Color

1. Color

2. What is Color? • Color is merely a concept, something we “see” within our minds • It’s interpretation involves both physics and biology • How would you describe the color “red” to a blind person? • Clearly, it plays a useful role in everyday life • Thus, building a mathematical description of color may also prove useful

3. Color is Complex • “Standard” mathematical models began in the early 20th century and have evolved (and evolved, and evolved…) • Confusion arises in that the early standards are not discarded as the evolution takes place • Today, “old” and “new” standards live side by side • Thus, when discussing color the first thing the participants must agree upon is the standard in which they are basing their discussion

4. The Standards • Based on a tristimulus system of additiveprimaries • Tristimulus – three primary colors • Additive – all other colors can be created by adding different proportions of the primaries

5. Preliminaries

6. Tristimulus, Additive Primaries • Red, Green, and Blue primaries were agreed upon based on a normal human visual system • A normal visual system consists of the eyes and sections of the brain, all operating properly • Color blindness is due to a deficiency in one type of cone – very common in males • Red and green receptor genes are carried on the X chromosome, and these are the ones that typically go wrong • Women need two bad X chromosomes to have a deficiency, which is less likely

7. The Eye

8. The Retina • The retina contains two types of light sensors • Rods that are highly sensitive to light and provide us with “night vision” • Located primarily in the outer (non-foveal) region of the retina • Cones that are highly sensitive to color and provide us with “color vision” • Located primarily in the central (foveal) region of the retina • Are adaptive to ambient light • Are susceptible to optical illusions • Color illusion

9. The Retina • There are 3 types of cones contained within the retina • Red-sensitive (long) • Green-sensitive (medium) • Blue-sensitive (short)

10. Cone Sensitivity(probable)

11. The Visual System • Once the eye has sensed the color it is up to the brain to interpret it • This is where things get very complex and relatively little is known about the actual inner-workings

12. The Visual System

13. So What? • With what we know (or think we know) about the visual system, we now try to develop useful models to support the more mundane tasks of everyday life

14. The Standards

15. Standard Observers • To set a standard a group of people were shown color patches of a given size and asked “what colors they saw” • Match color by adjusting primaries • Results were averaged and thus the standards were created

16. Standard Observers • 1931 (2°) and 1964 (10°) standard observers

17. The Color Spaces Mathematical Descriptions of Color

18. CIE Color Spaces • Used primarily for matching/comparing colors • Various different forms of charts • Charts were made using “standard observers” • Groups of people with “normal” color vision • Ties wavelengths to colors • Can specify coordinates to compensate for monitor characteristics • There are numerous versions of the CIE color space based on differing observer parameters and differing basis standards

19. XYZ Color Space (the grand-daddy of them all) • Combine • Known illuminant • Colors on known (non-reflective) material • Standard observer • The result is a tristimulus space for describing colors • XYZ cannot be visualized directly

20. xyY Color Space(the first offspring) • Since there’s no good way to visualize the XYZ color space… • The xyY space is a normalized (projected) version of XYZ • x and y correspond to normalized X and Y respectively (projected onto a plane where the RGB cube is mapped to XYZ space) • The luminance (black/white level) is lost in the normalization process so Y (which is luminance and not the same Y as in XYZ space) in xyY is also computed from XYZ • z is not needed since the normalization process constrains x + y + z = 1

21. xyY Color Space(well, one of them anyway) Planckian (blackbody) Locus Monochromatic (saturated) Colors Monitor Gamut Line of Purples (not monochromatic) Single Wave Lengths (400nm to 780 nm) Mixed Wave Lengths

22. xyY Color Space • Pro • We can visualize the XYZ standard • We can visualize the proximity of one color to another • Con • The space is non-uniform so we cannot use it to compare colors

23. Other Useful Color Spaces • What do we know? • Color spaces should be tristimulus • XYZ and xyY are not very intuitive • We need something to suit our [varied] needs • So, we invent new color spaces

24. Gray (black to white) axis Black White RGB Color Space • RGB is a linear color space • Pure red, green, and blue are the basis vectors for the space • Useful for cameras, monitors, and related manipulations (of light)

25. Back Surfaces Front Surfaces RGB Color Space

26. green yellow + = RGB Operations • Color mixing is performed by vector addition and subtraction operations • Adding/subtracting colors is the same as adding/subtracting vectors (with clamping at 0) red

