Color I trichromatic theory CS 178 Spring 2011 Marc Levoy Computer Science Department Stanford University Outline 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 mapping 2 Marc Levoy Newton s Experimentum Crucis Isaac Newton 1643 1727 Robin 3 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 1672 Marc Levoy Newton s Experimentum Crucis Robin Isaac Newton 1643 1727 4 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 original Marc Levoy The visible light spectrum wikipedia 5 wavelengths between 400nm and 700 nm 0 4 0 7 exactly the colors in a rainbow Marc Levoy The visible light spectrum Dan Bush 6 wavelengths between 400nm and 700 nm 0 4 0 7 exactly the colors in a rainbow Marc Levoy The visible light spectrum Rene Descartes Formation of a Rainbow 1637 Dan Bush 7 wavelengths between 400nm and 700 nm 0 4 0 7 exactly the colors in a rainbow Marc Levoy Spectral power distribution SPD LampTech 8 units of power are watts joules per second shown here are spectra of common illumination sources plots above are relative amounts of each wavelength Marc Levoy Interaction of light with matter light is reflected by an object illumination reflectance stimulus that enters your eye spectrum of illumination is multiplied wavelength bywavelength by reflectance spectrum of object cause is absorption by the material so the spectrum you see depends on the illumination 9 transmittance operates the same way Marc Levoy Examples of reflectance spectra 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 outdoors Que s t ions two different spectra may appear alike to us white petal and white flower above left these are called metamers 10 Newton observed this but could not explain it Marc Levoy Outline 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 mapping 11 Marc Levoy Monochromats contents of whiteboard 1 1 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 crab 12 Marc Levoy Dichromats contents of whiteboard 2 3 4 2 this organism can discrimate a response in the range wavelengths covered by A versus B but cannot discriminate with those ranges 3 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 at 4 this organism has a larger range of color vision 13 example dog horse Marc Levoy Trichromats contents of whiteboard 5 5 humans can discrimate wavelengths from 400nm to 700nm we can also discriminate mixtures of wavelengths that dichromats cannot this will become clearer later 14 at the retinal level our response to light is linear a if the response to a unit stimulus at 1 of is 1 1 1 and to a 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 linear Marc Levoy Human response to an arbitrary stimulus Berns spectrum of stimulus arriving in one small area on retina spectral sensitivity of each type of cone L M S multiply wavelength bywavelength to get response spectra integrate over wavelengths to get total response for that type of cone 15 output is three numbers per area on retina Marc Levoy Human response to an arbitrary stimulus 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 Berns Le 700nm 700nm 700nm Le d Le d Le d 400nm 400nm 400nm 16 Que s t ions Marc Levoy Outline 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 mapping 17 Marc Levoy Human 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 Flash demo http graphics stanford edu courses cs178 applets locus html sensitivity functions 18 spectral locus Marc Levoy Properties of human 3D colorspace 1 of 2 contents of whiteboard 1 2 3 1 our response to any mixture 1 of two pure wavelengths falls on a line connecting the responses to each wavelength 2 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 triangle and the origin 19 3 our responses to all possible mixtures 1 of all visible wavelengths forms an irregular volume called the gamut of perceivable colors equal to the convex hull of the spectral locus Marc Levoy Properties of human 3D colorspace 2 of 2 contents of