Why do we need color for visual processing? Lecture 2: Color Tuesday, Sept 4 Color Radiometry: some definitions • Color of light arriving at camera depends on • Radiance : power emitted per unit area in a direction – Spectral reflectance of the surface light is leaving • Irradiance : total incident power falling on a surface – Spectral radiance of light falling on that patch • Color perceived depends on Directions – Physics of light specified by e c (polar angle, n – Visual system receptors a i azimuth) d a r r – Brain processing, environment i e c n a d i a r Radiometry: BRDF Radiometry: BRDF • BRDF is a very general notion • Bidirectional reflectance distribution function : Model of local reflection that tells how bright a surface – some surfaces need it (underside of a CD; tiger eye; appears when viewed from one direction when light etc) falls on it from another. – very hard to measure • illuminate from one direction, view from another, repeat Directions – very unstable specified by • minor surface damage can change the BRDF (polar angle, • e.g. ridges of oil left by contact with the skin can act as azimuth) radiance / lenses irradiance • For many surfaces, light leaving the surface is largely independent of exit angle Slide from Marc Pollefeys 1
Color and light Lambertian surfaces • E.g.: Lambertian / diffuse surfaces: appear White light: equally bright from all viewing directions composed of about equal Constant energy in all wavelengths of the visible spectrum Newton 1665 Image from http://micro.magnet.fsu.edu/ Since light can arrive in different quantities at different wavelengths… Spectral radiance / spectral irradiance …extend radiometry terms to incorporate spectral units (per unit wavelength) Image credit: nasa.gov Measuring spectra Spectral power distribution • the power per unit area per unit wavelength of a radiant object Spectroradiometer : separate input light into its different wavelengths, and measure Blue skylight Tungsten bulb the energy at each Foundations of Vision , B. Wandell Foundations of Vision , B. Wandell 2
The color viewed is also affected by the surface’s spectral reflectance properties. Spectral power of daylight varies depending on Spectral Spectral power reflectances for time of day, some natural year, and other objects: how much conditions. of each wavelength is reflected Violet Indigo Blue Green Yellow Orange Red Measurements by J. Parkkinen and P. Silfsten. Forsyth & Ponce, measurements by E. Koivisto Color mixing Additive color mixing Colors combine by adding color spectra Light adds to black. Adapted from W. Freeman Examples of additive color systems Subtractive color mixing Colors combine by multiplying color spectra. Pigments remove multiple projectors color from incident CRT phosphors light (white). http://www.jegsworks.com http://www.crtprojectors.co.uk/ 3
Examples of subtractive color systems Why specify color numerically? • Accurate color reproduction is commercially valuable • Printing on paper – Many products are identified by color (“golden” arches) • Crayons • Few color names are widely recognized by English speakers • Most photographic film – About 10; other languages have fewer/more, but not many more. – Common to disagree on appropriate color names . • Color reproduction problems increased by prevalence of digital imaging – e.g. digital libraries of art. – How to ensure that everyone perceives the same color? – What spectral radiances produce the same response from people under simple viewing conditions? Forsyth & Ponce Color matching experiment Color matching experiment 1 Observer adjusts weight (intensity) for primary lights (fixed SPD’s) to match appearance of test light. Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 After Judd & Wyszecki. Color matching slides from W. Freeman Color matching experiment 1 Color matching experiment 1 p 1 p 2 p 3 p 1 p 2 p 3 4
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 Color matching The primary color We say a • Lights forming a perceptual match may be amounts needed “negative” for a match: physically different amount of p 2 – Match light: must be combination of primaries was needed to make the match, – Test light: any light because we p 1 p 2 p 3 • Metamers : pairs of lights that match added it to the test color’s side. perceptually but not physically p 1 p 2 p 3 p 1 p 2 p 3 5
Measuring color by color-matching Grassman’s Laws Mixing the matches for • Pick a set of 3 primary color lights. two test lights will • Find the amounts of each primary, e 1 , e 2 , e 3 , match the mixture of the two test lights. needed to match some spectral signal, t. • If you have some other spectral signal, s, and s If same weights used matches t perceptually, then e 1 , e 2 , e 3 will also to match two test form a match for s, by Grassman’s laws. lights, then test lights match. • Useful: – Predict the color of a new spectral signal Positive scaling of test – Translate to representations using other primary light -> scaling of lights. weights (additive matching is linear). Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 Adapted from W. Freeman Measuring color by color-matching Computing color matches • Why is computing the color • How to compute the weights match for any color signal for that will yield a perceptual any set of primaries useful? match for any test light using – Want to paint a carton of Kodak any set of primaries: film with the Kodak yellow color. 1. Select primaries – Want to match skin color of a person in a photograph printed 2. Estimate their color on an ink jet printer to their true matching functions : skin color. observer matches series – Want the colors in the world, on ⎛ λ Λ λ ⎞ c ( ) c ( ) … ⎜ ⎟ 1 1 1 N a monitor, and in a print format of monochromatic lights, = λ Λ λ ⎜ ⎟ C c ( ) … c ( ) to all look the same. 2 1 2 N one at each wavelength ⎜ ⎟ λ Λ λ … ⎝ c ( ) c ( ) ⎠ 3 1 3 N Adapted from W. Freeman Image credit: pbs.org Computing color matches Computing color matches λ λ λ λ Color matching functions for a c ( ), c ( ), c ( ) matches particular set of primaries 1 i 2 i 3 i i p 1 = 645.2 nm Now have matching functions for all monochromatic light sources p 2 = 525.3 nm Arbitrary new spectral signal is a linear combination of the p 3 = 444.4 nm monochromatic sources λ ⎛ ⎞ t ( ) Rows of matrix C ρ ⎜ ⎟ 1 = Μ ⎜ ⎟ t t … ⎜ ⎟ λ ⎝ ⎠ t ( ) N Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 Adapted from W. Freeman 6
How do you translate colors between different Computing color matches systems of primaries? p 1 = (0 0 0 0 0… 0 1 0) T p’ 1 = (0 0.2 0.3 4.5 7 …. 2.1) T p 2 = (0 0 … 0 1 0 ...0 0) T p’ 2 = (0.1 0.44 2.1 … 0.3 0) T Intensities of primary lights needed to p 3 = (0 1 0 0 … 0 0 0 0) T p’ 3 = (1.2 1.7 1.6 …. 0 0) T obtain match: Primary spectra, P Primary spectra, P’ Color matching functions, C Color matching functions, C’ Any input spectrum, t C ρ ρ The amount of The amount of = t CP ' C ' t each primary in each P’ primary P needed to needed to match t match the color The spectrum of a perceptual with spectrum t. match to t, made using the The color of that match to t, primaries P’ described by the primaries, P. Fig from B. Wandell, 1996 Slide by W. Freeman How do you translate colors between Standard color spaces different systems of primaries? • Use a common set of primaries/color The values of the 3 The values of the 3 matching functions primaries, in the primaries, in the • Linear unprimed system primed system e = – CIE XYZ CP ' e ' – RGB – CMY a 3x3 matrix • Non-linear • Transforms one set of primaries to another – HSV • Each column is vector of intensities of the original primaries (P) that are needed to match the new primaries (P’) Adapted from W. Freeman CIE XYZ color space RGB color space • Established by the commission • Single wavelength primaries international d’eclairage (CIE), 1931 • Phosphors for monitor • Usually projected to display: (x,y) = (X/(X+Y+Z), Y/(X+Y+Z)) RGB color matching functions CIE XYZ Color matching functions 7
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