Page 69 - Computational Colour Science Using MATLAB

56 COMPUTING COLOUR DIFFERENCE
The subscript S,asin C , denotes that the terms S , S , S , F and T are
C
H
L
S
computed using the CIELAB lightness, chroma and hue angle (in degrees) of the
standard. The terms S , S and S define the lengths of the semi-axes of the
L
C
H
tolerance ellipsoid at the position of the standard in CIELAB space in each of the
three directions (S for lightness, S for chroma and S for hue). The ellipsoids
H
C
L
were fitted to visual tolerances determined from psychophysical experiments and
the semi-axes in the CMC(l:c) formula are used to effectively convert these
ellipsoids into spheres at each point in CIELAB space. The parametric terms l
and c constitute an important feature of the formula. These parameters allow the
relative tolerances of the lightness and chroma components to be modified. For
the textile industry it was recommended that l ¼ c ¼ 1 for perceptibility decisions,
whereas for acceptability decisions it was recommended that l ¼ 2 with c ¼ 1. The
reason for this difference is that it is considered that, in terms of acceptability,
differences in lightness should be weighted to be half as important as differences
in either chroma or hue. The CMC(l:c) formula has been widely used in a
number of industries and was adopted, for example, as a British Standard
(BS 6923) and an AATCC test method (AATCC 173). However, it was never
adopted as a CIE standard.

5.4.2 CIE94

Berns (2000) and others argued that the complexity of the CMC equation and
the use of large numbers of significant figures in its definition suggest a degree of
precision that cannot be supported on statistical grounds. Detailed analyses of
large sets of psychophysical data suggested that simple S , S and S weighting
L
C
H
functions would be sufficient and this led to the publication of a new formula
known as CIE94 (Berns, 1993). The CIE94 formula is given by
2 2 2 1=2
94
DE* ¼½ðDL*=ðk L S L ÞÞ þðDC* ab =ðk C S C ÞÞ þðDH* ab =k C S H Þ Š , ð5:15Þ
where

S L ¼ 1,
S C ¼ 1 þ 0:045C* ab,S ,
S H ¼ 1 þ 0.015C* ab,S .

The parametric variables k , k and k are all set to unity and the values of S C
L
H
C
and S are computed using the CIELAB values of the standard. When neither
H
sample can logically be deemed a standard, the geometric mean of the two
samples should be used.