Thursday, June 15, 2006

The Eyes

My brother and I have been going back and forth on the random tile question (1, 2, 3). Related, at least in my mind, is an information theoretic question dealing with what see see and how much the optic nerve is capable of transmitting (as best we know of our own mechanics and the principles involved). Perhaps I should research this more (and find the source), but take, for example, this comment from Robert Cringley in 2004:

"What we need to emulate here is the eye, itself. Look at the optic nerve that connects the retina of your eye to the visual cortex of your brain. The optic nerve is composed of approximately one million stringy cells called ganglia that fire in parallel over a distance of two to three centimeters with the actual visual signal travelling at about 4,400 feet-per-second. Taking into account recovery time between signals, the optic nerve has a total bandwidth of approximately 100 kbps..."

Let's suppose that 100kbps for the optic nerve is in the ball park (even within an order of magnitude). The next obvious question is the information content of a single frame of what we see given our visual accuity. Compare what you see with, for example, a 10 megapixel image.

Comparisons I've seen are on the order of a 100 megapixels per frame (HDR, of course). Given the amount of information we see in a single frame, the number of theoretical frames per second we see and the supposed diminutive nature of the pipe through which it's transmitted, something doesn't add up.

Is the brain doing a whole lot of synthesizing and hallucinating with the little data it gets via the optic nerve, is there some incredible feature extraction, encoding and amazing compression going on somewhere in the process, both? What's going on?

The thing about noise is that it has high entropy as its defined in information theory. Gaussian noise has the maximum possible entropy (e.g., information on distribution entropy here); this is a factor contributing to my surprise at the results. It leaves me asking questions about how our human visual systems respond to data that presents a serious encoding challenge in light of Shannon, what gets passed through to our brains, etc.


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