1. 1

2. Possible Color Specification sys
If we were to select and define three particular primaries [R], [B]
and [G],
then the amounts of these
required to match any colour (the tristimulus values R, G and B)
could be used to specify the colour.
Each different colour would have a different set of
tristimulus values,
and with practice we could deduce the appearance of the colour
from the tristimulus values.
Such a system would appear to suffer from several defects,
however. These will be considered below,
together with descriptions of how potential
problems are overcome in the CIE system.
2

3. Use of arbitrarily
chosen primaries
3

4. Arbitrary chosen Primaries
Different results would be obtained by
any two observers
using different sets of primaries.
Sets of tristimulus values obtained using one set of primaries can,
however, be converted to the values
that would have been obtained using a second set,
provided that the amounts of one set of primaries
required to match each primary of
the second set of primaries in turn are known.
Hence either we could insist that
the same set of primaries is always used,
or we could allow the use of different sets,
but insist that the results are converted to those
that would have been obtained using a standard set.
In practice this does not matter, as we will see later.
4

5. 5

6. Inadequacy of real primaries
Even if we use pure colours for our set of primaries, there will still be
some very pure colours
that we cannot match.
 For example, a very pure cyan (blue-green) might be more saturated
than the colours obtained by mixing the blue and green primaries.
Adding the third primary [R] would produce even less saturated mixtures.
A possible solution in this case would be
 to add some of the red primary to the pure cyan colour,
and then match the resultant colour
 using the blue and green primaries (Eqn 3.5):
6

7. Inadequacy of real primaries
In practice, following this procedure allows all colours to be matched
using one set of primaries,
the only restriction in the choice of primaries being that
it must not be possible to match any one of the primaries
using a mixture of the other two.
Rearranging
Eqn 3.5 gives Eqn 3.6:
7

8. Inadequacy of real primaries
Hence the tristimulus values of C are
– R,
B
and G:
that is, one of the tristimulus values is negative.
Negative values are undesirable.
It would be easy to omit the minus sign or fail to notice it.
Careful choice of primaries enables us
to reduce the incidence of negative tristimulus values.
The best primaries are red, green and blue spectrum colours.
Although mixtures of these give the widest possible range of colours,
however, there is no set of real primary colours
that can be used to match all colours using
Positive amounts of the primaries.
In other words, no set of real primaries exists that will eliminate
negative tristimulus values entirely.
8

9. Real and Imaginary primaries
Since it is possible to calculate tristimulus
values for one set of primaries
from those obtained using a second set,
there is no need to restrict ourselves
to a set of real primary colours.
We can use purely imaginary primaries; it is
only necessary that these have been defined
in terms of the three real primaries
being used to actually produce a match.
This is not just a hypothetical possibility.
Negative tristimulus values would be
nuisance in practice
and in the CIE system imaginary primaries are indeed
used so as
to avoid negative values.
It is therefore worth considering this point a
little further.
9

10. 2D Representation of Color
Any two-dimensional representation of colour
 must omit or ignore
some aspect of colour
 and should therefore be treated with caution.
Two-dimensional plots are normally used to represent
the proportions of primaries used
rather than the amounts.
Equal proportions of [R], [G] and [B]
 could look neutral,
 but the mixture
could be very bright or almost invisible
depending on the amounts used.
10

11. 2D Representation of Color
Similarly for surface colours:
a very dark grey and a very light grey would require
 roughly the same proportions of three primary dyes,
 but would require very different amounts.
(Students often confuse proportions and amounts, but the distinction should
always be maintained.)
11

12. 2D Representation of Color
A two-dimensional plot can illustrate the
problem
under discussion, and its solution (Figure 3.3).
Suppose [R], [G] and [B] represent our three
primaries,
and positions on the diagram represent
the proportions of the primaries used
to produce the colour
 corresponding
to the position at any point.
The proportions of the primaries
[R] [G] and B] can be represented by
r, g and b (Eqn 3.7):
12

