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  1. H331: Computer Graphics http://www.cs.kuleuven.ac.be/~graphics/H331/Philip Dutré Department of Computer Science Wednesday, April 30

  2. Today • Color & Perception • Chapter 12

  3. Shading … 5 10 27 n = 3 200 0.1 0.25 ks = 0.5 (by David Kurlander, Columbia University)

  4. Shading • Repeat shading formula for each color channel red, green, blue • R,G,B “works”, because most output devices use R,G,B phosphors

  5. Color in CG • How are colors described in numerical terms? • How do the numbers correspond to daily descriptions of colors? • How are colors compared? • What range of colors can we display on an output device? • …

  6. Color in CG • How can a color be reproduced on a TV screen, using only 3 phosphors? R,G,B ? (PCG-Cornell University)

  7. Color in CG • How can a color be reproduced on a printer, using only 3 inks? CMY ? (PCG-Cornell University)

  8. What is color? • Light = electro-magnetic waves • Visible spectrum • 400 nm (violet)  700 nm (red) wavelength

  9. Power Power 400 Wavelength (nm) 700 400 Wavelength (nm) 700 D55: typical sunlight D65: typical average daylight D75: typical ‘north-sky’ light Power distributions of light sources Test lamp CIE standard (PCG-Cornell University)

  10. Reflectance distributions (PCG-Cornell University)

  11. Reflected spectrum Source Spectrum Product Reflectance Spectrum ? X (PCG-Cornell University)

  12. Fovea gaze Optical center Blind Spot Human eye (PCG-Cornell University)

  13. Human eye: retina Light passes through blood vessels & retinal layers before reaching rods & cones (PCG-Cornell University)

  14. Human eye: rods and cones Rods,Cones in Foveola (PCG-Cornell University)

  15. Human eye: rods and cones • Cones: color-sensitive cells • 3 types, respond to particular ‘color’ • ~6M cones in human eye • Rods • Sensitive to low levels of light • (colors disappear when it’s dark)

  16. Cone responses • S,M,L cones • Each type of cone is sensitive to a specific spectrum of light • Trichromatic visual system (PCG-Cornell University)

  17. P l 400 700 Trichromacy X This is what we ‘see’ S,M,L

  18. P l 400 700 Color metamers • Metamers produce the same visual sensation S1,M1,L1 X = P S2,M2,L2 X l 400 700

  19. Advantage of metamers: • Color on a monitor produces the same visual sensation as the ‘real’ color (PCG-Cornell University)

  20. How to describe colors? • Basic idea: describe a specific power spectrum P(l) that produces the visual sensation of the desired color

  21. Color Matching • Experiment: match a sample light with 3 test lights C(l) B(l) sample lamp S(l) A(l) observer

  22. Color Matching • Adjust intensity of 3 test lights, such that we have metamers: S(l) = aA(l) + bB(l) + cC(l) (read as: ‘are metamers’)

  23. Color Algebra • If (S(l) = P(l)) then (S(l)+N(l) = P(l)+N(l)) • If (S(l) = P(l)) then (aS(l) = aP(l))

  24. Color Matching • Color perception is 3-dimensional • S,M,L responses •  3 test lights R(l), G(l), B(l) • Think “red, “green, “blue” • Chosen because of cone responses • Any color C(l): C(l) = rR(l) + gG(l) + bB(l)

  25. 700 nm 546 nm Pure spectral Light (single wavelength) 438 nm observer Color Matching mono(l) = r(700 nm) + g(546 nm) + b(438 nm)

  26. 700 nm 546 nm Orange (600 nm) 438 nm observer Color Matching (600 nm) = 0.37(700 nm) + 0.08(546 nm) + 0.0(438 nm)

  27. Color Matching mono(l) = r(700 nm) + g(546 nm) + b(438 nm) Or … mono(l) = r (l) (700 nm) + g (l) (546 nm) + b (l) (438 nm) Color matching functions Normalization:

  28. Color Matching functions (PCG-Cornell University)

  29. Color Matching functions • Negative values? spectral light 700 nm 546 nm 438 nm observer

  30. Summary so far • We have 3 test lights: • 3 because color perception is 3-D (S,M,L) • Chosen in red, green, blue wavelengths • Every pure spectral color (power = 1): Color matching functions, can be negative

  31. So … • Any color with spectrum C(l):

  32. C l 400 700 So… r,g,b X

  33. Problems • Negative values! • Which R,G,B to choose? • Different R,G,B produce different color matching functions • Answer: CIE XYZ standardized color system

  34. XYZ color matching functions • 3 matching functions are chosen: • All positive • Computational convenience • standardized (PCG-Cornell University)

  35. C l 400 700 XYZ color matching functions x,y,z X

  36. XYZ color matching functions • X, Y, Z are NOT physical lights, they are defined only by their color matching functions • There is no color with x=1, y=0, z=0

  37. “Real” colors in RGB and XYZ (PCG-Cornell University)

  38. Chromaticity Diagram (PCG-Cornell University)

  39. Chromaticity Diagram

  40. I J K Chromaticity Diagram

  41. Monitor • Monitors have 3 types of phospors 0.012 Typical CRT 0.01 0.008 0.006 “B” Spectral Power (watts/m2) “G” 0.004 “R” “R” 0.002 0 350 400 450 500 550 600 650 700 750 λ(wavelength in nm) (PCG-Cornell University)

  42. Monitor color gamut • Not all colors are possible on a CRT • Chromaticity coordinates for each phosphor are different for each monitor

  43. Monitor • If you want to work correctly … • Compute everything in spectral space • Convert spectrum to XYZ • Convert XYZ to RGB (display device dependent) • Display RGB on device

  44. XYZ  RGB? • Find the XYZ coordinates of the primaries R, G, B: • Xr, Yr, Zr • Xg, Yg, Zg • Xb, Yb, Zb • Write color as linear combination in XYZ space • Same linear combination applies in RGB space

  45. XYZ  RGB? Example

  46. Interpolation in color space • for anti-aliasing • for Gouraud shading • for blending two images (fade-in, fade-out) • RGB, CIE: (affine transformation)straight lines  straight linessame interpolation results