Next: 4 Constraining the rectifying Up: Rectification with unconstrained stereo Previous: 2 Notation and basics

 

3 The rectification transformation

We now show that, if is the projection matrix which rectifies one of the two views, the linear transformation (in projective coordinates) that maps the retinal plane of onto the rectified retinal plane is given by the matrix . For any 3-D point w we can write

We know that the equation of the optical ray associated to is

hence

Assuming that rectification does not alter the optical center ( ), we obtain

This is a clearer and more compact result than the one reported in [ 1 ], in which is not written as the inverse of a projection matrix.



Next: 4 Constraining the rectifying Up: Rectification with unconstrained stereo Previous: 2 Notation and basics

Adrian F Clark
Wed Jul 23 16:48:44 BST 1997