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Colorimetry and prime colours--a theorem.

Hans Petter Hornaes¹, Jan Henrik Wold, Ivar Farup

¹Gjøvik University College, P.O.Box 191, 2802, Gjøvik, Norway.

Journal of Mathematical Biology

|July 14, 2005

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Prime colours, optimal for colour matching, are not unique to human vision. Their existence is an algebraic outcome of how colour-matching functions are defined and transformed, not a biological specific.

Area of Science:

Color science
Visual perception
Mathematical modeling

Background:

Human colour vision involves complex physics and perception.
Light's spectral power distribution is infinite-dimensional, but colour perception is 3D.
Three reference lights can match various colours, leading to the concept of prime colours.

Purpose of the Study:

To demonstrate that prime colours are an algebraic consequence of colour-matching functions.
To show that the existence of prime colours is not exclusive to the human visual system.
To analyze the mathematical conditions for the existence and optimality of prime colours.

Main Methods:

Maximization of a determinant to determine colour gamut size.
Application of Cramer's rule for solving linear equations.

Related Experiment Videos

Algebraic analysis of colour-matching function transformations.

Main Results:

The existence of prime colours is an algebraic consequence of colour-matching functions.
The optimal set of reference lights (prime colours) is not always unique.
Maximizing the determinant is not strictly necessary for prime colours to exist.

Conclusions:

Prime colours are a mathematical property related to colour-matching functions.
The concept of prime colours extends beyond specific biological systems.
Understanding these algebraic properties enhances the theory of colour spaces and matching.