Page 40 - Computational Colour Science Using MATLAB

4

Computing CIE Tristimulus Values

4.1 Introduction

In the reproduction of colour and coloured images, trained experts known as
colourists have traditionally been responsible for the assessment of the colour
appearance of the colour match (Rich, 2002). Although this approach worked well
for many years, in today’s fast-moving global workplace more objective methods
are required. Colorimetry attempts to capture the essence of colour perception and
provides an objective procedure for accurate colour matching and reproduction.
Tristimulus values are the basis of colorimetry and their accurate calculation is
highly desired by industry for a wide range of applications. In order to compute the
tristimulus values for a surface that is defined by a set of spectral reflectance values
it is necessary to specify an illuminant and a set of colour-matching functions. The
spectral reflectance values, the relative energy of the illuminant and the colour-
matching functions must be multiplied together at each wavelength and then
summed. In some cases the surface is specified at a wavelength interval that is
smaller or larger than the wavelength interval of the illuminant data or the colour-
matching functions. This chapter reviews methods for computing tristimulus values
from spectral reflectance data and considers the use of interpolation and
extrapolation where appropriate.

4.2 Standard colour-matching functions

The CIE (see Chapter 1, Section 1.3 for a brief review) originally defined the
tristimulus values in terms of an integration over wavelength l, thus:

R
X ¼ k EðlÞPðlÞxðlÞdl,
R
Y ¼ k EðlÞPðlÞyðlÞdl, ð4:1Þ
R
Z ¼ k EðlÞPðlÞzðlÞdl,

Computational Colour Science Using MATLAB. By Stephen Westland and Caterina Ripamonti.
& 2004 John Wiley & Sons, Ltd: ISBN 0 470 84562 7