Terminology edit
- F (3×3) is the fundamental matrix.
- E (3×3) is the essential matrix
- P (3×4) is the Camera matrix (the projection matrix from world to image)
- C (3×1 or 4×1, homogeneous) is the center of projection in 3D space.
- T (3×1 or 4×1, homogeneous) is the T column of the RT matrix.
- K is the intrinsic parameters -- the camera matrix
From http://www.ecse.rpi.edu/~rjradke/papers/radkemcn08.pdf:
where is the extrinsic parameters.
If you know P, K, and P' then you can compute F many ways (epipolar-4.pdf):
where .
The essential matrix is given by
and so
and
- .
Epipolar lines are represented as 3-vectors -- normals to the 3D planes from a camera center such that where that plane intersects the corresponding image plane is the epipolar line on that image.