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 Cross section of retina Pigmented epithelium Ganglion axons Ganglion cell layer Bipolar cell layer Receptor layer Retina up-close Light Two types of light-sensitive receptors Cones cone-shaped less sensitive operate in high light color vision Rods rod-shaped highly sensitive operate at night gray-scale vision © Stephen E. Palmer, 2002 Rod / Cone sensitivity The famous sock-matching problem… Distribution of Rods and Cones # Receptors/mm2 . Fovea 150,000 Rods Blind Spot Rods 100,000 50,000 0 Cones Cones 80 60 40 20 0 20 40 60 80 Visual Angle (degrees from fovea) Night Sky: why are there more stars off-center? © Stephen E. Palmer, 2002 Electromagnetic Spectrum Human Luminance Sensitivity Function http://www.yorku.ca/eye/photopik.htm Visible Light Why do we see light of these wavelengths? …because that’s where the Sun radiates EM energy © Stephen E. Palmer, 2002 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 400 - 700 nm. # Photons (per ms.) 400 500 600 700 Wavelength (nm.) © Stephen E. Palmer, 2002 The Physics of Light Some examples of the spectra of light sources . B. Gallium Phosphide Crystal # Photons # Photons A. Ruby Laser 400 500 600 700 400 500 Wavelength (nm.) 700 Wavelength (nm.) D. Normal Daylight # Photons C. Tungsten Lightbulb # Photons 600 400 500 600 700 400 500 600 700 © Stephen E. Palmer, 2002 Radiometry Radiometry Radiant exitance Irradiance Radiometry Radiance Radiant intensity Photometry i ,i , e ,e , Radiometry for color Horn, 1986 Spectral radiance: power in a specified direction, per unit area, per unit solid angle, per unit wavelength L( e , e , ) BRDF f ( i , i , e , e , ) E ( i , i , ) 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 % Photons Reflected Some examples of the reflectance spectra of surfaces Red 400 Yellow 700 400 Blue 700 400 Wavelength (nm) Purple 700 400 700 © 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 mean area # Photons 400 500 variance 600 700 Wavelength (nm.) © Stephen E. Palmer, 2002 The Psychophysical Correspondence # Photons Mean blue Hue green yellow Wavelength © Stephen E. Palmer, 2002 The Psychophysical Correspondence # Photons Variance Saturation hi. high med. medium low low Wavelength © Stephen E. Palmer, 2002 The Psychophysical Correspondence Area Brightness # Photons B. Area Lightness bright dark Wavelength © Stephen E. Palmer, 2002 Physiology of Color Vision Three kinds of cones: 440 RELATIVE ABSORBANCE (%) . 530 560 nm. 100 S M L 50 400 450 500 550 600 650 WAVELENGTH (nm.) © Stephen E. Palmer, 2002 More Spectra metamers Metameric Whites Metameric lights Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 Color Matching Q r ( ) R g ( )G b( ) B Color matching experiment 1 Color matching experiment 1 p1 p2 p3 Color matching experiment 1 p1 p2 p3 Color matching experiment 1 The primary color amounts needed for a match p1 p2 p3 Color matching experiment 2 Color matching experiment 2 p1 p2 p3 Color matching experiment 2 p1 p2 p3 Color matching experiment 2 We say a “negative” amount of p2 was needed to make the match, because we added it to the test color’s side. p1 p2 p3 The primary color amounts needed for a match: p1 p2 p3 p1 p2 p3 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 p1 = 645.2 nm p2 = 525.3 nm p3 = 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.” 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 blackbody 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 • 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 600 700 nm 400 500 600 700 nm 400 500 600 700 nm blue magenta 500 green 400 yellow red cyan Color names for cartoon spectra 400 500 600 700 nm 400 500 600 700 nm 400 500 600 700 nm red Additive color mixing 500 600 700 nm 400 500 600 700 nm yellow green 400 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. Red and green make… Yellow! 400 500 600 700 nm 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 = cyan Subtractive color mixing 500 600 700 nm yellow 400 500 600 700 nm green 400 When colors combine by multiplying the color spectra. Examples that follow this mixing rule: most photographic films, paint, cascaded optical filters, crayons. Cyan and yellow (in crayons, called “blue” and yellow) make… Green! 400 500 600 700 nm NTSC color components: Y, I, Q 0.114 R Y 0.299 0.587 I 0.596 0.274 0.322 G Q 0.211 0.523 0.312 B NTSC - RGB CMY color model 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 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*) • The reference perceptually uniform color space • L: lightness • a and b: color opponents • X0, Y0, and Z0 are used to colorbalance: they’re the color of the reference white Source: [Wyszecki and Stiles ’82] 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