CSCE441: Computer Graphics: Color Models Jinxiang Chai

1. CSCE441: Computer Graphics:Color Models Jinxiang Chai

2. 3D Rendering pipeline Modeling transformation Transform into 3D world system Illuminate according to lighting and reflectance lighting Transform into 3D camera coordinate system Viewing transformation Transform into 2D camera system Project transformation Clip primitives outside camera’s view Clipping Draw pixels (includes texturing, hidden surface, etc.) Scan conversion Image

3. 3D Rendering pipeline Modeling transformation Transform into 3D world system Illuminate according to lighting and reflectance lighting Transform into 3D camera coordinate system Viewing transformation Transform into 2D camera system Project transformation Clip primitives outside camera’s view Clipping Draw pixels (includes texturing, hidden surface, etc.) Scan conversion Image

4. Light and Colors • How to describe light color? • Why the same object appears different color under different light? • How to model the color of reflected light? • Why do we RGB to define the color? (255,255,255)

5. Outline • Color Models • Required readings: HB 19-1 to 19-8

6. Human Vision Model of human vision • Vision components: • Incoming light • Human eye Color/light is electromagnetic radiation within a narrow frequency band!

7. Electromagnetic Spectrum Visible light frequencies range between: • Red: 3.8x1014 hertz (780nm) • Violet: 7.9x1014 hertz (380nm)

8. Visible Light The human eye can see “visible” light in the frequency between 380nm-780nm red violet

9. Visible Light The human eye can see “visible” light in the frequency between 380nm-780nm 380nm 780nm

10. Visible Light The human eye can see “visible” light in the frequency between 380nm-780nm 380nm 780nm • Each frequency value between 380nm-780nm corresponds to a distinct spectral color • Not strict boundary • Some colors are absent (brown, pink)

11. Spectral Energy Distribution A light source emits all frequencies within the visible range to produce white light Three different types of lights

12. Perception of Object Colors • Why does the same object appear different color under different light?

13. Perception of Object Colors • When light is incident upon an object, some frequencies are reflected and some are absorbed. • The combination of frequencies present in the reflected light determines what we perceive as the color of the object. Incoming color light Surface reflectance property Perceived object color

14. Questions • Why does some object appear black under sunlight? • How does the white object appear lit only by blue light? • How does the red object appear lit only by blue light?

15. Questions • Why does some object appear black under sunlight? Absorb all the frequencies • How does the white object appear lit only by blue light? “blue” • How does the red object appear lit only by blue light? “black”

16. Spectral Energy Distribution Three different types of lights Can we use spectral energy distribution to represent color?

17. Spectral Energy Distribution Three different types of lights Can we use spectral energy distribution to represent color? - Not really, different distribution might result in the same color (metamers)!

18. Spectral Energy Distribution The six spectra below look the same purple to normal color-vision people

19. Ideal Color Representation • Unique – one to one mapping • Compact – require minimal number of bits. • General – represent all the visible light. • Perceptually appropriate – tell us hue, luminance, purity of color.

20. Hue, Brightness & Purity • Hue: the color of the light corresponding to the dominant frequency of the color • Brightness corresponds to the total light energy and can be quantified as the luminance of the light • Purity (or saturation): describes how close a color appears to be a pure spectral color, such as red

21. Color Representation? So how to represent color? 380nm 780nm

22. Human Vision Photoreceptor cells in the retina: - Rods - Cones

23. Light Detection: Rods and Cones Rods: -120 million rods in retina -1000X more light sensitive than Cones - Discriminate B/W brightness in low illumination - Short wave-length sensitive Cons: - 6-7 million Cones in the retina - Responsible for high-resolution vision - Discriminate Colors - Three types of color sensors (64% red, 32%, 2% blue) - Sensitive to any combination of three colors

24. Tristimulus of Color Theory Spectral-response functions of each of the three types of cones

25. Tristimulus of Color Theory Spectral-response functions of each of the three types of cones Color matching function based on RGB - any spectral color can be represented as a linear combination of these primary colors R B G Ctarget=R*Cr+ G*Cg+B*Cb

26. Tristimulus of Color Theory Spectral-response functions of each of the three types of cones Color matching function based on RGB - any spectral color can be represented as a linear combination of these primary colors Negative weight for red! Ctarget+R*Cr=B*Cb + G*Cg

27. Tristimulus Color Theory So, color is psychological - Representing color as a linear combination of red, green, and blue is related to cones, not physics - Most people have the same cones, but there are some people who don’t – the sky might not look blue to them (although they will call it “blue” nonetheless)

