The fundamental ** geometric** relationship between two perspective cameras.

- The
**epipole**: is the*point*of intersection of the line joining the optical centres---the*baseline*---with the image plane. The epipole is the image in one camera of the optical centre of the other camera. - The
**epipolar plane**: is the*plane*defined by a 3D point and the optical centres. Or, equivalently, by an image point and the optical centres. - The
**epipolar line**: is the*straight line*of intersection of the epipolar plane with the image plane. It is the image in one camera of a ray through the optical centre and image point in the other camera. All epipolar lines intersect at the epipole.

** Epipolar pencil**

As the position of the 3D point varies, the epipolar planes ``rotate'' about the baseline. This family of planes is known as an epipolar pencil. All epipolar lines intersect at the epipole.

** Correspondences between images**

A ** point** in one image generates a ** line** in the other
on which its corresponding point must lie. The search for
correspondences is thus reduced from a region to a line.
This ** epipolar constraint** arises
because, for image points corresponding to the same 3D point, the image points,
3D point and optical centres are coplanar.

Wed Apr 16 00:58:54 BST 1997