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

The nearest neighbour principle is a natural constraint because it arises from the
geometry of the typical viewing conditions for motion (Ullman, 1979, pp. 114–118).
When movement in a three-dimensional world is projected onto a two-dimensional
surface (e.g., the retina), slower movements occur with much higher probability on
the retina than do faster movements. A preference for slower movement is equivalent
to exploiting the nearest neighbour principle, because a short correspondence
match represents slow motion, while a long correspondence match represents fast
motion.
Another powerful constraint on the motion correspondence problem is called
the relative velocity principle (Dawson, 1987, 1991). To the extent that visual elements
arise from physical features on solid surfaces, the movement of neighbouring elements
should be similar. According to the relative velocity principle, motion correspondence
matches should be assigned in such a way that objects located near one
another will be assigned correspondence matches consistent with movements of
similar direction and speed. This is true of the two matches illustrated in Figure
8-7B, which are of identical length and direction, but not of the two matches illustrated
in Figure 8-7C, which are of identical length but represent motion in different
directions.
Like the nearest neighbour constraint, the relative velocity principle is a natural
constraint. It is a variant of the property that motion varies smoothly across a scene
(Hildreth, 1983; Horn & Schunk, 1981). That is, as objects in the real world move,
locations near to one another should move in similar ways. Furthermore, Hildreth
(1983) has proven that solid objects moving arbitrarily in three-dimensional space
project unique smooth patterns of retinal movement. The relative velocity principle
exploits this general property of projected motion.
Other natural constraints on motion correspondence have also been proposed.
The element integrity principle is a constraint in which motion correspondence
matches are assigned in such a way that elements only rarely split into two or fuse
together into one (Ullman, 1979). It is a natural constraint in the sense that the physical
coherence of surfaces implies that the splits or fusions are unlikely. The polarity
matching principle is a constraint in which motion correspondence matches are
assigned between elements of identical contrast (e.g., between two elements that are
both light against a dark background, or between two elements that are both dark
against a light background) (Dawson, Nevin-Meadows, & Wright, 1994). It is a natural
constraint because movement of an object in the world might change its shape
and colour, but is unlikely to alter the object’s contrast relative to its background.
The natural computation approach to vision is an alternative to a classical
approach called unconscious inference, because natural constraints can be
exploited by systems that are not cognitive, that do not perform inferences on the
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