24 May 2008

Why nearby things whoosh by quickly you when you drive, but distant ones don't

Hi -

Tonight J-Fav is out of the house, so I am left to my own devices here as T-Fav sleeps. In an idle moment I decided to submit an answer to New Scientist's weekly question in their "The Last Word" column. This week's question is:

Driving along in the car the other day, my four-year-old son asked why things that were closer to us were moving faster than those further away. What should I tell him? (Milton Inverdale, London, UK)

Here's my response, which is the real techie answer for the parent plus a little experiment for the 4 year-old:

We can answer this question and provide a simple manual "demonstration" that might appeal to Milton's 4 year-old. The complicated-sounding answer is that the type of optical system used by our eyes causes us to perceive a particular object as "smaller" the more distant it is; this is called foreshortening. Foreshortening causes nearby objects to appear to sweep past our vision much more rapidly than distant ones because it implicitly converts the angles subtended by the things you're looking at into distances on your retina. Therefore, nearby objects whoosh past your vision almost instantly because they have a high angular velocity with respect to the vertex of your pupil - but distant objects appear to creep along because they have a low angular velocity.

If our eyes were designed differently, with so-called "orthoscopic imaging," it would operate on the lengths of objects rather than their angles. That is, as you drove along in your car, everything would appear to move at the same rate. However, unless your eyes were very large, you wouldn't be able to see very far around the direction you're looking at!

You can demonstrate these things by placing your hand on a newspaper. Make a "V" with your index and middle finger and sweep it along the text. Your hand is the car, and the V is your field of view. You can see that the text near your fingernails takes a long time to move from one finger to the text, while the text closer to your hand transits more rapidly. In contrast, extend your index and ring fingers in parallel. When you sweep those along, every line of text takes the same amount of time to move from one finger to the other.


ps Fun diversion: check out NaturalMotion Euphoria, software for game developers that incorporates physics and AI to simulate really natural-looking motion of game characters. This is a big deal because it can replace "keyframing," a hard-coded approach. Anyway, take a look.


Matthias said...

That's a good answer. At first I thought you said you submitted the *question*, which seemed kind of dumb since you clearly knew the answer, and why would you use a weird pseudonym like "Milton Inverdale, London, UK," which sounds like something from Monty Python anyway? But then I reread it and all became clear. Pun not intended.

Here's what I want to hear more about though, Mister Fun With Optics. Would it actually be possible for eyes to function orthoscopically? My vague sense is that the angularity of vision has something to do with the ability to focus. I'm not sure that's at all true, but I'm too tired to bring my extremely limited understanding of optics to bear (see also previous paragraph). Explain!

G-Fav said...

Hey Matthias -

I've been wondering about your question today but I'm afraid I don't know the answer.

I used "orthoscopic" as a teaching-tool rather than a practical suggestion, so that there could be a counterexample to how usual imaging systems work, like our eyes. My comment was sort-of justified by the existence of orthoscopic optics in the field of camera-based inspection of microscopic parts. (They eliminate foreshortening in the images of the specimen you're looking at.) Also, they are available as a theoretical construct in the field of computer graphics. I am not aware of any large-scale optical systems that are, by default, orthoscopic.

I think it would be VERY impractical for a biological eye to work over long distances in a parallax-free (ie orthoscopic) manner. I googled around quite a bit for a good answer to your question but am coming up empty. (I can architect display systems, but am not a lens designer.) One far-fetched way for an animal to have orthoscopic vision might be the use of a fly's-eye (lots of little lenslets) in conjunction with really weird neural wiring that effectively ignores everything but the rays entering exactly perpendicular to the eye's surface.

Two extremes of how I might imagine more biologically-plausible orthoscopic vision are: well, actually, none. The implausible extremes are: (1) an eye with just one photoreceptor, on the optic axis of its lens, or (2) something involving a freakishly huge lens and considerable intervening optics that only accept parallel bundles of light to strike your photoreceptors.

There is some theoretical work being done in the generalization of all picture-taking ("imaging") systems, but just because you can do it in a computer, doesn't always mean you can do it with a biological lens. See Figure 5 in this paper for examples of funky imaging transformations.

There are also orthoscopic eyepieces in the fields of astronomy and marksmanship.


G-Fav said...

(smacks self on forehead) Optical engineer Michael Thomas reminds me that the type of lens I'm thinking of is a so-called telecentric lens. Shame on me for not remembering that, as we've used these before. Anyhow, Matthias, here is a page from Edmund Optics that might help.