28. Additive and Subtractive Color Normalized weights: between 0 and 1 RGB color model CMY color model White: [0 0 0]T Green: [1 0 1]; White: [1 1 1]T Green: [0 1 0]; Complementary color models: R=1-C; G = 1-M; B=1-Y;

29. RGB Color Space blue green red

30. RGB Color Space blue White (1,1,1) green red

31. RGB Color Space blue magenta (1,0,1) green red

32. RGB Color Space blue magenta (1,0,1) green red RGB cube • Easy for devices • Can represent all the colors? No • But not perceptual • Where is brightness, hue and saturation?

33. Tristimulus • Since 3 different cones, the space of colors is 3-dimensional. • We need a way to describe color within this 3 dimensional space. • No finite set of light sources can be combined to display all possible colors. • We want something that will let us describe any visible color with additive combination of three primary (imaginary) colors!

34. The CIE XYZ system • CIE – Comission Internationale de l’Eclairage - International Commission on Illumination - Sets international standards related to light • Defined the XYZ color system as an international standard in 1931 • X, Y, and Z are three Primary colors. - imaginary colors - all visible colors can be defined as an additive combination of these three colors. - The weights to combine three primary colors defines the 3 dimensional color space

35. Color Matching Functions • Given an input spectrum, , we want to find the X, Y, Z coordinates for that color. • Color matching functions, , , and tell how to weigh the spectrum Image taken from http://upload.wikimedia.org/wikipedia/commons/8/87/CIE1931_XYZCMF.png

36. XYZ space • Any color can be represented in the XYZ space as an additive combination of three primary colors

37. XYZ space • The visible colors form a “cone” in XYZ space. • For visible colors, X, Y, Z are all positive. • But, Cx, Cy, and Cz themselves are not visible colors! Image taken from http://fourier.eng.hmc.edu/e180/handouts/color1/node27.html

38. Luminance and Chromaticity • The intensity (luminance) is just X+Y+Z. • Scaling X, Y, Z just increases intensity. • We can separate this from the remaining part, chromaticity. • Color = Luminance + Chromaticity (Hue & purity) • Chromaticity is 2D, Luminance is 1D • To help us understand chromaticity, we’ll fix intensity to the X+Y+Z=1 plane.

39. Chromaticity Diagram • Project the X+Y+Z=1 slice along the Z-axis • Chromaticity is given by the x, y coordinates Image taken from http://fourier.eng.hmc.edu/e180/handouts/color1/node27.html

40. Functions of Chromaticity Diagram • Determining purity and hue (dominant wave length) for a given color • Identify complementary colors • Compare color gamuts generated by different primaries Image taken from http://fourier.eng.hmc.edu/e180/handouts/color1/node27.html

41. White Point • White: at the center of the diagram. • Approximation of average daylight Image taken from http://fourier.eng.hmc.edu/e180/handouts/color1/node27.html

42. Spectral Color • Where is visible color? 380nm 780nm

43. Spectral Colors • Visible Spectrum along outside curve Image taken from http://fourier.eng.hmc.edu/e180/handouts/color1/node27.html

44. Spectral Colors • Visible Spectrum along outside curve But this is not Spectral color! Image taken from http://fourier.eng.hmc.edu/e180/handouts/color1/node27.html

45. Saturation/Purity • As you move on line from white to edge, you increase the saturation of that color. • Royal blue, red: high saturation • Carolina blue, pink: low saturation Image taken from http://fourier.eng.hmc.edu/e180/handouts/color1/node27.html

46. Saturation/Purity • How to compute the purity of this color? C B - The ratio between dAB and dAC A Image taken from http://fourier.eng.hmc.edu/e180/handouts/color1/node27.html

47. Hue • Hue is the “direction” from white. • Combined with saturation, it gives another way to describe color • Also called dominant wavelength Image taken from http://fourier.eng.hmc.edu/e180/handouts/color1/node27.html

48. Hue • What’s the dominant wavelength of this color? Image taken from http://fourier.eng.hmc.edu/e180/handouts/color1/node27.html

49. Hue • What’s the dominant wavelength of this color? • What’s the purity? Image taken from http://fourier.eng.hmc.edu/e180/handouts/color1/node27.html

50. Hue • What’s the dominant wavelength of this color? Image taken from http://fourier.eng.hmc.edu/e180/handouts/color1/node27.html