Perspective Projection – Recap

We've talked in earlier lectures about perspective projection. This is the transformation of points in a three-dimensional world into a two-dimensional image. And involves the loss of a dimension it leads to artifacts such as lines which are parallel in the three-dimensional world appearing to converge in the two-dimensional image or projection of that three-dimensional world.

Another example here a bunch of parallel lines, parallel three trunks which appear to converge at a point. We talked early on about the pinhole imaging model. We have a three-dimensional scene and it projects into a two-dimensional image. There is no unique inverse of the perspective projection. Any number of different three-dimensional models will lead to exactly the same two-dimensional projection. The lack of a unique inverse is really important consequence of the perspective projection.

For robotics, knowledge of the three-dimensional world is really important. A robot needs to know how far away is the object that it wants to grasp. A mobile robot needs to know whether the space in front of it is free to be driven in or whether there is an obstacle there.

So the important topic that we can uncover in this lecture is how do we recover the third dimension. That’s been lost in the perspective projection process when we capture an image.