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 additive primaries
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. Mathematical Descriptions of Color
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)
Mixed Wave Lengths
Single Wave Lengths
(400nm to 780 nm)

22. xyY Color Space Pro Con 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. 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)
Gray (black
to white) axis
Black
White

25. RGB Color Space
Back Surfaces
Front Surfaces

26. 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
green +
yellow =

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

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

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

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-Yellow-blacK
RGB
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

51. Hue/Saturation/Lightness
Mapping the RGB cube to a hex-cone

52. Hue/Saturation/Lightness
RGB
Saturation
Lightness

53. Hue/Saturation/Lightness
Pro
Captures the “human” qualities of color
Con
Difficult to describe
Difficult to compute

54. L*a*b* Color Space
While convenient for various reasons, the previous color spaces are not great for comparing colors
Most attempts treat the colors as a 3-vector and try to do some modified Euclidian distance measure and some sort of clustering algorithm
But, the color spaces are non-uniform
La*b* is a uniform color space
A small perturbation in a color component is equally perceptible across the entire range

55. L*a*b* Color Space L*
RGB a* b*

56. L*a*b* Color Space Pro Con Uniform space
Colors can be compared [accurately] using the Euclidian distance formula
Con
Not very intuitive
Not easy to convert from/to RGB
Requires knowledge of a reference white
Requires computation of cube-roots

57. Summary Color is complex
The human visual system is complex and very good at processing light
Together they comprise a system that we aren’t even close to understanding but utilize very effectively