Vision and motion

It's going to be useful to say a little bit more about the point correspondence problem.

Here we have again the initial view of our triangular object and here we have the final view, or the desired view, of our triangle object. 

When the points move in the image plane it's possible for them to move like this and this is the example that we just looked at a moment ago. But it's also possible for the points to move like this and if they did that then the motion of the object in three dimensional space is going to be much more complex. It's almost going to require the object to flip around in the three-dimensional world.

Another way we could define the correspondence is like this and again it involved a different kind of three-dimensional motion.

And finally we could have this particular way of point moving on the image plane.

Each different way of associating a yellow dot with a red dot is going to result in a different motion in the three-dimensional world. The net result will be the same in the image plane but the actual three-dimensional motion will be different.