cs781 - Colour for Computer Graphics - Winter 2012

Course Notes

Lecture 5 - Tristimulus Values

And Now from our Sponsor

The Principle on which the Computer Graphics Use of Colour is Based.

`If the photoreceptors provide the same signal to the brain, the perceptual systems of the brain will provide the same visual experience.'

This principle is made operational by the principle of univariance: `the signal provided by any photoreceptor depends only on the number of photons absorbed.'

Colour Matching & Tristimulus Values

Expressing a colour as a spectral power distribution

Matching the monochromatic colours

Measuring tristimulus values

3D Colour Geometry

We said earlier that the linear algebra Grassmann created includes many colours that cannot be realised physically. We will now invetigate the set of physically possible colours.

The physically realisable colours are a subset of a three dimensional colour space. Construct it as follows:

Then, all physically realisable colours lie in the +++ octant. Why?

Spectral colours

Choose a wavelength in the visible region of the spectrum.

Choose a second wavelength, and draw the line from black through it.

If we continue taking more wavelengths we fill out a `cone' the cross-section of which is determined by the colour matching functions.

The 2D manifold that is the surface of the cone has blue at one end, red at the other.

The gamut of physically realisable colours

This is a volume that is neither easy to draw nor easy to understand.

One things is clear

2D Colour Geometry

Chromaticity coordinates

An increase in brightness increases all tristimulus values by the same amount

We can take out the brightness by doing any transformation that produces values independent of a. The standard transformation, used for a century, is

(x, y) are called the chromaticity coordinates of a colour. The 2D map of chromaticities is called the chromaticity diagram.

The transformation to chromaticity coordinates is a projective transformation, which gives it an attractive property.

Spectrum locus

Where do the spectral colours lie? We can practically read this off the colour matching functions.

This curve is called the spectrum locus; the straight line that closes the curve is called the purple line.

The long straight line from 780nm to 550nm indicates that humans are essentially dichromats for these wavelengths.

Black body curve

The colours emitted by black bodies lie on a curve:

The temperatures of the points on the diagram are

The standard lights Dx are black-body radiators at xK. x is called the colour temperature.

Concepts related to the white point

There is a region of colours called white.

The dominant hue of a chromaticity is the wavelength at which a line from the white point through the chromaticity intersects the spectrum locus.

The excitation purity of a chromaticity is a measure of how far a chromaticity is from the white point.

Return to: