This paper argues for a new explanation of illusory contours, and thus brain functions, by a theory that the author called directional harmonic resonance theory. From the paper itself, it is unclear what the harmonic resonance theory is, since the paper does not present a single mathematical expression or an algorithmic description of the grouping procedure. Then I have to read the authors unpublished manuscript and the uncensored Ph.D thesis to figure out what the theory was.[author's response]
The paper has three valid points, unfortunately, these points are written in a non-scientific style and disconnected from the literature.
The first is an observation that the connectivity pattern to a vertex (the input to cells in the cooperative layer in the author's language) can be represented by a circular vector. Thus by a Fourier transform, the vector is projected into various Harmonic bases. Obviously these bases correspond to connectivity degree d=1,2,3,4 respectively. This projection is nothing but a dimension reduction step. One could argue for any other set of bases instead of the Fourier harmonics. For example, by a principle component analysis from a connectivity graph in naturally observed patterns, or by some independent component analysis and sparse coding ideas. In the later cases, these bases don't have to be orthogonal. The sparse non-orthogonal bases are more likely than the Fourier bases. [author's response]
The second part is a propagation of the local hypothesis through dynamic equations which exercise some excitatory and inhibitory connections between cells. But the paper has no understanding of what the functions are doing. Are they going to converge? If yes, what does a converge state mean? Is it optimizing certain functional that formulate a certain goal? Without answering these questions, the paper provides very little information to the audience. [author's response]
The Third valid point is its demonstrated results over a large set of patterns. Though these results are good. But many other theories in computer vision can easily account for them. [author's response] Of course, the author seemed not following the recent computer vision theories, including various Markov random field models. It is unclear in the paper what the basic representational elements are. For example, do you model surface and curves, or stochastic graphs as a way for guiding the grouping of edge elements? What is your representation? Of course, I am asking the question at the representation and algorithm levels. Without understanding them, it is not interesting to discuss the issue just at an implementation level. [author's response]
The paper is badly written. [author's response] The first half reviews the literature which is very redundant. You should get to the point with rigorous mathematical expression for what you want to compute, and how you do it. The paper also miss a huge amount of recent literature in computer vision. The paper stays in the 1980s level. [author's response]
In summary, I recommend the paper being rejected or a major revision. [author's response]