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