Shape as Memory Storage - Ambient Intelligence for Scientific Discovery - page 85

Fig. 5. Sixteen extrema imply sixteen symmetry axes.
5 The Interaction Principle
The reason for involving symmetry axes is that it will be argued that they are
closely related to process-histories. This proposed relationship is given by the
following principle:
Interaction Principle (Leyton, 1984): Symmetry axes are the directions
along which processes are hypothesized as most likely to have acted.
The principle was extensively corroborated in Leyton [7], in several areas of per-
ception including motion perception as well as shape perception. The argument
used in Leyton [7] to justify the principle, involves the following two steps: (1)
A process that acts along a symmetry axis tends to preserve the symmetry; i.e.
to be structure-preserving. (2) Structure-preserving processes are perceived as
the most likely processes to occur or to have occurred.
6 The Inference of Processes
We now have the tools required to understand how processes can be recovered
from the curvature extrema of shape; i.e., how curvature extrema can be con-
verted into memory stores. In fact, the system to be proposed consists of two
inference rules that are applied successively to a shape. The rules can be illus-
trated by considering Fig 6.
The first rule is the Symmetry-Curvature Duality Theorem (section 4) which
states that, to each curvature extremum, there is a unique symmetry axis termi-
nating at that extremum. The second rule is the Interaction Principle (section
5), which states that each of the axes is a direction along which a process has
acted. The implication is that the boundary was deformed along the axes; e.g.
each protrusion was the result of pushing out along its axis, and each indentation
was the result of pushing in along its axis. In fact, each axis is the trace or record
of boundary-movement!