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Section 3.1 Human Color Perception 70

P 1

Test Weighted
light
Mixture
of P 2
primaries
T
P 3

FIGURE 3.2: Human perception of color can be studied by asking observers to mix colored
lights to match a test light shown in a split field. The drawing shows the outline of such
an experiment. The observer sees a test light T and can adjust the amount of each of
three primaries in a mixture displayed next to the test light. The observer is asked to
adjust the amounts so that the mixture looks the same as the test light. The mixture of
primaries can be written as w 1P 1 + w 2P 2 + w 3P 3; if the mixture matches the test light,
then we write T = w 1P 1 + w 2P 2 + w 3P 3. It is a remarkable fact that for most people
three primaries are sufficient to achieve a match for many colors, and three primaries are
sufficient for all colors if we allow subtractive matching (i.e., some amount of some of the
primaries is mixed with the test light to achieve a match). Some people require fewer
primaries. Furthermore, most people choose the same mixture weights to match a given
test light.

there are some caveats. First, subtractive matching must be allowed; second, the
primaries must be independent, meaning that no mixture of two of the primaries
may match a third. There is now clear evidence that trichromacy occurs because
there are three distinct types of color transducer in the eye (Nathans et al. 1986a,
Nathans et al. 1986b). Given the same primaries and test light, most observers
select the same mixture of primaries to match that test light, because most people
have the same types of color receptor.
Matching is (to an accurate approximation) linear. This yields Grassman’s
laws. First, if we mix two test lights, then mixing the matches will match the
result—that is, if
T a = w a1 P 1 + w a2 P 2 + w a3 P 3
and
T b = w b1 P 1 + w b2 P 2 + w b3 P 3 ,
then
T a + T b =(w a1 + w b1 )P 1 +(w a2 + w b2 )P 2 +(w a3 + w b3 )P 3 .

Second, if two test lights can be matched with the same set of weights, then
they will match each other—that is, if

T a = w 1 P 1 + w 2 P 2 + w 3 P 3
and
T b = w 1 P 1 + w 2 P 2 + w 3 P 3 ,