Today Why does a visual system need color? Color • Reading: – Chapter 6, Forsyth & Ponce • Optional reading: – Chapter 4 of Wandell, Foundations of Vision, Sinauer, 1995 has a good treatment of this. Feb. 17, 2005 MIT 6.869 Prof. Freeman http://www.hobbylinc.com/gr/pll/pll5019.jpg Why does a visual system need color? (an incomplete list…) Lecture outline • To tell what food is edible. • Color physics. • Color physics. • To distinguish material changes from shading changes. • Color representation and matching. • Color representation and matching. • 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 1
color Spectral colors http://hyperphysics.phy-astr.gsu.edu/hbase/vision/specol.html#c2 Radiometry Radiometry for colour (review) θ , i φ i θ , e φ • All definitions are now “per unit wavelength” e • All units are now “per unit wavelength” • All terms are now “spectral” Horn, 1986 • Radiance becomes spectral radiance – watts per square meter per steradian per unit wavelength radiance θ φ • Irradiance becomes spectral irradiance L ( , ) = θ φ θ φ = e e BRDF f ( , , , ) – watts per square meter per unit wavelength θ φ i i e e E ( , ) i i irradiance Simplified rendering models: reflectance θ φ λ , , i i Often are more interested in relative spectral Radiometry composition than in overall intensity, so the θ φ λ , , for color e e spectral BRDF computation simplifies a wavelength-by-wavelength multiplication of relative energies. Horn, 1986 Spectral radiance θ φ λ L ( , , ) = θ φ θ φ λ = = .* e e BRDF f ( , , , , ) θ φ λ i i e e E ( , , ) i i Spectral irradiance Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 2
How measure those spectra: Simplified rendering models: transmittance Spectrophotometer (just like Newton’s diagram…) .* = Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 Two illumination spectra 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 Blue sky albedoes are typically Tungsten light bulb quite smooth functions. Measurements by E.Koivisto. Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 Forsyth, 2002 Color names for cartoon spectra Additive color mixing When colors combine by red adding the color spectra. Examples that follow this 400 500 600 700 nm mixing rule: CRT phosphors, cyan multiple projectors aimed at a red screen, Polachrome slide film. green 400 500 600 700 nm 400 500 600 700 nm Red and green make… magenta green 400 500 600 700 nm 400 500 600 700 nm 400 500 600 700 nm yellow yellow blue Yellow! 400 500 600 700 nm 400 500 600 700 nm 400 500 600 700 nm 3
Subtractive color mixing Overhead projector demo When colors combine by cyan multiplying the color spectra. Examples that follow this mixing rule: most photographic 400 500 600 700 nm • Subtractive color mixing films, paint, cascaded optical yellow filters, crayons. Cyan and yellow (in crayons, called “blue” and yellow) 400 500 600 700 nm make… green Green! 400 500 600 700 nm Low-dimensional models for color spectra Matlab demonstration ω ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ M M M M ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 1 λ = λ λ λ ω ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ e ( ) E ( ) E ( ) E ( ) 1 2 3 2 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ω 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 , :)' n-dimensional linear models for color spectra Basis functions for Macbeth color checker n = 3 n = 2 n = 1 Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 4
Outline Why specify color numerically? • Accurate color reproduction is • Color reproduction • Color physics. commercially valuable problems increased by • Color representation and matching. – Many products are identified prevalence of digital by color (“golden” arches); imaging - eg. digital • Few color names are widely libraries of art. recognized by English speakers - – How do we ensure that everyone sees the same – About 10; other languages color? have fewer/more, but not many more. – It’s common to disagree on appropriate color names. Forsyth & Ponce Color standards are important in industry Color matching experiment 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. Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 5
Color matching experiment 1 Color matching experiment 1 p 1 p 2 p 3 Color matching experiment 1 Color matching experiment 1 The primary color amounts needed for a match p 1 p 2 p 3 p 1 p 2 p 3 Color matching experiment 2 Color matching experiment 2 p 1 p 2 p 3 6
Color matching experiment 2 Color matching experiment 2 The primary color We say a amounts needed “negative” for a match: amount of p 2 was needed to make the match, because we p 1 p 2 p 3 added it to the test color’s side. p 1 p 2 p 3 p 1 p 2 p 3 p 1 p 2 p 3 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. Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 Forsyth & Ponce Measure color by color-matching paradigm How to compute the color match for any color signal for any set of primary colors • Pick a set of 3 primary color lights. • Find the amounts of each primary, e 1 , e 2 , e 3 , λ λ λ p ( ), p ( ), p ( ) • Pick a set of primaries, 1 2 3 needed to match some spectral signal, t. λ λ λ c ( ), c ( ), c ( ) • Measure the amount of each primary, 1 2 3 • Those amounts, e 1 , e 2 , e 3, describe the color of ( λ t ) needed to match a monochromatic light, t. If you have some other spectral signal, s, λ at each spectral wavelength (pick some spectral and s matches t perceptually, then e 1 , e 2 , e 3 step size). These are called the color matching will also match s, by Grassman’s laws. functions. • Why this is useful—it lets us: – Predict the color of a new spectral signal – Translate to representations using other primary lights. 7
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