Light and Color Jehee Lee Seoul National University With a lot of slides stolen from Alexei Efros, Stephen Palmer, Fredo Durand and others.

Light and Color

Jehee Lee

Seoul National University

With a lot of slides stolen from Alexei Efros, Stephen Palmer, Fredo Durand and others

The Eye

• The human eye is a camera!– Iris - colored annulus with radial muscles

– Pupil - the hole (aperture) whose size is controlled by the iris– What’s the “film”?

• photoreceptor cells (rods and cones) in the retina

The Retina

Cross-section of eye

Ganglion cell layer

Bipolar cell layer

Receptor layer

Pigmentedepithelium

Ganglion axons

Cross section of retina

Retina up-close

Light

© Stephen E. Palmer, 2002

Cones cone-shaped less sensitive operate in high light color vision

Two types of light-sensitive receptors

cone

rod

Rods rod-shaped highly sensitive operate at night gray-scale vision

Rod / Cone sensitivity

The famous sock-matching problem…


Distribution of Rods and Cones

.

0

150,000

100,000

50,000

020 40 60 8020406080

Visual Angle (degrees from fovea)

Rods

Cones Cones

Rods

FoveaBlindSpot

# R

ecep

tors

/mm

2

Night Sky: why are there more stars off-center?

Electromagnetic Spectrum

http://www.yorku.ca/eye/photopik.htm

Human Luminance Sensitivity Function

Why do we see light of these wavelengths?


.

0 1000 2000 3000

En

erg

y

Wavelength (nm)

400 700

700 C

2000 C

5000 C

10000 C

VisibleRegion

…because that’s where theSun radiates EM energy

Visible Light

The Physics of Light

Any patch of light can be completely describedphysically by its spectrum: the number of photons (per time unit) at each wavelength 400 - 700 nm.

400 500 600 700

Wavelength (nm.)

# Photons(per ms.)



.

# P

ho

ton

s

D. Normal Daylight

Wavelength (nm.)

B. Gallium Phosphide Crystal

400 500 600 700

# P

ho

ton

s

Wavelength (nm.)

A. Ruby Laser

400 500 600 700

400 500 600 700

# P

ho

ton

s

C. Tungsten Lightbulb

400 500 600 700

# P

ho

ton

s

Some examples of the spectra of light sources


Radiometry

Radiometry

Radiant exitance Irradiance

Radiometry

Radiance Radiant intensity

Photometry

Horn, 1986

),,(

),,(),,,,(

ii

eeeeii E

LfBRDF

,, ii

,, ee

Radiometry for color

Spectral radiance: power in a specified direction, per unit area, per unit solid angle, per unit wavelength

Spectral irradiance: incident power per unit area, per unit wavelength

Simplified 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.

.* =

Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995

.* =

Simplified rendering models: transmittance



Some examples of the reflectance spectra of surfaces

Wavelength (nm)

% P

hoto

ns R

efle

cted

Red

400 700

Yellow

400 700

Blue

400 700

Purple

400 700


The Psychophysical Correspondence

There is no simple functional description for the perceivedcolor of all lights under all viewing conditions, but …...

A helpful constraint: Consider only physical spectra with normal distributions

area

Wavelength (nm.)

# Photons

400 700500 600

mean

variance



Mean Hue

yellowgreenblue

# P

hoto

ns

Wavelength



Variance Saturation

Wavelength

high

medium

low

hi.

med.

low# P

hoto

ns



Area Brightness#

Pho

tons

Wavelength

B. Area Lightness

bright

dark



.

400 450 500 550 600 650

RE

LAT

IVE

AB

SO

RB

AN

CE

(%

)

WAVELENGTH (nm.)

100

50

440

S

530 560 nm.

M L

Three kinds of cones:

Physiology of Color Vision

More Spectra

metamers

Metameric Whites

Metameric lights


Color Matching

BbGgRrQ )()()(

Color matching experiment 1


p1 p2 p3


p1 p2 p3


p1 p2 p3

The primary color amounts needed for a match



p1 p2 p3


p1 p2 p3


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


Grassman’s Laws

• For color matches:– symmetry: U=V <=>V=U– transitivity: U=V and V=W => U=W– proportionality: U=V <=> tU=tV– additivity: if any two (or more) of the statements

U=V, W=X, (U+W)=(V+X) are true, then so is the third

• These statements are as true as any biological law. They mean that additive color matching is linear.

Forsyth & Ponce

Color Matching Functions

p1 = 645.2 nmp2 = 525.3 nmp3 = 444.4 nm

Since we can define colors using almost any set of primary colors, let’s agree on a set of primaries and color matching functions for the world to use…

CIE XYZ color space

• Commission Internationale d’Eclairage, 1931• “…as with any standards decision, there are some

irratating aspects of the XYZ color-matching functions as well…no set of physically realizable primary lights that by direct measurement will yield the color matching functions.”

