There are two camera coordinate systems, related by a rotation and a translation :

Taking the vector product with , followed by the scalar product with

which expresses that the vectors , and are coplanar. Using

gives a relation between image points in the camera coordinate systems, . This can be written , where

is the ** Essential** matrix.
This is the algebraic representation of epipolar
geometry for known calibration.

Then using the calibration matrices to relate the image point in pixels to the point in the camera coordinate system:

which defines the ** Fundamental** matrix, by

where

Wed Apr 16 00:58:54 BST 1997