needed for a match

from: Bill Freeman

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Color matching experiment 2

from: Bill Freeman

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Color matching experiment 2

p1 p2 p3 from: Bill Freeman

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Color matching experiment 2

p1 p2 p3 from: Bill Freeman

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Color matching experiment 2

p1 p2 p3 p1 p2 p3

We say a “negative” amount of p2 was needed to make the match, because we added it to the test color’s side.

The primary color amounts needed for a match:

p1 p2 p3

from: Bill Freeman

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Color matching experiment for Monochromatic lights

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0.5

1

400 500 600 7000

0.5

1

400 500 600 7000

0.5

1

Primary Intensities

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r()

g()b()

400 500 600 700

0

1

2

3

Wavelength (nm)

Pri

ma

ry In

ten

sity

Stiles & Burch (1959) Color matching functions. Primaries are: 444.4 525.3 and 645.2

Problems: Some perceived colors cannot be generated. This is true for any choice of visible primaries.

The The ColorColor Matching Functions (CMF) Matching Functions (CMF)

48Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 from: Bill Freeman

The superposition principle

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• Observation - Color matching is linear:– if (SP) then (S+NP+N) – if (SP) then ( S P)

• Let T()=c(-0)+d(-1) a double chromatic color: How should we adjust the 3 primaries?

101010 ;; bdbcbgdgcgrdrcr

0 1

cd

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• Outcome 1: Any T() can be matched:

• Outcome 2: CMF can be calculated for any chosen primaries U(), V(), W():

dbTbdgTgdrTr ;;

b

g

r

ccc

bbb

aaa

w

v

u

321

321

321

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• The CIE (Commission Internationale d’Eclairage) defined in 1931 three hypothetical lights X, Y, and Z whose matching functions are positive everywhere:

The CIE Color StandardThe CIE Color Standard

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TristimulusTristimulus

• Let X, Y, and Z be the tri-stimulus values.• A color can be specified by its trichromatic

coefficients, defined as

X

xX Y Z

Y

yX Y Z

Zz

X Y Z

X ratio

Y ratio

Z ratio

Two trichromatic coefficients are enough to specify a color (x + y + z = 1).

From: Bahadir Gunturk

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Input light spectrum

x

y

From: Bahadir Gunturk

CIE Chromaticity DiagramCIE Chromaticity Diagram

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Input light spectrum

x

y

From: Bahadir Gunturk

CIE Chromaticity DiagramCIE Chromaticity Diagram

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Input light spectrum

x

y

From: Bahadir Gunturk

CIE Chromaticity DiagramCIE Chromaticity Diagram

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Input light spectrum

Boundary

x

y

380nm

700nm

From: Bahadir Gunturk

CIE Chromaticity DiagramCIE Chromaticity Diagram

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Input light spectrum

Boundary

From: Bahadir Gunturk

CIE Chromaticity DiagramCIE Chromaticity Diagram

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Light composition

From: Bahadir Gunturk

CIE Chromaticity DiagramCIE Chromaticity Diagram

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CIE Chromaticity DiagramCIE Chromaticity Diagram

Light composition

Light composition

From: Bahadir Gunturk

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• The sRGB is a device-independent color space. It was created

in 1996 by HP and Microsoft for use on monitors and printers.

• It is the most commonly used color space.

• It is defined by a transformation from the xyz color space.

The sRGB Color StandardThe sRGB Color Standard

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Color matching predicts matches, Color matching predicts matches, not appearance not appearance

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Color AppearanceColor Appearance

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Color AppearanceColor Appearance

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Color AppearanceColor Appearance

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Color SpacesColor Spaces

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RGB Color Space (additive)RGB Color Space (additive)

• Define colors with (r, g, b) ; amounts of red, green, and blue

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CMY Color Space (subtractive)CMY Color Space (subtractive)

• Cyan, magenta, and yellow are the complements of red, green, and blue– We can use them as filters to subtract from white– The space is the same as RGB except the origin is white

instead of black

Color names for cartoon spectraColor names for cartoon spectra

400 500 600 700 nm

400 500 600 700 nm

400 500 600 700 nm

red

gree

nbl

ue

400 500 600 700 nm

cyan

mag

enta

yello

w

400 500 600 700 nm

400 500 600 700 nm

From: B. Freeman

Additive color mixingAdditive color mixing

400 500 600 700 nm

400 500 600 700 nm

red

gree

n

Red and green make…

400 500 600 700 nm

yello

w

Yellow!

When colors combine by adding the color spectra. Example color displays that follow this mixing rule: CRT phosphors, multiple projectors aimed at a screen, Polachrome slide film.

Subtractive color mixingSubtractive color mixing

When colors combine by multiplying the color spectra. Examples that follow this mixing rule: most photographic films, paint, cascaded optical filters, crayons.

400 500 600 700 nm

cyan

yello

w

400 500 600 700 nm

Cyan and yellow (in crayons,called “blue” and yellow)

make…

400 500 600 700 nmGreen!gr

een

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Red

Green Blue

Magenta

Cyan

Yellow

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HSV color spaceHSV color space

• Hue - the chroma we see (red, green, purple).• Saturation - how pure is the color (how far the color from

gray ).• Value (brightness) - how bright is the color.

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HSV color spaceHSV color space

Value

Saturation

Hue

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T H E E N D