Affine Reconstruction

Section 4.1 described the advantages of recovering affine space and provided some methods of computing the location of the plane at infinity $\Pi_{\infty}$. The easiest way to proceed is to use prior information, for instance the knowledge that lines in the scene are parallel or that a point is the half way between two others.

Prior constraints on the camera motion can also be used. For example, a translating camera is equivalent to a translating scene. Observing different images of the same point gives a line in the direction of motion. Intersecting several of these lines gives the point at infinity in the motion direction, and hence one constraint on the affine structure.

On the other hand, any line through two scene points translates into a line parallel to itself, and the intersection of these two lines gives further constraints on the affine structure. Given three such point pairs we have in all four points at infinity, and the projective reconstruction of these allows the ideal points to be recovered -- see [16] for details and experimental results.