Figure 1.
Illustrations of noisy encoding of monochromatic inputs by the cone responses.
On the left is the cone spectral sensitivity (with
, where
s are derived from the Smith and Pokorny cone fundamentals[15], the cone density ratio is
, the pre-receptor light transmission factors
, and Max
). A monochromatic input of wavelength
evokes response
from the three cones, L, M, and S. Due to input noise, there is a range of possible responses
from this input. If the mean response to a monochromatic input of nearby wavelength
is one of the typical responses within this range of responses
to input
, then it will be difficult to perceptually distinguish the input
from input
.
Figure 2.
Wavelength discrimination assuming input intensity is fixed and known during color matching.
It is by maximum likelihood decoding of the cone responses using the simple model. The solid curve plots the discrimination threshold
as a function of
from the model. The data points with error bars are the mean
and the standard deviation
of the discrimination thresholds of the four observers of Pokorny and Smith[1]. In fitting the model to the data,
is chosen such that the quantity
is minimized.
Figure 3.
Illustration of 2D decoding in the full model.
Given the true input ,
is the estimated input parameters. This plot illustrates the conditional probability
, since a given
may evoke different responses
leading to different
. The wavelength discrimination threshold
when
is allowed to deviate from
is larger than otherwise.
Figure 4.
Wavelength discrimination under input intensity confound.
A: Wavelength discrimination by maximum likelihood decoding of cone inputs using the full model, assuming that the color matching is done by adjusting both the input intensity and wavelength
of the comparison field. The solid curve shows the results from the full model. The parameter
(of the standard field) is chosen such that the quantity
is minimized. The dashed curve shows the results from the simple model using this same input intensity
. The data points with error bars are the mean
and the standard deviation
of the discrimination thresholds of the four observers of Pokorny and Smith[1]. B: cone sensitivities plotted on a linear scale.
Figure 5.
Variations of the model predictions due to variations in the cone fundamentals, cone densities, and pre-receptor transmission.
The is normalized to the same peak value Max
, the cone factor
combines the cone density
and pre-receptor transmission factor
, to determine the cone sensitivity
, with normalizations Max
. Each plot is like Fig. 4A, having a full model predicted threshold with an optimal
. Each is labeled with the literature source for
and the
used. A–C have the Smith and Pokorny cone fundamentals[15] with different
. A is a modified plot of Fig. 4A. C–F show the best predictions (the
that minimizes
) for four different cone fundamentals. Only integer values of
,
, and
are used (
in all cases).
Figure 6.
Illustration of how reducing the density of S cones should create a threshold peak near nm.
Because the L and M cones have their spectral sensitivity co-vary with each other as varies near
nm, they act as if they are a single cone type around that
. As threshold eventually increases when
approaches
nm, this local threshold peak at 460 nm creates a threshold dip between
and
nm.
Figure 7.
Theoretical preditions of the wavelength discrimination by dichromatics as compared to that by the trichromats.
All these curves are by fixing input intensity , while using
in which
is normalized by Max
, while
are no longer normalized by Max
. The values
are
,
,
, and
for protanopes, deuteranopes, tritanopes, and trichromats, respectively.