Page 66 - Computational Colour Science Using MATLAB

CIELAB COLOUR DIFFERENCE 53
(L* ¼ a* ¼ b* ¼ 0) is 100 DE* units, whereas industrial tolerances usually are
ab
about 1.0 CIELAB units.
If we imagine DE* to be computed from polar coordinates, then we could
ab
write an equivalent equation in terms of DL*, DC* and DH* ,
ab
ab
2 2 2 1=2
DE* ab ¼½ðDL*Þ þðDC* ab Þ þðDH* ab Þ Š , ð5:11Þ
where DH* is the difference in hue that is both commensurate with the other
ab
variables of CIELAB colour difference and orthogonal to both DL* and DC* .
ab
Whereas the other terms are computed as simple differences (DC* is simply the
difference between C* of the standard and the trial) DH* is defined by equating
ab
Equations (5.10) and (5.11) to yield the algebraic expression given as Equation
(5.12) (Smith, 1997). Thus,

2 2 2 1=2
DH* ab ¼½ðDE* ab Þ ðDL*Þ ðDC* ab Þ Š ð5.12Þ
or simply

2 2 2 1=2
.
DH* ab ¼½ðDa*Þ þðDb*Þ ðDC* ab Þ Š
Sometimes an alternative method is used to compute a hue difference as given by
Equation (5.13),

DH* ab ¼ C* ab Dh ab ðp=180Þ, ð5.13Þ

where the term p/180 converts the difference in hue angle Dh ab into radians.
However, Smith (1997) notes that this method is only applicable for small colour
differences away from the achromatic axis and prefers Equation (5.12) which is
more generally applicable.
Normally when a colour difference is computed between two samples one of
the samples is regarded as the standard and the other as the trial or batch. The
components of the colour difference therefore have a positive or negative sign
and are computed as, for example, the chroma of the trial minus the chroma of
the standard. Thus, if DC* 4 0, then the trial is stronger than the standard,
ab
whereas if DC* 5 0, then the trial is weaker than the standard. Similarly, the
ab
trial can be lighter or darker than the standard depending upon the sign of the
DL* component. However, the definition of the hue component of colour
difference as in Equation (5.12) leads to some ambiguity in the sign of DH* .By
ab
convention, it is to be regarded as positive if it indicates that in terms of hue the
trial is anticlockwise from the standard and negative if it is clockwise.
The signs of the colour-difference components are most useful in determining
colour-difference descriptors between a trial and a standard. Whereas the
determination that the trial is either stronger or weaker and lighter or darker
than the standard derives simply from the sign of DL* or DC* , the
ab
determination of hue difference descriptors is more complicated. The CIE