Computing a homography between two images

The first recipe of this chapter showed you how to compute the fundamental matrix of an image pair from a set of matches. In projective geometry, another very useful mathematical entity also exists. This one can be computed from multi-view imagery and, as we will see, is a matrix with special properties.

Getting ready

Again, let's consider the projective relation between a 3D point and its image on a camera, which we presented in the introduction section of this chapter. Basically, we learned that this equation relates a 3D point to its image using the intrinsic properties of the camera and the position of that camera (specified with a rotation and a translation component). If we now carefully examine this equation, we realize that there are two special situations of particular interest. The first situation is when two views of a scene are separated by a pure rotation. We can then observe that the fourth column of the extrinsic matrix will be...