188 Visual Perception of Objects
AB C D E
Figure 7.10 An image (A) that is perceived as a square occluding an
amodally completed circle (B) rather than as a square abutting a pac-man
(C), a square occluding some odd-shaped object (D), or a pac-man occluding
some odd-shaped object (E). Source: From Palmer, 1999.grouping, and parsing—it is possible to see how a rudimen-
tary part-whole hierarchy might be constructed by some
appropriate sequence of operations. One of the main further
problems that the visual system must solve is how to per-
ceive partly occluded objects as such. In Figure 7.1 (A), for
example, the part of the branch above the leopard is per-
ceived as the extension of the branch below it. This is more
than simple grouping of the two corresponding image regions
because the observer completesthe branch in the sense of
perceiving that it continues behind the leopard. The various
patches of sky between and around the leopard and branches
must likewise be perceived as parts of the uninterrupted sky
behind them. The crucial ecological fact is that most environ-
mental surfaces are opaque and therefore hide farther sur-
faces from view. What is needed to cope with the incomplete,
piecewise, and changeable montage of visible surfaces that
stimulate the retina is some way to infer the nature of hidden
parts from visible ones.
The visual system has evolved mechanisms to do this,
which will be referred to collectively as processes of visual
interpolation(Kellman & Shipley, 1991). They have limita-
tions, primarily because all they can do is make a best guess
about something that can be only partly seen. Completely
occluded objects are seldom interpolated, even if they are
present, because there is no evidence from which to do so,
and even partly visible objects are sometimes completed
incorrectly. Nevertheless, people are remarkably adept at per-
ceiving the nature of partly occluded objects, and this ability
requires explanation.
Amodal Completion
Amodal completionis the process by which the visual system
infers the nature of hidden parts of partly occluded surfaces
and objects from their visible projections. It is called amodal
because there is no direct experience of the hidden part in any
sensory modality; it is thus experienced amodally. A simple
example is provided in Figure 7.10 (A). Observers sponta-
neously perceive a full circle behind a square, as indicated in
Figure 7.10 (B), even though one quarter of the circle is not
visible.
Amodal completion is logically underdetermined. The real
environmental state of affairs corresponding to Figure 7.10
(A) might be a square covering a whole circle (B), a mosaic,
of a square abutting a three-quarter circle (or pac-man; C), or
a square in front of a circle with odd protrusions (D). It might
also be a pac-man in front of a square with odd protrusions
(E), or an infinite number of other possibilities. The visual
system therefore appears to have strong preferences about
how to complete partly occluded objects, aimed at maximiz-
ing veridical perception of whole objects in the world. There
are at least three general types of explanations of how this
might happen.
One possibility is that the visual system completes the cir-
cle behind the square based on frequency of prior experi-
ences. Although people have all seen three-quarter circles,
most have probably seen a good many more full circles.
Perhaps people complete partly occluded figures according
to the most frequently encountered shape compatible with
the visible stimulus information. Novel shapes can also be
amodally completed (e.g., Gregory, 1972), however. This
shows that familiarity cannot be the whole story, although it
may be part of it.
A second possibility is that partly occluded figures are
completed in the way that results in the simplestperceived
figures. For example, a square occluding a complete circle in
Figure 7.10 (A) is simpler than any of the alternatives in this
set of completions, and the same could be true for the possi-
ble completions of novel shapes. Explaining phenomena of
perceptual organization in terms of maximizing simplicity—
or, equivalently, minimizing complexity—was the theoretical
approach favored by Gestalt psychologists (e.g., Koffka,
1935). They called this proposal the principle of Prägnanz,
which was later dubbed the minimum principle(Hochberg &
McAlister, 1953): The percept will be as good or as simple,
as the prevailing conditions allow.
Gestaltists were never very clear about just what consti-
tuted goodness or simplicity, but later theorists have offered
explicit computational theories that are able to show that
many completion phenomena can be predicted by minimizing
representational complexity (e.g., Buffart & Leeuwenberg,
1981; Leeuwenberg, 1971, 1978). One problem faced by such