real world columns; stereo vision

How many of you have heard of the book ‘Flatland’? Written in Victorian Britain by Edwin A. Abbott, it tells the story of a two-dimensional world peopled by shapes. The higher nobility are shapes with lots of sides, the upper class are pentagons, the middle classes are squares (real Victorian stuff this!) and the lower classes are triangles, the lower they are the thinner the triangle, criminals are incredibly thin triangles, and then the women are straight lines. A wonderful exercise in two-dimensional topology but a truly sad reflection on the values of those times.

Thankfully we live in a 3D world (and a world where women have a somewhat better perception in society). But is it really all that 3D? How often do we go swooping around in the third dimension? When was the last time you did a ‘loop the loop’? We actually live a sort of 'two and a half'-D existence. Confined to live in a thin, 3D layer occasionally going upstairs to another thin, 3D layer that just happens to be located above the first.

You can tell we have always been confined to this 'two and a half'-D existence in the way our ears have evolved. We can gauge direction with our ears thanks to some complex integration between the signals reaching both ears. But our ears are separated on the horizontal plain meaning that we are sensitive to direction on the horizontal plane but on the vertical plain there is no vertical separation between our ears and thus we cannot pinpoint vertical direction.

In practical terms what this means is that we get confused when someone shouts to us from a balcony. We can tell that the shout is coming from a particular direction but not from how high above the ground it is coming. One solution to this is to separate out ears in the vertical plane. This sounds painful but it can be done by the simple act of tilting our heads to one side. Cats and dogs sometimes tilt their heads when listening so there could be something in it.

What about eyes? Do they triangulate in the same way? Are our eyes geared up to life in the plane? Well, due to the difference in velocity between sound and light they can’t do the same trick that the ears do, and anyway, they don’t need to. Direction in vision is implicit, you don’t see something and wonder, ‘Which direction is that in?’ You can see which direction it is in!

If we can judge direction with just one eye then why do we have two? One factor is redundancy. One only has to think of Jason and the Cyclops to realize the drawbacks of monocular vision. But binocular vision is useful for other things. We get different views from different eyes and the integration of these two views provides us not with direction information, but with depth information about what we can see.

That is the key to why our two eyes are next to each other and not one above the other. We need to see what things are in front of other things and that depends on how the edges of things overlap each other. When things are in front of one another they have more edge overlaps in the vertical plane than in the horizontal plane. In general things are tall and thin and not short and fat. Think of tree trunks, cliff walls, people, edges of mammoths etc. Furthermore, those things that move are usually, like us, confined to moving on the flat, they don’t go higher or lower but they do go from side to side. And we ourselves are going to navigate in this plane going in between these things we can see.

This integration of views from two eyes is just one of the factors that govern our perception of depth, there are many others. There are cues that are inherent in the view itself. The loss of detail and the blue shift of color as things get further away. The brain is also aware of how much our eyes have to move together when we look at something. This sense can get confused when we look at patterns that repeat horizontally like curly telephone cords, mesh fencing or random dot stereograms, making them look nearer or further away than they really are. Another small detail that the brain is aware of is the amount that the eye lens has to stretch to bring something into focus. Ever seen orange icons on a blue background? The orange things really do seem to float in front of the blue even though they are the same distance away. The difference in wavelength between blue and orange light means that the eye lens has to do different amounts of stretching to focus them and thus the brain is tricked into perceiving them as being at different depths.

In conclusion then we have evolved in amazing ways over millions of years to integrate all sorts of information regarding the world around us. We have evolved to be almost perfect. All we have to do now is sort out the last vestiges of that Victorian attitude to women and we will be there!