13. 2D Representation of Color
For example
 the point C,
halfway between [R] and [G],
represents the colour formed by
mixing equal amounts of [R] and [G].
(Actual amounts are not shown on this
plot.)
Thus for C we can say that
r = 0.5,
g = 0.5,
b = 0.
Similarly for
[R] r = 1, b = 0, g = 0.
All points within the triangle [R][G][B] can be
matched using the appropriate proportions
of the primaries.
13

14. 2D Representation of Color
Suppose also that the boundary of real
colours (strictly those real colours
for which r + b + g = 1) is denoted by
the shape [R]N[B]M[G]P[R].
Points within the shaded area correspond to
real colours, but cannot be matched by
positive proportions of the three primaries.
The point M,
for example, might require
r = – 0.2,
b = g = 0.6,
i.e. equal quantities of [B] and [G] together
with a negative amount of [R],
the proportions adding up to unity.
.
14

15. 2d representation
Consider the straight line [B] D[R][X],
where [R][X] = [B][R].
For all points on the line,
g = 0.
For [B], b = 1
and r = 0;
for D, b = 0.5 and r = 0.5; for [R], b = 0 and r = 1,
while for [X] b = –1, r = 2. Thus although [X] is
well outside the boundary of real colours,
its position can be specified simply
and unambiguously using r, b and g.
Points [Y] and [Z] can be defined similarly, and by drawing the triangle [X][Y][Z] we can see
that
all real colours fall within the triangle;
all real colours can be matched using positive proportions of three imaginary primaries
situated at [X], [Y] and [Z] respectively.
Obviously there are many alternative possible positions for [X], [Y] and [Z],
all simply specified and allowing all real colours to be matched
using positive proportions of the primaries.
15

16. Similar argument for 3D Color
If the problem is considered in three dimensions,
the corresponding diagram is much more complicated,
 but the argument is similar.
The volume (rather than the area) corresponding to all real colours is
somewhat larger than
that represented by positive amounts
 (note, amounts not proportions) of any three real primaries.
It is however possible to specify in the three-dimensional space
positions for three imaginary primaries such that
all real colours can be matched
 by positive amounts of the three primaries.
16

17. 17

18. VISUAL Tristimulus colorimeter
the potential problems associated with the
 use of different primaries
 and with the use of negative amounts of primaries,
 can be overcome (as indeed they are in the CIE system).
We also have to consider
how a sample could actually be measured,
or how a specification could be arrived at.
We seem to be required to produce a visual match, i.e. to use
an instrumental arrangement whereby we may adjust the amounts of three
suitable primaries (mixed additively)
until in our judgement a mixture is obtained
that matches the colour to be measured
or specified.
Such an instrument is called a visual tristimulus colorimeter.
18

19. Problems lying in the precision
The amounts of the primaries required could be noted, and the results
converted to
the equivalent values for a standard set of primaries.
A procedure like this is perfectly possible, the main problem lying in the
precision and accuracy achievable.
The results will vary from one observer to another
because of differences between eyes.
Even for one observer repeat measurements will not be very satisfactory.
Under the controlled conditions necessary in such an instrumental
arrangement
(usually one eye, small field of view and low level of illumination)
it is impossible to achieve the precision of unaided eyes under normal
conditions,
for example, when judging whether a colour difference exists
between two adjacent panels on a car body under good daylight.
19

20. Metameric problems
the matches in the instrumental arrangement being considered are
likely to be highly metameric (physically quite different)
and this gives rise to many of the problems.
The widest range of colours can be matched using primaries each
corresponding
to a single wavelength.
If three such primaries are used to match a colour
consisting of approximately equal quantities of all wavelengths
in the visible spectrum,
the two colours are physically very different
even though they look the same to the observer.
20

21. Observer eye problem minimization
Not surprisingly it turns out that
such a pair of colours is unlikely to match
for a second observer.
Even for one observer, the differences between the different parts of
his eyes are likely to cause problems .
These problems can be minimised by
using a small (<2 ) field of view,
but then the precision of matching is reduced by a factor of about 5,
compared with that obtained using a 10 field of view.
Some of these problems can be overcome by using more than three primaries
(as in the Donaldson six-filter colorimeter .
Using more primaries allows a wide range of colours to be matched even when
the primaries are not monochromatic.
The degree of metamerism can be greatly reduced and a large field of view can
be used.
21