Perceptual Coherence : Hearing and Seeing

312 Perceptual Coherence
Color Appearance Models and Color Constancy
I now shift orientation and consider models and experiments in which
observers attempt to match the surface colors viewed under different
illuminations, termed asymmetric color matching. For any stimulus, we can
calculate the expected number of absorptions for each of the three cones
by multiplying the illumination by the surface reflectance by the respective
spectral absorption curve [i.e., E(λ)R(λ)S s(λ), E(λ)R(λ)S m(λ), and
E(λ)R(λ)S l (λ)].
First, color constancy will be perfect if the surface reflectance of the
match color is identical to the standard color. Therefore, the number of
cone absorptions will differ between the standard and test because the illumination
is different.
Second, color constancy will be zero if the reflectance of the test color
multiplied by the test illumination by the absorption curve yields the same
number of cone absorptions as the standard stimulus. In this case, observers
are unable to abstract the reflectance from the light energy reaching
the eye.
Consider a simple example of achromatic asymmetric matching. The
standard gray might have a reflectance of .40 and be illuminated by 10,000
units. The test gray would have variable reflectance and be illuminated by
40,000 units. The subject would be asked to adjust the test gray so that it
matched the standard gray. If the subject displayed perfect constancy, then
the reflectance of the test gray would be set at .40, even though the excitation
from the test gray is four times greater than that from the standard
gray. If the subject displayed zero constancy, then the reflectance would be
set at .10, so that the amount of excitation from the two grays would be
equal (right now I am not considering any effects due to the receptor absorption
curves). Reflectance values between .10 and .40 represent intermediate
degrees of constancy.
Now consider a more representative chromatic case, but still use simplified
discrete frequency illumination and reflectance functions. The standard
illumination projects 10,000 units at 550 nm and 10,000 units at 600 nm.
The standard color reflects .40 of illumination at 550 nm and .20 of the illumination
at 600 nm, thereby reflecting 4,000 units at 550 nm and 2,000
units at 600 nm. The test illumination projects 15,000 units at 550 nm, and
5,000 units at 600 nm. The observer’s task is to select a test color that
matches the standard color. Following the identical logic as above, if the
subject displayed perfect constancy, the reflectance of the test color would
match that of the standard color (e.g., .40 and .20), so that the excitation
reaching the eye would be different (4,000 vs. 6,000 units at 550 nm and
2,000 vs. 1,000 units at 600 nm). If the subject displayed zero constancy,
the excitations due to the standard and test color would be made equal, so