• “Although they have served quite well as a technical standard, and are understood by the mandarins of vision science, they have served quite poorly as tools for explaining the discipline to new students and colleagues outside the field.”


CIE XYZ: Color matching functions are positive everywhere, but primaries are “imaginary” (require adding light to the test color’s side in a color matching experiment). Usually compute x, y, where x=X/(X+Y+Z)

y=Y/(X+Y+Z)Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995

A qualitative rendering of the CIE (x,y) space. The blobby region represents visible colors. There are sets of (x, y) coordinates that don’t represent real colors, because the primaries are not real lights (so that the color matching functions could be positive everywhere).

Forsyth & Ponce

• CIE chromaticity diagram encompasses all the perceivable colors in 2D space (x,y) by ignoring the luminance

A plot of the CIE (x,y) space. We show the spectral locus (the colors of monochromatic lights) and the black-body locus (the colors of heated black-bodies). I have also plotted the range of typical incandescent lighting.

Forsyth & Ponce

Pure wavelength in chromaticity diagram

• Blue: big value of Z, therefore x and y small


• Then y increases


• Green: y is big


• Yellow: x & y are equal


• Red: big x, but y is not null

Color Gamut

• The color gamut for n primaries in CIE chromaticity diagram is the convexhull of the color positions

Color Gamut

Complementary Colors

• Illuminant C (Average sunlight)

Dominant Wavelength

• The spectral color which can be mixed with white light in order to reproduce the desired color

• C2 have spectral distributions with subtractive dominant wave lengths

CIE color space

• Can think of X, Y , Z as coordinates

• Linear transform from typical RGB or LMS

• Always positive(because physical spectrum is positive and matching curves are positives)

• Note that many points in XYZ do not correspond to visible colors!

Color Gamut of RGB

XYZ vs. RGB

• Linear transform• XYZ is rarely used for storage• There are tons of flavors of RGB

– sRGB, Adobe RGB– Different matrices!

• XYZ is more standardized• XYZ can reproduce all colors with positive values• XYZ is not realizable physically !!

– What happens if you go “off” the diagram– In fact, the orthogonal (synthesis) basis of XYZ requires

negative values.

RGB color space

• RGB cube– Easy for devices– But not perceptual– Where do the grays live?– Where is hue and saturation?

HSV

• Hue, Saturation, Value (Intensity)– RGB cube on its vertex

• Decouples the three components (a bit)• Use rgb2hsv() and hsv2rgb() in Matlab

Color 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

yell

ow

400 500 600 700 nm

400 500 600 700 nm

Additive color mixing

400 500 600 700 nm

400 500 600 700 nm

red

gree

n

Red and green make…

400 500 600 700 nm

yell

ow

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.

Simplified 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.

.* =


Subtractive 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

yell

ow

400 500 600 700 nm

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

400 500 600 700 nmGreen!gr

een

NTSC color components: Y, I, Q

B

G

R

Q

I

Y

312.0523.0211.0

322.0274.0596.0

114.0587.0299.0

NTSC - RGB

subtractive model (colors of pigments are subtracted) used in color output devices

CMYK color model - K for black ink for reducing the amount of ink

CMY color model

Uniform color spaces

• McAdam ellipses (next slide) demonstrate that differences in x,y are a poor guide to differences in color

• Construct color spaces so that differences in coordinates are a good guide to differences in color.

Forsyth & Ponce

Variations in color matches on a CIE x, y space. At the center of the ellipse is the color of a test light; the size of the ellipse represents the scatter of lights that the human observers tested would match to the test color; the boundary shows where the just noticeable difference is. The ellipses on the left have been magnified 10x for clarity; on the right they are plotted to scale. The ellipses are known as MacAdam ellipses after their inventor. The ellipses at the top are larger than those at the bottom of the figure, and that they rotate as they move up. This means that the magnitude of the difference in x, y coordinates is a poor guide to the difference in color.

Forsyth & Ponce

Perceptually Uniform Space: MacAdam

• In perceptually uniform color space, Euclidean distances reflect perceived differences between colors

• MacAdam ellipses (areas of unperceivable differences) become circles

• Non-linear mapping, many solutions have been proposed

Source: [Wyszecki and Stiles ’82]

CIELAB (a.k.a. CIE L*a*b*)

Source: [Wyszecki and Stiles ’82]

• The reference perceptually uniform color space

• L: lightness • a and b: color opponents

• X0, Y0, and Z0 are used to color-balance: they’re the color of the reference white

White Balance

• Chromatic adaptation– If the light source is gradually changed in color,

humans will adapt and still perceive the color of the surface the same

Color Temperature

• Blackbody radiators

Light and Color Jehee Lee Seoul National University With a lot of slides stolen from Alexei Efros, Stephen Palmer, Fredo Durand and others.

Documents

stephen palmer

primary color amounts

normal distributions

unit area

brian wandell

unit wavelengthsimplified

time unit

unit solid angle