Re: 2-D images of 3-D objects

From: Harnad, Stevan (
Date: Mon Mar 03 1997 - 21:36:03 GMT

> From: Taylor, Karl <>
> > According to a theorem in solid geometry, if you mark three points on
> > the surface of a 3-D object, and look at the shadow it casts in 2D,
> > then the whole shape of the object can be recovered from just 2
> > different 2-D views. This is a view-based invariance. It means that your
> > visual system (or a machine's) could tell what the shape of a 3-D object
> > was from just two views of it.
> I understand that this theory says my visual system can
> recover the shape of an object from two different 2-D views.
> Does this mean that the two (slightly) different 2-D views
> that I receive (one in each eye) when I look at an object
> are enough? Or do the views need to be more different or
> less different under different circumstances?

The slight difference between what you see from each
eye is enough. (It's called "binocular disparity".)

> e.g. if I look at my fingernail with my hand up close to my
> eye the two images I get of it are quite different. But if I
> look at the side of a house from a few feet away the two
> images I get are virtually the same.

Yes, and your sense of depth in nearby space is more "3-D" than your
sense of depth in faraway things. But there other depth cues besides
binocular disparity. There's motion parallex (images of nearby things
move faster across your retina than images of faraway things); and the
moon illusions makes the moon looks bigger (and nearer) on the horizon
because of perspective cues than it does in mid-sky.

> Does that mean the difference necessary is related to
> some external things (like the distance between my eyes, the
> size of the object, my distance from it)?

Yes, all of those things.

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