In my PhD thesis I was working with Grossberg's vision model, which is designed to replicate a number of visual illusory effects using a neural network model. However Grossberg's model only really does collinear completion properly as seen in the Kanizsa figure, although he claims that it also performs orthogonal completion as seen in the Ehrenstein illusion. But there are other kinds of completions observed, including diagonal completion, and I was interested in generalizing Grossberg's model to account for all forms of completion with a single model. The most direct approach however leads to a combinatorial explosion in the number of required receptive field patterns, a specific one being required for every type of completion (collinear, orthogonal, diagonal, etc.) each of which would have to be replicated at every orientation at every spatial location.
I began to think that there was a problem with the central concept of neurocomputation embodied in the neuron doctrine, of the cell as a feature detector with a fixed spatial receptive field. This concept is no different than a template theory, whose limitations are well known, and these very limitations become apparent when attempting to generalize Grossberg's model. In my PhD thesis therefore I explored a completely different paradigm of neurocomputation, by way of harmonic resonances, or patterns of standing waves in the neural substrate, as an alternative pattern formation mechanism in the brain. I developed a theory of Orientational Harmonics , as a more general model of completion that could account for both collinear and non-collinear effects.
Although I had a specific model to address specific illusory effects, the most interesting aspect of the model was in the proposed alternative paradigm of neurocomputation, which I could see promised a solution to a great many fundamental problems of neuroscience. Unfortunately I did not manage to get the paper published.