Chapter 6: Color

1. Chapter 6: Color Preview 。The world is colorless 。Color is caused by the vision system (dominated by the visual cortex) responding differently to different wavelengths of light Macro-structure Ordered Feature Map Cortex:

2. visual cortex Micro-structure auditory cortex Auditory cortex: tonotopic map Visual cortex: retinotectal map Hippocampal cortex: geographic map Somatosensory cortex: somatic map 6.1 Physics of Color A color we perceive is resulting from (a) the color of object surface (b) the colors of light sources

3. 6.1.1 Colored Lights ○ Spectral (wavelength) units (quantities) -- Units with the phrase “per unit wavelength” e.g., Spectral radiance Spectral irradiance Spectral BRDF Spectral exitance

4. 6.1.2 The Colors of Sources ○ Black body: absorbs light without reflection The distribution of spectral radiation where T : color temperature, h : Plank’s constant k : Boltzmann’s constant c : speed of light, : wavelength

5. ○ Sun – a distant bright point source • Light from the sun • strikes a surface and is reflected into camera or eye (sunlight/daylight) • (ii) is scattered by the air, strikes a surface, and is reflected into camera or eye (airlight/skylight) Airlight (skylight) Sunlight (daylight)

6. ○ Sky: (a) Crude geometrical model -- a hemisphere with constant exitance However, sky is substantially brighter at the horizon than at the zenith because a viewing ray along the horizon passes through more sky (b) Natural model – air emits a constant amount of light per unit volume

7. ○ Illumination during the day by: (a) Sunlight, (b) Airlight wavelength

8. ○ Application – Dehazing

9. An image is contributed by two light sources I = D + A, where D: direct light, A: airlight

10. Direct light: the light emitted from the object and passes through the air x : image pixel; z: object distance J(x) : light emitted from object surface t(z) : atmosphere transmittance scatter function

11. Airlight A: the amount of light within the conical volume

15. ○ (a)Light of a long wavelength can travel farther than light of a short wavelength (Rayleigh scattering) atmosphere (b) The sun looks yellow; the sky looks blue (c) The intensity of spectral radiation scattered by a unit volume of air depends on the 4th power of frequency, i.e.,

16. ○ Application -Shadow Detection Cast shadows Shadow Self shadows

17. Input Background Foreground • Intensity test-- a shadow area should be darker • than its corresponding background areas Dark regions

18. (2)Blue ratio test -- distinguishes between dark and shadow areas Non-shadow area Shadow areas

19. Let p bea shadow point. (needs to be proven)

20. Dark regions Shadow areas (3) Reflectance test -- distinguishes between cast and self shadows Non-shadow image area Shadow image areas

21. Normalization: Training of different materials Cast shadows Self shadows

22. ○ Artificial Illuminants Incandescent light: metal filament (e.g., tungsten) is heated to a high temperature Fluorescent light: high speed electrons strike gas; gas releases ultravioletradiation; the radiation causes phosphorsto fluoresce Arc lamp: contains gaseous metal (e.g., mercury) and inert gases; light is produced by electrons in metal atoms dropping from an excite state to a lower energy state

24. 6.1.3 The Color of Surfaces ○ Spectral reflectance

25. 6.2 Human Color Perception ○ Types of photoreceptors: Rod : sensitive to light Cone: sensitive to color Types of cone: S (blue) – short wavelength light M (green) – medium wavelength light L (red) – long wavelength light

26. ○ Principle of Uni-Variance -- Receptors respond strongly or weakly, but do not signal the wavelength of the light falling on them The response of the kth type of receptor

27. 6.2.1 Color Matching -- is to figure out how a color is composed of primaries Two ways of color matching: Additive matching, Subtractive matching ○ Additive matching

28. ○ Subtractive matching For some colors, their may be negative. Subtractive matching adds some amount of some primaries to the test light. ○ Principle of Trichromacy (1) The primaries must be independent (2) Both additive and subtractive matching are allowed 6.3 Representing Color Unit radiance source: : primaries : color matching function

29. Single wavelength source: Source:

30. ○ Grassman’s Laws -- matching is linear

31. ○ Color Matching Function 。 RGB Color Space R,G,B are real primaries Color matching functions may be negative 。 CIE XYZ Color Space CIE: Commission International D’eclairage X,Y,Z are not real primaries Color matching functions are positive everywhere

32. Definitions:

33. 6.3.1 Linear Color Spaces -- A color lies on a straight line connecting two colors. The color can be formed by a linear combination of the two colors -- A color lies on a planar patch formed by connecting three colors. The color can be formed by a linear combination of the three colors

34. ○ RGB Color Space R: 645.16 nm, G: 526.32nm, B: 444.44nm ○ YIQ color space

35. ○ YUV color space ○ CIE XYZ Color Space The volume of visible colors in the XYZ space is a cone whose vertex is at the origin

36. 。The relationship between RGB and XYZ

37. 。CIE xy Space -- The space results from intersecting the XYZ space with plane Chromaticity Diagram

38. Spectral locus: the curved boundary along • which the colors are experienced • (ii) Neutral point: the color whose weights are • equal for all three primaries • (iii) Colors that lie • farther away • from the neutral • point are more • saturated

39. ○ CMY -- primaries of pigments Cyan = White – Red, Magenta = White – Green, Yellow = White – Blue 。A pigmentremoves the colors other than the pigment color from the incident light, which is then reflected from surface e.g., Red ink removes green and blue lights; red light passes through the ink and is reflected from the paper

40. 6.3.2 Nonlinear Color Spaces -- The coordinates of a color in a linear space may not encode properties that are familiar to human ○ HSI Space: Hue, Saturation, Intensity if

42. ○ Lu*v* color space

45. ○ Uniform Color Space 。 Noticeable difference – the difference when modifying a color until one can tell it has changed. The noticeable difference of a color forms the boundary of the color and can be fitted with an ellipse (macadam ellipse) 。 The color difference in the CIE xy space is poor (a) the ellipses at the top are larger than those at the bottom (b) the ellipses rotate as they move up

46. CIE u’v’ Space – a more uniform space than CIE xy space

47. ○ La*b* color space is a substantial uniform space

48. 6.3.3 Spatial and Temporal Effects ○ Chromatic adaptation – the color system adapts (the color diagram is skewed) when the visual system has been exposed to an illuminant for some time Assimilation– the surrounding colors of a color cause the color to move toward the surrounding colors Contrast-- the surrounding colors of a color cause the color to move away from the surrounding colors

49. 6.4 Surface Color from Image Color Image color depends on (a) Camera (b) Physical effects (i) The color of object surface (ii) The colors of light sources

50. ○ Cameras 。A color camera contains an imaging device that is composed of a set of sensory elements CCD (charge coupled device) 。EachCCDcontains one of three filters, each realizing a spectral sensitivity function(SSF) 。 In terms of SSF, CCDs are arranged in a mosaic with a particular pattern, called the Bayer pattern 。Gamma correctionis a form of compression for compressing the incoming dynamic range e.g., , where I: intensity