27. 2 brighter yellow * = RGB Operations • Increasing or decreasing luminance is performed by scalar multiplication • Same as scalar multiplication of vectors (with clamping at some maximum) yellow

28. RGB Operations • A word of caution… • Operations must be clamped… • …at 0 to make sure components don’t go negative • …at some pre-specified maximum to ensure display compatibility • Scaling down from a value greater than the allowed maximum can be performed but care must be taken • Bright colors may end up less bright than other colors in the scene • The answer is to scale ALL colors in the scene which can be expensive

29. Red Green RGB Blue RGB Color Space

30. RGB Color Space • Pro • Very intuitive and easy to manipulate when generating colors • Works well with hardware (light related) • Con • Very unintuitive when it comes to comparing colors • Consider the Euclidian distance between red and green and between green and blue • Bad for some applications

31. Luminance-Chrominance Color Spaces (there are many) • Luminance channel • Corresponds to the black and white signal of a color television • Two chrominance channels • Red and blue • Correspond to the color signal that “rides” on top of the black and white signal of a color television • Various forms • YUV, YIQ, YCbCr, YPbPr…

32. Luminance-Chrominance Color Spaces (there are many) • Luminance is a square wave • Chrominance is a sine wave (modulation) on top of the square wave

33. Simple conversion from RGB and YPbPr And from YPbPr to RGB Luminance-Chrominance Color Spaces (there are many)

34. Luminance Chrominance Blue RGB Chrominance Red Luminance-Chrominance Color Spaces

35. Luminance-Chrominance Color Spaces • Pro • Separate high frequency components from low frequency components • Easy to compute (fast in hardware) • Facilitates image compression (JPEG, MPEG) • Good for various applications (e.g. face detection, shadow detection…) • Con • Not very intuitive • Requires signed, floating point (or scaled) representation • Multiple forms causes confusion (e.g. people regularly confuse YCbCr with YUV)

36. Luminance-Chrominance Color Spaces • Note that there are various different matrices for these conversions • Based on different needs • Be careful about the one you select • Chrominance channels are +/- so to display you must translate and scale

37. Compression(uses for luminance/chrominance) • Trade-off between the amount of data and the quality of the picture • Throw away as much data as possible without degrading the picture • JPEG, MPEG, …

38. JPEG/MPEG • The edge/structure detail is contained in the luminance channel • This is referred to as “high frequency” data • The color information is in the chrominance channels which are lacking edges/structure detail • These are referred to as “low frequency” data

39. Color Image (RGB)

40. Y Channel (high frequency)

41. Cb Channel (low frequency)

42. Cr Channel (low frequency)

43. Subsampling • By subsampling we achieve a 2:1 compression without doing any “work” • This is the default mode for MPEG • The default mode for JPEG is to subsample in 1 dimension only so it’s 3:2 compression without doing any “work” • The decompressed image still looks good because of the low frequency nature of the chrominance channels

44. Subsample Cb and Cr (mpeg mode)

45. MPEG/JPEG • There’s a lot more processing involved but they’re not specific to the chosen color space

46. Cyan-Magenta-Yellow-blacK • Used in printing • Colored pigments (inks) remove color from incident light that is reflected off of the paper • CMYK is a subtractive set of primaries • K (Black) is not actually necessary but is added for practical printing applications • CMYK is a linear color space

47. Cyan Magenta RGB Yellow Black Cyan-Magenta-Yellow-blacK

48. Cyan-Magenta-Yellow-blacK • Pro • Good for printing (as long as you include the K ink) • Con • Difficult to convert from RGB to CMYK as it is not a simple subtraction from white if high accuracy is required

49. Hue/Saturation/Lightness • Also Hue/Saturation/Value or Hue/Saturation/Intensity • Suitable to processing images for “human consumption” (viewing) • Easy to make colors more “vibrant” (and other features that we can name but can’t really describe) • Used in artistic endeavors

50. Hue/Saturation/Lightness • Hue is the pure color content • Corresponds to the edges of the RGB cube • Saturation is the intensity of color • The faces of the RGB cube are fully-saturated • Lightness is the brightness of the color • Ranges from black to white