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

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

Rod / Cone sensitivity The famous sock-matching problem…

© Stephen E. Palmer, 2002 Distribution of Rods and Cones Night Sky: why are there more stars off-center?

Electromagnetic Spectrum Human Luminance Sensitivity Function

Why do we see light of these wavelengths? © Stephen E. Palmer, 2002 …because that’s where the Sun radiates EM energy Visible Light

The Physics of Light Any patch of light can be completely described physically by its spectrum: the number of photons (per time unit) at each wavelength nm. © Stephen E. Palmer, 2002

The Physics of Light Some examples of the spectra of light sources © Stephen E. Palmer, 2002

Radiometry

Radiant exitance Irradiance

Radiometry Radiance Radiant intensity

Photometry

Horn, 1986 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 Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995

The Physics of Light Some examples of the reflectance spectra of surfaces Wavelength (nm) % Photons Reflected Red Yellow Blue Purple © Stephen E. Palmer, 2002

The Psychophysical Correspondence There is no simple functional description for the perceived color of all lights under all viewing conditions, but …... A helpful constraint: Consider only physical spectra with normal distributions area mean variance © Stephen E. Palmer, 2002

The Psychophysical Correspondence MeanHue # Photons Wavelength © Stephen E. Palmer, 2002

The Psychophysical Correspondence VarianceSaturation Wavelength # Photons © Stephen E. Palmer, 2002

The Psychophysical Correspondence AreaBrightness # Photons Wavelength © Stephen E. Palmer, 2002

Three kinds of cones: Physiology of Color Vision

More Spectra metamers

Metameric Whites

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

Color Matching

Color matching experiment 1

p 1 p 2 p 3

Color matching experiment 1 p 1 p 2 p 3

Color matching experiment 1 p 1 p 2 p 3 The primary color amounts needed for a match

Color matching experiment 2

p 1 p 2 p 3

Color matching experiment 2 p 1 p 2 p 3

Color matching experiment 2 p 1 p 2 p 3 We say a “negative” amount of p 2 was needed to make the match, because we added it to the test color’s side. The primary color amounts needed for a match: p 1 p 2 p 3

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

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 p 1 = nm p 2 = nm p 3 = 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. ” Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995

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

Pure wavelength in chromaticity diagram Then y increases

Pure wavelength in chromaticity diagram Green: y is big

Pure wavelength in chromaticity diagram Yellow: x & y are equal

Pure wavelength in chromaticity diagram 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 C 2 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 nm red green blue nm cyan magenta yellow nm

Additive color mixing nm red green Red and green make… nm yellow 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..* = Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995

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 nm cyan yellow nm Cyan and yellow (in crayons, called “blue” and yellow) make… nm Green! green

NTSC color components: Y, I, Q

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 X 0, Y 0, and Z 0 are used to color- balance: they ’ re the color of the reference white

Color Sensing in Camera (RGB) 3-chip vs. 1-chip: quality vs. cost Why more green? Why 3 colors?

Practical Color Sensing: Bayer Grid Estimate RGB at ‘G’ cels from neighboring values words/Bayer-filter.wikipedia

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