Why does a visual system need color? Color Reading: Chapter 6, - PDF document

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. 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…) Lecture outline • To tell what food is edible. • Color physics. • Color physics. • To distinguish material changes from shading changes. • Color perception and color matching. • Color perception and color 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 color Spectral colors http://hyperphysics.phy-astr.gsu.edu/hbase/vision/specol.html#c2 1

Radiometry Radiometry for colour (review) θ , i φ i • All definitions are now “per unit wavelength” θ , e φ 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 • Irradiance becomes spectral irradiance θ φ L ( , ) = θ φ θ φ = BRDF f ( , , , ) e e – watts per square meter per unit wavelength i i e e θ φ 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 = BRDF f ( , , , , ) e e i i e e θ φ λ E ( , , ) i i Spectral irradiance Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 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 2

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 Subtractive color mixing demos When colors combine by cyan multiplying the color spectra. • Additive color Examples that follow this mixing rule: most photographic 400 500 600 700 nm • Subtractive color 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 3

Low-dimensional models for color spectra Basis functions for Macbeth color checker      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 , :)' Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 n-dimensional linear models for color spectra Outline n = 3 • 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 • Color reproduction commercially valuable problems increased by – 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 have fewer/more, but not many color? more. – It’s common to disagree on appropriate color names. 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 Color matching experiment 1 p 1 p 2 p 3 p 1 p 2 p 3 5

Color matching experiment 1 Color matching experiment 2 The primary color amounts needed for a match p 1 p 2 p 3 Color matching experiment 2 Color matching experiment 2 p 1 p 2 p 3 p 1 p 2 p 3 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 Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 6

Measure color by color-matching paradigm Grassman’s Laws • Pick a set of 3 primary color lights. • Find the amounts of each primary, e 1 , e 2 , e 3 , • For color matches: needed to match some spectral signal, t. – symmetry: U=V <=>V=U • Those amounts, e 1 , e 2 , e 3, describe the color of – transitivity: U=V and V=W => U=W t. If you have some other spectral signal, s, – proportionality: U=V <=> tU=tV and s matches t perceptually, then e 1 , e 2 , e 3 – additivity: if any two (or more) of the statements will also match s. U=V, • Why this is useful—it lets us: W=X, (U+W)=(V+X) are true, then so is the third – Predict the color of a new spectral signal • These statements are as true as any biological law. – Translate to representations using other primary They mean that additive color matching is linear. lights. Forsyth & Ponce Color matching functions for a particular set of monochromatic primaries How to do this, mathematically p 1 = 645.2 nm λ λ λ p ( ), p ( ), p ( ) • Pick a set of primaries, p 2 = 525.3 nm 1 2 3 λ λ λ c ( ), c ( ), c ( ) p 3 = 444.4 nm • Measure the amount of each primary, 1 2 3 ( λ t ) needed to match a monochromatic light, λ at each spectral wavelength (pick some spectral step size). Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 How do you translate colors between Using the color matching functions to predict different systems of primaries? the primary match to a new spectral signal Store the color matching functions in the rows of the matrix, C p 1 = (0 0 0 0 0… 0 1 0) T p’ 1 = (0 0.2 0.3 4.5 7 …. 2.1) T λ λ  c ( ) c ( )  L p 2 = (0 0 … 0 1 0 ...0 0) T p’ 2 = (0.1 0.44 2.1 … 0.3 0) T  1 1 1 N  p 3 = (0 1 0 0 … 0 0 0 0) T p’ 3 = (1.2 1.7 1.6 …. 0 0) T = λ λ C c ( ) c ( )  L  2 1 2 N Primary spectra, P Primary spectra, P’   λ λ c ( ) c ( ) Color matching functions, C L Color matching functions, C’   3 1 3 N Any input spectrum, t Let the new spectral signal to be characterized be the vector t. C r r The color of t, as = t CP ' C ' t λ  t ( )  described by the  1  r Then the amounts of each primary needed to primaries, P. = t   M match t are: C r A perceptual match to t, made   t λ t ( )   using the primaries P’ The color of that match to t, N described by the primaries, P. 7

How do you translate from the So color matching functions color in one set of primaries to translate like this: that in another? C r r But this holds for any = CP ' C ' t t From previous slide input spectrum, t, so… e = CP ' e ' C = CP ' C ' C C the same 3x3 matrix P’ P’ a 3x3 matrix P’ are the old primaries P’ are the old primaries C are the new primaries’ color matching functions C are the new primaries’ color matching functions What’s the machinery in the eye? Eye Photoreceptor responses (Where do you think the light comes in?) Human eye photoreceptor Human Photoreceptors spectral sensitivities Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 8