1

A POSSIBLE COLOUR SPECIFICATION

SYSTEM

2

Possible Color Specification sysIf 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 oftristimulus 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 potentialproblems are overcome in the CIE system.

3

Use of arbitrarily chosen primaries

4

Arbitrary chosen PrimariesDifferent 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.

5

Inadequacy of real primaries

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):

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.

RearrangingEqn 3.5 gives Eqn 3.6:

8

Inadequacy of real primariesHence 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 eliminatenegative tristimulus values entirely.

9

Real and Imaginary primariesSince 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 asto avoid negative values.

It is therefore worth considering this point a little further.

10

2D Representation of ColorAny two-dimensional representation of colour must omit or ignoresome 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.

11

2D Representation of ColorSimilarly 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.)

12

2D Representation of ColorA 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):

13

2D Representation of ColorFor example the point C, halfway between [R] and [G], represents the colour formed bymixing 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

proportionsof the primaries.

14

2D Representation of ColorSuppose also that the boundary of real colours (strictly those real coloursfor 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.

.

15

2d representationConsider 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.

16

Similar argument for 3D ColorIf 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.

17

INADEQUACY OF VISUAL

OBSERVATION

18

VISUAL Tristimulus colorimeterthe 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.

19

Problems lying in the precisionThe 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 normalconditions, for example, when judging whether a colour difference exists between two adjacent panels on a car body under good daylight.

20

Metameric problemsthe 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.

21

Observer eye problem minimizationNot 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.