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On Flies' Eyes

If you're not already aware of it, it will probably be surprising to you how well the biological intermediate processing involved in vision is understood. For one thing, when I mentioned photoreceptors producing signals, above, you probably didn't even stop to think that photoreceptors are neurons rather than, say, stereo systems. Each neuron produces not an analog electrical signal but rather an irregular series of pulses, with the analog data encoded in the timing of the pulses. The encoding, known as the neural code, is understood, and seems to be used universally within the brain to represent analog signals.

The neural code, however, isn't exactly an example of intermediate processing. As a real example, it turns out there's a neuron in the visual system of the fly the output of which, when properly decoded, describes the overall horizontal motion of the input image, even in the presence of random noise. The fly, we may imagine, uses this signal plus an analogous vertical one to stabilize itself during flight.

I'm no expert in all this, of course, only a generalist who's skimmed over a tiny part of the literature, to wit, a couple of theses by students of W. Bialek.

Toward a Predictive Theory of Neural Computation: Motion Estimation in the Fly's Visual System

Optimization Principles for the Neural Code

If you want to know more about this sort of thing, there are plenty of references in the theses, or you can just search for recent publications by Bialek and go from there. It's also worth reading about the how the eye itself works … Optics, for example, has a very nice explanation.

The thing that got me into literature-searching in the first place was something I remembered hearing about once, that there was a field-theoretic way to compute the best possible estimate of overall horizontal motion from noisy data, and that the fly performs at nearly the theoretical optimum. This was memorable because it let me think of flies as performing field-theoretic calculations, even though that may not be exactly how they do it.

Here are two separate quotations that explain the general concept, both from the first thesis mentioned above.

The performance of the nervous system often comes close to the physical limits inherent to its task. Therefore by understanding the structure of specific problems solved by real brains, we can hope to formulate a predictive theory of neural computations. A large class of signal processing problems—such as those solved by the sensory nervous system—are equivalent to the computation of the response to external fields in statistical mechanics.

In many cases, when the task can clearly be identified, biological systems perform within a factor of 2 of the optimum (for a review, see [10, 12]). The usual explanation is that natural selection has had enough time to push the species toward a local optimum, …

The optimizing power of evolution is well understood (see, for example, Constraints on Perfection), but, for some reason, examples involving physical constraints really bring it home to me. Here are two amazing examples, as described in the same thesis.

For example, humans and toads can count single photons down to the limit imposed by thermal isomerization of pigment molecules, more over the performance of a cold blooded animal, as the toad, improves at lower temperatures as expected when the thermal noise is reduced [1, 7, 26].

The next one is about chemotaxis, which I had to look up in my dictionary.

Characteristic orientation or motion of a freely moving living organism relative to a chemical substance.

It may help to think of phototaxis, which includes the light-seeking behavior of plants.

One can understand the chemotaxis of the bacterium E. coli with consideration of size, molecular diffusion, Brownian motion and viscosity and other physical limits. In order to achieve its chemotactic performance, it must count almost every molecule that binds to its membrane. Also, in order to perform optimally, E. coli should filter its chemoreception data through a bandpass filter centered at about 1 Hz depending on experimental conditions [9, 50]. This prediction has been quantitatively verified [21].

With all those quotations to get you in the right frame of mind, I think you'll now be able to appreciate an interesting experience I had recently, one that I interpreted in terms of low-level visual processing. I'd gone to see a movie (Gladiator, if you must know) and was sitting way up front in one of those big new movie theaters. When objects moved quickly across the screen, I didn't perceive them as moving, I distinctly perceived them as a succession of images in different positions. The way I figure it, as a result of the fast angular motion the neurons responsible for recognizing moving objects were simply not firing! The fact that a movie is a sequence of static images rather than a continuous image may have contributed, but it wasn't the whole cause, since the effect went away when I moved further back.

Later, it occurred to me that maybe the same thing is a cause of motion sickness … maybe the fast angular motion you get when you look out the side window of a car causes your motion detectors to fail, while the slow motion out the front window doesn't.

As a quick final example of a limitation of the visual system, consider the fact that the cones (color-sensitive photoreceptors), which cluster in, and dominate, the center of the visual field, are less sensitive to dim light than the rods. The principle Don't Fight Your Mind, when applied to this fact, leads to the idea, well known to stargazers, of using peripheral vision to see fainter stars.


  See Also

  Complexity of Driving, The

@ June (2000)