Color I:trichromatic theoryMarc LevoyComputer Science DepartmentStanford UniversityCS 178, Spring 2011! Marc LevoyOutline!spectral power distributions!color response in animals and humans!3D colorspace of the human visual system•and color filter arrays in cameras!reproducing colors using three primaries!additive versus subtractive color mixing!cylindrical color systems used by artists (and Photoshop)!chromaticity diagrams•color temperature and white balancing•standardized color spaces and gamut mapping2! Marc LevoyNewton’s Experimentum Crucis!sunlight can be divided into colors using a prism!these colors cannot be further divided using a 2nd prism !experiment performed 1665, drawing made in 16723Isaac Newton(1643-1727)(Robin)! Marc LevoyNewton’s Experimentum Crucis!alternatively, the divided colors can be recombined using a lens and 2nd prism into a new beam that has exactly the same properties as the original4Isaac Newton(1643-1727)(Robin)! Marc LevoyThe visible light spectrum!wavelengths between 400nm and 700 nm (0.4µ - 0.7µ)!exactly the colors in a rainbow5(wikipedia)! Marc LevoyThe visible light spectrum!wavelengths between 400nm and 700 nm (0.4µ - 0.7µ)!exactly the colors in a rainbow6(Dan Bush)! Marc LevoyThe visible light spectrum!wavelengths between 400nm and 700 nm (0.4µ - 0.7µ)!exactly the colors in a rainbow7(Dan Bush)Rene Descartes,Formation of a Rainbow (1637)! Marc LevoySpectral power distribution (SPD)!units of power are watts (joules per second)!shown here are spectra of common illumination sources!plots above are relative amounts (%) of each wavelength8(LampTech)! Marc LevoyInteraction of light with matter!spectrum of illumination is multiplied wavelength-by-wavelength by reflectance spectrum of object•cause is absorption by the material•so the spectrum you see depends on the illumination!transmittance operates the same way9!=illuminationreflectancestimulus thatenters your eyelight is reflectedby an object! Marc LevoyExamples of reflectance spectra!two different spectra may appear alike to us•white petal and white flower (above left)•these are called metamers!Newton observed this, but could not explain it10•two reflectance spectra that match (i.e. are metamers) under one illuminant may not match under another•clothes that match in the store may not match outdoorsQuestions?! Marc LevoyOutline!spectral power distributions!color response in animals and humans!3D colorspace of the human visual system•and color filter arrays in cameras!reproducing colors using three primaries!additive versus subtractive color mixing!cylindrical color systems used by artists (and Photoshop)!chromaticity diagrams•color temperature and white balancing•standardized color spaces and gamut mapping11☞! Marc Levoy1. organisms having only one kind of retinal receptor cannot distinguish changes in intensity from changes in wavelength, hence they have no color discrimination-for example a unit amount of !1 versus !2 above-or a unit amount of !1 versus half as much of !3(assuming the sensitivity to !3 is twice the response to !1)-example: horseshoe crab12Monochromats(contents of whiteboard)1! Marc Levoy2. this organism can discrimate a response in the range wavelengths covered by A versus B, but cannot discriminate with those ranges3. this organism has color discrimination over the range of wavelengths shown-for each wavelength within this range, the ratio of responses of receptors A and B is unique; hence the organism can identify which wavelength (e.g. !1 or !2) it’s looking at4. this organism has a larger range of color vision-example: dog, horse13Dichromats(contents of whiteboard)432! Marc Levoy5. humans can discrimate wavelengths from 400nm to 700nm-we can also discriminate mixtures of wavelengths that dichromats cannot; this will become clearer later!at the retinal level, our response to light is lineara. if the response to a unit stimulus at !1 of is (!1, "1, #1), and toa unit stimulus at !2 is (!2, "2, #2), then the response to a superposition of stimuli !1 and !2 is (!1 + !2, "1 + "2, #1 + #2)b. the response to n units of a stimulus at !1 is (n !1, n "1, n #1)c. a system that obeys superposition (a) and scaling (b) is linear14Trichromats(contents of whiteboard)5! Marc LevoyHuman response to an arbitrary stimulus!output is three numbers (!, ", #) per area on retina15spectrum of stimulus arriving in one small area on retina spectral sensitivity of each type of cone (L,M,S)multiply wavelength-by-wavelength to get response spectra!"#integrate over wavelengths to gettotal response for that type of cone!="(Berns)! Marc Levoy!stated another way, given a stimulus spectrum Le(!), the human response to it (!, ", #) are the integrals over all visible wavelengths of our responses! Le(!) !(!), Le(!) "(!),! Le(!) #(!)to each constituent wavelength !, i.e.16(!,",#) = Le($)400nm700nm%!($) d$, Le($)400nm700nm%"($) d$, Le($)400nm700nm%#($) d$&'()*+(Berns)Questions?Human response to an arbitrary stimulusLe(!)!(!)"(!)#(!)! Marc LevoyOutline!spectral power distributions!color response in animals and humans!3D colorspace of the human visual system•and color filter arrays in cameras!reproducing colors using three primaries!additive versus subtractive color mixing!cylindrical color systems used by artists (and Photoshop)!chromaticity diagrams•color temperature and white balancing•standardized color spaces and gamut mapping17☞! Marc LevoyHuman 3D colorspace!the three types of cones in our retina (Long, Medium, Short wavelength) define the axes of a three-dimensional space!our response to any stimulus spectrum can be summarized by three numbers (!, ", #) and plotted as a point in this space!our responses to all visible single-wavelength spectra (a.k.a. pure wavelengths !, i.e. positions along the rainbow), if connected together, form a curve in this space, called the locus of spectral colors; the sequence of (!, ", #) numbers form the tristimulus sensitivity functions !($), "($), and #($)18(Flash demo)http://graphics.stanford.edu/courses/cs178/applets/locus.htmlsensitivity functionsspectral locus! Marc Levoy1. our response to any mixture (# = 1) of two pure wavelengths falls on a line connecting the responses to each wavelength2. our response to any mixture (# = 1) of three pure wavelengths falls on a triangle connecting the responses to each wavelength; our response to any mixture (# $ 1) of three pure wavelengths falls in a tetrahedron defined by this