Graphics Reference
In-Depth Information
An alternative model (Stevens' law) says that the response should be modeled
by a power law:
S
=
cI
b
,
(28.9)
where
b
is a number slightly less than 1. The shapes of the graphs of
log
and
y
=
x
b
are somewhat similar—both concave down, both slowly growing—so it's
no surprise that both can be used to fit the data decently. Each model has its detrac-
tors, but from our point of view, the important feature is that either one can be used
to generate a good fit to the data,
particularly
when the range of brightnesses being
considered is relatively small. In fact, as we'll discuss later, the eye adapts to the
prevailing light in an environment, and intensities that differ from this by modest
amounts can be compared to one another. But our sensation of lights that are very
bright or very dim compared to the average is quite different (“too dark to see” or
“too bright to look at”).
The Commission Internationale de l'Éclairage (CIE), a group responsible for
defining terms related to lighting and color, chose to use a modified version of
Stevens' law to characterize perceptual responses to light, and it's this model that
we'll use in further discussing the perception of brightness. To be explicit, the CIE
defines
lightness
as
L
∗
=
116
(
Y
Y
n
)
3
Y
/
−
16
Y
n
<
0.008856
0.008856
,
(28.10)
Y
903.3
Y
Y
n
≥
where
Y
(called
luminance
) denotes a CIE-defined quantity that's proportional
(for any fixed spectrum) to the energy of the light, and
Y
n
denotes the
Y
value for
a particular light that you choose to be the “reference white.”
You can see that
L
∗
is defined by a 1
/
3 power law that's been shifted down-
ward a little (the
16 does this), and which has had a short linear segment added
to deal with very low light values. In practice, this linear segment applies only
to intensities that are a factor of more than 100 smaller than that of the reference
white; in a typical computer graphics image, these are effectively black, so the
linear segment is mostly irrelevant.
In practice, this logarithmic or power-law nature of things is somewhat con-
founded by “adaptation” of the rods and cones. The luminance we encounter in
ordinary experience ranges over a factor of 10
9
between a moonless overcast night
and a snowy region on a sunny day. Both rods and cones react to arriving light with
chemical changes, which in turn generate an electrical change that is communi-
cated to the brain. Plotting the output of the various sensors against the log of the
luminance, we get a graph like the one shown in Figure 28.8; the rods react to
varying luminance by changing their output ...uptoapoint.Afterthatpoint,any
further increase in luminance doesn't affect the rods' output, and they are said to
be
saturated.
The cones, on the other hand, begin to change their output substan-
tially at about that point, so differences in brightness are detected by the photopic
system. The placement of the cones' curve on the axes, though, is not fixed: Upon
exposure to light of a certain level, like
D
on the chart, the cones, which were near
the limit of their output, will gradually
adapt
and shift their response curve so that
it's centered at
D
, thus responding to light changes at or near
D
. This ability to
adapt is limited—at some point, all light begins to seem “very bright.” The func-
tion of the “reference white” in the CIE definition is to characterize the interval of
intensities over which we want to characterize lightness.
−
