CS781 - Colour for Computer Graphics - Winter 2009

Lecture 8

Visual Response to Light

Colour Matching Functions

Metamerism

Light Metamerism

Many to one transformation

Evolution says:

• Colour differences that matter are likely to be discriminable
• This is a statement about surfaces
• The colour of an object is the colour of its surface
  • Note the difference between transparence/translucence and whiteness/opacity

Illuminant Metamerism

Hold the surface constant

Surface Matemerism

Hold the illuminant constant

Geometric Representations of Colour

Special Properties of the Spectral Colours

Colours in the rainbow/spectrum = Colours of monochromatic lights

• call them spectral colours

Mix a spectral colour and white

• Move along a straight line in colour space
  • Why straight?
• As white decreases we get to a point where we can't go any farther

Mix the same spectral colour with any other colour

• Arrive at the same point

Remove a little of the spectral colour

• Do the same.
• Arrive at a point joining the first point to the origin

Choose another spectral colour

• In fact, just use the spectral colours to do this for all spectral colours
• The result is a curve that delimits a cone

Convex Hull of the Spectral Colours

This is the set of physically realisable colours

• The purple line

Chromaticity Coordinates

The two meanings of `colour' when we say, `the same colour.'

1. Unique hue, saturation and brightness
   • Note ambiguity of `bright'
   • Intensity might be better than brightness
2. Unique hue and saturation

Remember (?) projective geometry

• If we treat all points on a line through the origin as a single point,
  • on a sphere for example
  • we get a projective space of one lower dimension
• Attractive because straight lines go to straight lines

Consider the projection

• x = X / (X + Y + Z)

  y = Y / (X + Y + Z)

  z = Z / (X + Y + Z)

• Then x + y + z = 1
  • We are projecting onto the (1,1,1) plane.
• Plot (x,y)
  • We are projecting the (1,1,1) plane to the (1,1,0) plane by dropping the z-coordinate

The resulting planar representation of colour is called `chromaticity coordinates'

• The chromaticity of a colour is its hue and saturation with brightness ignored
• Because additive mixture of two colours in colour space is convex combination
  • additive mixture of two colours in chromaticity coordinates is convex combination

It is pretty well impossible to make a true colour picture of the chromaticity diagram

• Why?

Concepts from chromaticity coordinates

The white point

The purple line

Dominant hue

• also dominant wavelength
• relative to a white point

Excitation purity

• also relative to a white point

Colour Temperature

• the black body curve

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