Mind, Body, World- Foundations of Cognitive Science, 2013a

For our purposes, though, the above Sudoku example illustrates how constraints
can be propagated to solve problems of underdetermination. Furthermore, it shows
that such solutions can be fairly mechanical in nature, not requiring higher-order
reasoning or problem solving. For instance, the “there can be only one” constraint
could be instantiated as a simple set of interconnected switches: turning the 5 on
in Figure 8-4 would send a signal that would turn the 5 off at all of the other greyshaded
locations.
The natural computation approach to vision assumes that problems of visual
underdetermination are also solved by non-cognitive processes that use constraint
propagation. However, the constraints of interest to such researchers are not formal
rules of a game. Instead, they adopt naïve realism, and they assume that the external
world is structured and that some aspects of this structure must be true of
nearly every visual scene. Because the visual system has evolved to function in this
structured environment, it has internalized those properties that permit it to solve
problems of underdetermination. “The perceptual system has internalized the most
pervasive and enduring regularities of the world” (Shepard, 1990, p. 181).
The regularities of interest to researchers who endorse natural computation are
called natural constraints. A natural constraint is a property that is almost invariably
true of any location in a visual scene. For instance, many visual properties of threedimensional
scenes, such as depth, colour, texture, and motion, vary smoothly. This
means that two locations in the three-dimensional scene that are very close together
are likely to have very similar values for any of these properties, while this will not
be the case for locations that are further apart. Smoothness can therefore be used to
constrain interpretations of a proximal stimulus: an interpretation whose properties
vary smoothly is much more likely to be true of the world than interpretations
in which property smoothness is not maintained.
Natural constraints are used to solve visual problems of underdetermination
by imposing additional restrictions on scene interpretations. In addition to being
consistent with the proximal stimulus, the interpretation of visual input must also
be consistent with the natural constraints. With appropriate natural constraints,
only a single interpretation will meet both of these criteria (for many examples, see
Marr, 1982). A major research goal for those who endorse the natural computation
approach to vision is identifying natural constraints that filter out correct interpretations
from all the other (incorrect) possibilities.
For example, consider the motion correspondence problem (Ullman, 1979),
which is central to Pylyshyn’s (2003b, 2007) hybrid theory of visual cognition. In the
motion correspondence problem, a set of elements is seen at one time, and another
set of elements is seen at a later time. In order for the visual system to associate a
sense of movement to these elements, their identities must be tracked over time.
The assertion that some element x, seen at time t, is the “same thing” as some other
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