ColorNext class: shape-from-shadingWhy does a visual system need color?Why does a visual system need color?(an incomplete list…)Lecture outlinecolorSpectral colorsRadiometry for colourSimplified rendering models: reflectanceSpectrophotometerTwo illumination spectraColor names for cartoon spectraAdditive color mixingSubtractive color mixingdemosBasis functions for Macbeth color checkerLow-dimensional models for color spectraOutlineWhy specify color numerically?Color matching experimentColor matching experiment 1Color matching experiment 1Color matching experiment 1Color matching experiment 1Color matching experiment 2Color matching experiment 2Color matching experiment 2Color matching experiment 2Grassman’s LawsMeasure color by color-matching paradigmHow to do this, mathematicallyColor matching functions for a particular set of monochromatic primariesUsing the color matching functions to predict the primary match for a new spectral signalHow do you translate colors between different systems of primaries?So color matching functions translate like this:How do you translate from the color in one set of primaries to that in another?What’s the machinery in the eye?Eye Photoreceptor responsesHuman PhotoreceptorsHuman eye photoreceptor spectral sensitivitiesColor matching functions (for a particular set of spectral primariesComparison of color matching functions with best 3x3 transformation of cone responsesCIE XYZ color spaceSome other color spaces…Uniform color spacesHSV hexconeColor metamerismMetameric lightsColor • Reading: – Chapter 6, Forsyth & Ponce• Optional reading:– Chapter 4 of Wandell, Foundations of Vision,Sinauer, 1995 has a good treatment of this.Sept. 26, 2002MIT 6.801/6.866Profs. Freeman and DarrellNext class: shape-from-shading• Reading: – Chapter 11 HornOct. 1, 2002MIT 6.801/6.866Profs. Freeman and DarrellWhy does a visual system need color?http://www.hobbylinc.com/gr/pll/pll5019.jpgWhy 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 someone’s appearance looks normal/healthy.• To compress imagesLecture outline• Color physics.• Color perception and color matching.• Inference about the world from color observations.• Color physics.• Color perception and color matching.• Inference about the world from color observations.colorSpectral colorshttp://hyperphysics.phy-astr.gsu.edu/hbase/vision/specol.html#c2Radiometry 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– watts per square meter per unit wavelengthHorn, 1986λφθ,,iiλφθ,,eeSpectral radiance),,(),,(),,,,(λφθλφθλφθφθiieeeeiiELfBRDF ==Spectral irradianceSimplified rendering models: reflectanceOften 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., 1995Simplified rendering models: transmittance=.*Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995SpectrophotometerFoundations of Vision, by Brian Wandell, Sinauer Assoc., 1995Two illumination spectraFoundations of Vision, by Brian Wandell, Sinauer Assoc., 1995Some reflectance spectraSpectral albedoes for several different leaves, with color names attached. Notice that different colourstypically 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.Forsyth, 2002Color names for cartoon spectra400 500 600 700 nm400 500 600 700 nm400 500 600 700 nmredgreenblue400 500 600 700 nmcyanmagentayellow400 500 600 700 nm400 500 600 700 nmAdditive color mixingWhen colors combine by adding the color spectra. Examples that follow this mixing rule: CRT phosphors, multiple projectors aimed at a screen, Polachrome slide film.400 500 600 700 nmred400 500 600 700 nmgreenRed and green make…400 500 600 700 nmyellowYellow!Subtractive color mixingWhen colors combine by multiplying the color spectra. Examples that follow this mixing rule: most photographic films, paint, cascaded optical filters, crayons.cyan400 500 600 700 nm400 500 600 700 nmyellowCyan and yellow (in crayons,called “blue” and yellow) make…400 500 600 700 nmGreen!greendemos• Additive color• Subtractive colorLow-dimensional models for color spectra=321321)()()()(ωωωλλλλMMMMMMMMEEEeHow 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::)',:1(*):1,:1(*):1(:, nvnnsnuD ≈Basis functions for Macbeth color checkerFoundations of Vision, by Brian Wandell, Sinauer Assoc., 1995Low-dimensional models for color spectraFoundations of Vision, by Brian Wandell, Sinauer Assoc., 1995Outline• Color physics.• Color perception and color matching.• Inference about the world from color observations.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 & PonceColor standards are important in industryColor matching experimentFoundations of Vision, by Brian Wandell, Sinauer Assoc., 1995Color matching experiment 1Color matching experiment 1p1 p2 p3Color matching