Epipolar Geometry
Pinhole model
or
 is a matrix, which transforms the normalized
image coordinates to pixel image coordinates.
 represents the displacement from the world
coordinate system to the camera coordinate system.
Epipolar Geometry
Fundamental equations: (pinhole model)
if in image 1 is matched to in image 2
Epipolar equation: eliminating M, and
where is a 3 3 antisymmetric matrix such that
Fundamental matrix: define
 Epipolar equation:
 completely characterizes the epipolar geometry between
two images: two epipoles (4 parameters) and the
homography between the two pencils of epipolar lines (3
parameters).
 has only seven degrees of freedom
(up to a scale factor & zero determinant)
at least 7 point matches to estimate  : epipolar line of

where is the essential matrix.
Author: Zhengyou Zhang
Email: zzhang@sophia.inria.fr
Wed Oct 9 14:50:47 MET DST 1996