This is indeed a serious restriction of the concept, for although the visual system does often appear to prefer a perceptual interpretation based on right angles, it is clearly not limited to right angled perceptual interpretation.

On the other hand extension of the model to account for other types of completion would seem to lead to a combinatorial explosion in the number of different kinds of receptive fields required at every location and depth and orientation in the volumetric representational matrix. A "neural network" implementation of this concept therefore would appear to be implausible.

This is exactly why the present solution is expressed in perceptual modeling terms, to discuss the information processing apparent in perception independent of neurophysiological considerations. This is however only an interim solution, for eventually the neurophysiological mechanism behind perceptual processing will have to be identified.

I do have such a neurophysiological model, in the form of a Harmonic Resonance Theory which does indeed exhibit a tendency to perform completion in either two or three dimensions in terms of orientational periodicities. But that is well beyond the scope of the present paper.

This highlights the problem of attempting to present a paradigmatic hypothesis through the peer review process, if the new hypothesis cannot be expressed in a single self-contained paper.