The Smith-Kettlewell Eye Research Institute 2232 Webster Street - San Francisco - California - 94115

July 29 1994

Dear Dr. Lehar,

Thank you for the submission of the manuscript "Symmetry and
resonance in visual perception" to the Feature Issue on Symmetry. The
comments of the two reviewers experienced in this topic are
attached. Despite the fact that some interesting ideas are sketched in
your paper, they are not expressed with sufficient rigor [Author's Response] to warrent publication in
__Spatial Vision__. As reviewer 2 makes clear, the core of your
proposal is based on Fourier shape descriptors, which have been well
known for decades. Overall the paper represents a syncretic
concatenation of ideas concerning resonance, but detailed predictions
from this melange are neither specified nor tested. I regret,
therefore, that the paper is not acceptable for the Feature Issue.

Yours sincerely,

Christopher W. Tyler, Ph.D.
Feature Issue
__Spatial Vision__

Review of Symmetry and Resonance... Lehar and Cameron.

This paper is not the usual sort of fare for Spatial Vision, but you might want to give it consideration for the special issue on Symmetry. It is right up that street. The paper starts with a very broad view of the importance of symmetry in all sorts of natural situations, with some neat demonstrations of how harmonic resonance ties many of them together.

Applications to vision seem to follow quite well within the framework of Steve Grossberg's modelling of visual processing of contour and surface formation. The ideas are quite clever, but lack tight empirical support. No consideration is given to alternative models or accounts of symmetry in perception, except for Attneave's ideas. Important as these were at the time, they are scarcely the present state of the art.

If you want an interesting and provocative new slant on symmetry, or perhaps I should say the application of one type of modelling to symmetry phenomena, you might find room for this paper. [Author's Response]Otherwise I tend to think it belongs in a journal less tied to the canons and traditions of experimental science than Spatial Vision.

Review of Lehar/Cameron

This paper appears to be a generalization of the Grossberg-Mingolla BCS theory. The BCS theory is based on a notion of diffusion, and the present paper is based on a notion of "reaction-diffusion". It is stated that there are "a number of illusory contours...which cannot be explained as a co-linear grouping" (page 9, last sentence), as in the Grossberg-Mingolla theory, and the present paper suggests that it provides a solution to these deficiencies of the BCS theory.

One problem with all this is that this type of modeling has little to do with the topic of "symmetry", which is the ostensible topic being addressed. [Author's Response] In fact, there are several mentions of symmetry in this paper: Rotation is dealt with by allusion to an encoding of rotation in temporal frequency, but this idea is never explained enough to evaluate it. Size is dealt with by presenting a model of "harmonic resonance", which will be discussed shortly. Translation is dealt with by alluding to "replication across space" of the basic harmonic resonance model. This is also not elaborated, and I have no idea what the authors have in mind here. Simply replicating some mechanism across space, in and off itself, does not solve the problem of translation invariance, as far as I can tell.

In partial summary, this model does not sufficiently address the issue of symmetry that it claims to, and so is not really appropriate for the special issue of Spatial Vision. [Author's Response] However, I feel that there are deeper problems with this paper, which I will now outline.

The basic idea of the paper is a notion of "harmonic resonance", which is never adequately explained, as far as I can tell. It appears to be an idea in which boundary angle is represented by periodic patterns, and as such, would appear to be closely related to the well known method of "Fourier Descriptors", although the authors do not cite any literature relevant to Fourier Descriptors (e.g.

author = {C. R. Zahn and R. Z. Roskies},

title = {Fourier descriptors for plane closed curves},

journal = {IEEE Trnas. Computers},

volume = {C-21},

pages = {269-281},

year = {1972},

keyword = {FD},

I am, to a certain extent, reading between the lines here, but it appears to me that some form of periodic representation of boundary contour is what the authors have in mind by the term "harmonic resonance". And, reading between the lines is necessary since the overall model is so vaguely presented. [Author's Response] For example, there is a long discussion at the beginning of reaction-diffusion phenomena. Once again, I try to read between the lines, and recall that under certain conditions, reaction-diffusion systems have "wave-like" solutions, i.e. are approximated by the Helmholtz equation, or wave equation. Presumably this introduction of the wave-equation is to take place via a reaction-diffusion system. But, they never quite say this. The authors state that:

"The system proposed here is fundamentally different [from systems based on lateral inhibition or excitation]. In this model, interactions occur by way of constructive and destructive interference between competing waveforms." (page 21)

So, some notion of wave-like activity in the brain is being asserted here. And, again,

"Allowing for a small propagation delay due to the inductance and capacitance of the cell, it would not be unreasonable to assume that such syncitia would also be able to sustain harmonic oscillations of electrical activity" (page 11).

Here, they are explaining "the most likely mechanism [for harmonic oscillations] as based on gap junctions in a ring shaped syncitium".

But, what on earth is a "syncitium". [Author's Response]They quote an obscure observation of Kandel, in invertibrates, of a group of neurons oscillating in unison, as the model for th enotion of "syncitium". But, can we really expect this to occur with any degree of likelihood, in the primate visual cortex? If so, why?[Author's Response]

What appears to be the basis of all this is a notion of wave-like activity, and interference patterns, occurring in the brain. I simply don't know of any reason to take this kind of modeling seriously,[Author's Response] although there was a fad, for some time, of "holography" in the brain, and Beurle, in the early 1950's, developed models based on wave-like activity propagating in the brain. But this, surely, is no longer taken seriously as a modeling stance? [Author's Response]And if so, the authors of the present paper provide little, outside of passing statements, and tangential references, to support these notions.

In summary, the present paper has little to do with symmetry. [Author's Response]Its underlying computational rationale appears to be closely related to a notion of "Fourier Descriptors". If so, this should be stated. If not, a clearer statement of the basic computational idea should be made. Its underlying neuronal mechanism must be shored up without reference to partially defined, (and far-out) aspects of the brain, such as "syncitia". [Author's Response]In its current form, I don't believe that this paper is publishable; the authors would need to fill in a large number of gaps, left by the vague statements summarized above. And, it is not appropriate for the special issue of Spatial Vision, since there is little treatment of the problem of invariance in vision.