The motivation for the previous
discussions in which we tried to match any color using various combinations of
three primary colors is that this process is based on how the eye really
perceives color.
The rods of the eye – the sensors that
are used when the light intensity is low, have some variation in their response
to different colors. They are most sensitive to colors in the green portion of
the spectrum near 500 nm, so that when the light is dim it is easiest to see
objects that either radiate or reflect green light. However, since there is
only one type of rod sensor, the rods cannot be used to discriminate among
different colors, since they respond only to the weighted sum of the intensity
that strikes them (where wavelengths in the vicinity of 500 nm green are more
heavily weighted than those in the red or blue).
The cones of the eye – the sensors that are used
when the light intensity is higher, come in three different types, where the
differences among the types are the wavelength bands they respond to most
strongly. The three types of cones
respond to all wavelengths to some extent, so that every color excites them all
– at least to some extent. However, the amplitude of the response of each type
is a function of the incident wavelength.
Unfortunately, each type of cone does not provide
any wavelength discrimination beyond its overall response function. In other
words, the short-wavelength cone, which is sensitive primarily to a broad band
of colors in the blue and green portions of the spectrum, cannot provide any
information on the wavelength of the incident light beyond the fact that it has
been triggered by some wavelength within its response band. Color
discrimination depends on the fact that every wavelength excites the three
types of cones by different amounts – every incident wavelength produces a unique
triplet of excitation values. This is an important design feature: if a band of
wavelengths excited only one type of the cones, then we would not be able to
distinguish differences in hue within this band, and if the response functions
did not overlap, then there would be wavelengths that we would not be able to
see at all, since those wavelengths would not excite any one of the cones or
would produce so little excitation that these wavelengths would appear very
dim. Finally, if the response functions of the cones were essentially identical
over any range of wavelengths then it would be difficult or impossible to
distinguish the hues in this wavelength range.
The details of the response functions of the 3 types
of cones can be derived from the observed response of the eye to various colors
– especially to the fact that only two complementary colors can combine to
produce white. These pairs of colors must therefore straddle the cross-over
points between the sensitivities of the 3 cones, so that the two colors can
excite all 3 types of cones more or less equally so as to give the sensation of
white.
Additional information comes from people who are
“color blind.” These people often have only two of the 3 types of cones, so
that every color that they see is some combination of the two types of cones
that are working. For example, if the green cones are not working, then these
people discriminate among colors based on the red and blue content alone, and
they cannot distinguish colors that have the same red and blue content but
which differ only in how much green they contain. In other words, they see all
colors as if they were on vertical lines through the color horseshoe (figure
9.11, page 245), since colors along these lines differ only in how much green
they contain.
The result of these considerations is that the
response curves of the 3 types of cones are as shown in the following figure, which
is taken from the textbook on page 273 (figure 10.5). The response function
marked S responds most strongly to the shortest wavelengths: blue and violet;
the response function marked I responds most strongly to yellow and green,
while the response function marked L responds to the longer wavelengths,
primarily yellow, orange and red.
These
response curves show how the blue and green primary colors were chosen, since
they are close to the peaks in the response functions of two of the 3 types of
cones. (Also note why some definitions use a primary blue at 425 nm – it is
closer to the peak response of one of the types of cones than 460 nm is.) The 3rd
primary has a longer wavelength than the peak in the response of the third
cone, which is why monochromatic red colors tend to look less bright than the
same amount of energy at shorter-wavelength parts of the spectrum. In addition,
the response of the “red cone” to red light is only somewhat greater than the response of the “green cone”
to the same wavelength, so that red light often has a hint of yellow in it even
when it is really a completely saturated red.
The fact that there are three types of cones whose
wavelength sensitivities are as shown above explains many of the phenomena that
we have described. For example, it is clear why color matching using the three
primary colors can work. Since each type of cone reports only its relative
excitation level and not the exact wavelength that caused the excitation, it is
possible in principle to match the three excitation levels resulting from any
incident wavelength using an appropriate combination of the three primaries.
It is also clear from the figure why some colors
(especially monochromatic blues and greens) cannot be matched using the usual
primaries. Any incident wavelength in the range of 460-500 nm will excite the
blue cone quite strongly, but will also excite both the green and red cones to
some extent. Thus matching colors in this region will need lots of the blue
primary. Since the green cone is also excited, some green primary will also be
required. Unfortunately, the response of the red cone to this green light is
quite significant – much more than the response of the red cone to the incident
wavelength. Thus adding green primary to the mix almost always produces too
much excitation in the red cone. The only way to match this unintended (but
unavoidable) excitation of the red cone is to add some red to the incident
wavelength. This conclusion is exactly the same as we came to from considering
the color matching horseshoe chart in the previous topics – highly saturated
blue/green wavelengths require a “negative” red contribution in order to be
matched.
Although the response curves of the cones explains
color many of the aspects of color matching, it does not explain all of the observed
phenomena of color vision. In particular, the fact that the combination of two
colors (such as red and green) can produce a third color, whose wavelength is
not related in any obvious way to its two parents is not a direct result of the
previous discussion. In addition, the interaction between intensity and
perceived hue is not explained either. Since the physical response functions of
the cones have been verified in many ways, these additional phenomena must be
implemented in the processing of the signals from the cones rather than in the
hardware of the cones themselves.
While there are only three types of
cones, there is some evidence that the processing of these 3 signals can be
characterized in terms of differences between the different channels.
There are 5 signals in this model: red, green, blue, yellow and intensity.
(Based on our previous discussion, the yellow channel is presumably implemented
internally as (red + green). The 3 signals that are processed by the brain are
the pair-wise differences: red – green, blue – yellow and the overall
intensity, which is presumably estimated as the sum of the excitations of the 3
types of cones. The intensity response
function is complicated by other factors. For example, the perceived brightness
of an object depends on its surroundings, so that the intensity channel
incorporates some kind of spatial differencing.
The wavelength values corresponding to these
physiological primaries are not quite the same as the primary colors of the previous
discussion. The largest discrepancy is the value of the “red” primary, which is
closer to what we defined above as magenta – a mixture of red and blue.
Therefore, using our previous primary values, the red – green signal is really
more like (red + a little blue) – green. Since there is no cone that explicitly
responds to yellow, the yellow – blue channel is presumably implemented as (red
+ green) – blue.
When both difference channels red –
green and yellow – blue respond with a 0 value, then the color is some shade of
white depending on the value of the intensity channel. The overall response is
summarized in the following figure (figure 10.12, page 277).
In
addition to the differencing in wavelength, there is also some spatial
differencing. That is, a color in one area can affect the perception of the
color of an adjacent area. That is, a bright yellow area makes an adjacent
uncolored area appear blue, etc.
Finally, there is an interaction between the
perceived color of a scene and its actual average intensity. This tends to work
in two ways: (1) since the color processing involves differences between
channels, a decrease in the overall illumination does not affect the
differences as much, so that we can perceive more or less the same color under
different levels of illumination. (2) a change in the intensity of only part of
a scene relative to the rest of it does have an effect on the perceived hue –
dim orange will look brown, for example.
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