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