Graphics Reference
In-Depth Information
square as being painted on a surface and illuminated by lights of varying intensity,
we get a very different set of images, as in Figure 5.9, in which the center square's
gray values are all different, but you have the perception that the center squares are
all fairly comparably dark.
This
is an instance of lightness constancy under varying
illumination. (An even more spectacular example of lightness constancy—and its
non
relation to incoming intensity—is shown in Figure 28.15.)
The materials available on this topic's website discuss further constancy
effects.
Applications.
The various constancy illusions show that surrounding bright-
ness can affect our perception of the brightness of a surface or of a light. This leads
to the use of different gamma values (discussed in Section 28.12) for studio mon-
itors, theatre projection, and ordinary office or home displays, where the average
brightness of the surroundings affects the appearance of displayed items. It also
suggests that during rendering, if you want to visually compare two renderings,
you should surround each with an identical neutral-gray “frame” to help avoid any
context-based bias in your comparison.
The other consequence of constancy, at least for brightness, is that relative
brightnesses matter more than absolute ones (which helps explain why edge detec-
tion is so important in early vision). This suggests that if we want to compare two
images, it may be the
ratio
of corresponding pixels that matters more than the
difference.
When one object seems to disappear behind another, and then reappear on the
other side (see Figure 5.10), your visual system tends to associate the two parts as
belonging to a whole rather than as separate things; this is an instance of the idea
from Gestalt psychology that the brain tends to perceive things as a whole, rather
than just as individual parts.
One proposed partial mechanism for this perception is the
C
1
random walk
theory [
?
, Wil94] in which we suppose that at
T
-junctions (where an outline of
one object appears to pass behind another object), the brain “continues” the line
in the same general direction it was going when it disappeared, but with some
random variation in direction. Some such continuations happen to terminate at the
other T
-junction, headed in the appropriate direction. If we consider all such con-
nections between the two, some are more probable than others (depending on the
probability model for variation in direction, and on the lengths of continuations).
Each point in the obscured area occurs on some fraction of all such continuations
(i.e., there's a probability density
p
with the property that the probability that a
random connection passes through the area
A
is the integral of
p
over
A
). The
ridge lines of the distribution
p
turn out to constitute very plausible estimates of
the “inferred” connection between the
T
-junctions, with the integral of
p
over the
curve providing a measure of “likelihood” that the lines are connected at all. If
the
T
-junctions are offset from each other (i.e., if the two segments are not part
of a single line), the probability decreases; if the two segments are nonparallel,
the probability decreases; only when the
T
-junctions are perfectly aligned is the
probability of connection at its maximum. Is such a “diffusion of probability of
connection” really taking place in the brain? That's not known. But this notion
that the ridge lines of
p
form the most likely connections cannot, as stated, tell the
Figure 5.9: The ratio of the cen-
ter square's darkness to the sur-
rounding square's darkness is
approximately the same in each
example; you tend to see the cen-
ter squares as exhibiting far less
variation in lightness than those
in the previous figure.
