A stimulus of a tri-angular vertex as shown below (left) stimulates a percept of a corner of a cube, or the intersection of three surfaces, either convex or concave, as show below (second figure). Consider the problem in terms of perceptual modeling, i.e. consider the appearence of the percept itself, rather than the neural mechanism which subserves that percept. An analog Gestalt model for this percept might be something like a piece of paper creased in three folds, corresponding to the three visual edges, which break the stiffness or resistance to bending along those edges, as shown below (third figure). This would tend to make the paper "pop" into either a convex or concave corner.

A visual edge in a two-dimensional image is constrained in *X*
and *Y*, but is undetermined in the depth dimension *Z*.
Therefore in the inverse optics projection, the visual edge is inverse
projected from a line to a plane in depth, in order to overlie all
points in space that represent a possible location of that line in
depth. In the example above, the image of the tri-angular vertex is
inverse projected from the front (near) surface of the block producing
three intersecting planes of influence backwards through the depth of
the perceptual block, as suggested by the gray planes in the figure
above (right).

In order to generate the proper percept, these planes would have to
influence the behavior of active units in the block so as to relax
their coplanarity constraint. This way the perceptual surface would
have a tendency to kink or fold at locations where it intersects the
inverse projection of a visual edge. Additional local interactions
could be defined in order to make the surface tend to fold in
right-angled corners.
In other words, it is possible to define a Gestalt-like analog dynamic
mechanism which would respond to a visual input like the one shown
above by constructing a three-dimensional *reification* of the
percept. The exact implementation is not as important as the fact
that it is certainly *possible* to define a system with the
required properties, and that system would correspond more closely to
the actual percept than *any* of the conventional models
proposed to account for vision. The *orthogonality
constraint*, or tendency for the surface to fold at right angles
would be a natural property of a system defined in orientational
harmonics.

The exact dynamics and details of this model have not been fully
worked out. But the *principle* behind this mechanism is
clear, and it is also clear that such a system is possible in
principle to define. It is also clear (at least to me) that this kind
of a system captures the subjective impression of these illusory
figures in a very compelling way.