Color Why does a visual system need color Reading Chapter 6 Forsyth Ponce Optional reading Chapter 4 of Wandell Foundations of Vision Sinauer 1995 has a good treatment of this Feb 19 2004 MIT 6 891 Prof Freeman for Prof Darrell http www hobbylinc com gr pll pll5019 jpg Why does a visual system need color an incomplete list To tell what food is edible To distinguish material changes from shading changes To group parts of one object together in a scene To find people s skin Check whether a person s appearance looks normal healthy To compress images color Lecture outline Color physics Color perception and color matching matching Spectral colors http hyperphysics phy astr gsu edu hbase vision specol html c2 1 Radiometry review i i e e Horn 1986 radiance BRDF f i i e e Radiometry for colour All definitions are now per unit wavelength All units are now per unit wavelength All terms are now spectral Radiance becomes spectral radiance watts per square meter per steradian per unit wavelength Irradiance becomes spectral irradiance L e e E i i watts per square meter per unit wavelength irradiance Simplified rendering models reflectance i i 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 Radiometry for color e e Horn 1986 Spectral radiance L e e BRDF f i i e e E i i Spectral irradiance Foundations of Vision by Brian Wandell Sinauer Assoc 1995 Simplified rendering models transmittance How measure those spectra Spectrophotometer just like Newton s diagram Foundations of Vision by Brian Wandell Sinauer Assoc 1995 Foundations of Vision by Brian Wandell Sinauer Assoc 1995 2 Two illumination spectra Blue sky Some reflectance spectra Spectral albedoes for several different leaves with color names attached Notice that different colours typically have different spectral albedo but that different spectral albedoes may result in the same perceived color compare the two whites Spectral albedoes are typically quite smooth functions Measurements by E Koivisto Tungsten light bulb Foundations of Vision by Brian Wandell Sinauer Assoc 1995 Forsyth 2002 Color names for cartoon spectra 500 600 700 nm blue 400 400 500 600 700 nm 400 400 400 500 500 500 600 600 600 700 nm 700 nm 700 nm 500 600 700 nm 400 500 600 700 nm green 700 nm 400 When colors combine by adding the color spectra Examples that follow this mixing rule CRT phosphors multiple projectors aimed at a screen Polachrome slide film Red and green make yellow 600 magenta 500 green 400 yellow red cyan red Additive color mixing Yellow 400 500 600 700 nm cyan Subtractive color mixing 500 600 700 nm 400 500 600 700 nm 500 600 700 nm green yellow 400 When colors combine by multiplying the color spectra Examples that follow this mixing rule most photographic films paint cascaded optical filters crayons demos Additive color Subtractive color Cyan and yellow in crayons called blue and yellow make Green 400 3 Low dimensional models for color spectra Basis functions for Macbeth color checker M M 1 M M e E1 E2 E3 2 M M M M 3 How to find a linear model for color spectra form a matrix D of measured spectra 1 spectrum per column u s v svd D satisfies D u s v the first n columns of u give the best least squares optimal n dimensional linear bases for the data D D u 1 n s 1 n 1 n v 1 n Foundations of Vision by Brian Wandell Sinauer Assoc 1995 n dimensional linear models for color spectra n 3 Outline Color physics Color perception and color matching n 2 n 1 Foundations of Vision by Brian Wandell Sinauer Assoc 1995 Color standards are important in industry Why specify color numerically Accurate color reproduction is commercially valuable Many products are identified by color golden arches Few color names are widely recognized by English speakers About 10 other languages have fewer more but not many more It s common to disagree on appropriate color names Color reproduction problems increased by prevalence of digital imaging eg digital libraries of art How do we ensure that everyone sees the same color Forsyth Ponce 4 An assumption that sneaks in here We know color appearance really depends on The illumination Your eye s adaptation level The colors and scene interpretation surrounding the observed color But for now we will assume that the spectrum of the light arriving at your eye completely determines the perceived color Color matching experiment Color matching experiment 1 Foundations of Vision by Brian Wandell Sinauer Assoc 1995 Color matching experiment 1 p1 p2 Color matching experiment 1 p3 p1 p2 p3 5 Color matching experiment 1 Color matching experiment 2 The primary color amounts needed for a match p1 p2 p3 Color matching experiment 2 p1 p2 Color matching experiment 2 p3 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 6 Measure color by color matching paradigm 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 Pick a set of 3 primary color lights Find the amounts of each primary e1 e2 e3 needed to match some spectral signal t Those amounts e1 e2 e3 describe the color of t If you have some other spectral signal s and s matches t perceptually then e1 e2 e3 will also match s Why this is useful it lets us Predict the color of a new spectral signal Translate to representations using other primary lights Forsyth Ponce How to do this mathematically Color matching functions for a particular set of monochromatic primaries p1 645 2 nm p2 525 3 nm p3 444 4 nm Pick a set of primaries p1 p2 p3 Measure the amount of each primary c1 c2 c3 needed to match a monochromatic light t at each spectral wavelength pick some spectral step size Foundations of Vision by Brian Wandell Sinauer Assoc 1995 Using the color matching functions to predict the primary match to a new spectral signal Store the color matching functions in the rows of the matrix C c1 1 L c1 N C c2 1 L c2 N c L c 3 N 3 1 Let the new spectral signal to be characterized be the vector t t 1 r t M t N Then the amounts of