Here I present Epipolar geometry, Fundamental matrix, Fundamental matrices arising from special motions.

1. Epipolar geometry, Fundamental
matrix, Fundamental matrices
arising from special motions
Md. Safayet Hossain
Student of M.Sc
Computer Science and Engineering (KUET)
Presented by:

2. Epipolar Geometry
The epipolar geometry is the intrinsic projective geometry between
two views.
It is independent of scene structure, but depends on the cameras
internal parameters and relative pose.

3. Epipolar Geometry

4. Epipolar Geometry

5. Epipolar Geometry

6. Epipolar Geometry

7. Epipolar Geometry

8. Fundamental matrix F
The fundamental matrix is the algebraic representation of
epipolar geometry.
Fundamental matrix denoted by “F”
F is a rank 2 homogeneous matrix with 7 degrees of freedom

9. Properties of The Fundamental Matrix

10. Properties of The Fundamental Matrix

11. The Epipolar Line Homography
The set of epipolar lines in each of the images forms a pencil of lines
passing through the epipole. Such a pencil of lines may be considered as
a 1-dimensional projective space.

12. Fundamental matrix arising from special
motions
A special motion arises from a particular relationship
between the translation direction, t and the direction of the
rotation axis, a .
2 cases:
a) Pure translation, where there is no rotation.
b) Pure planar motion, where t is orthogonal to a.

13. Pure translation

14. Pure translation

15. Pure Planar Motion
In this case the rotation axis is orthogonal to the
translation direction. Orthogonality impose one
constraint on the motion. It reduce the number of
degrees of freedom from 7, for a general motion, to
6 degrees of freedom for a pure planar motion.

16. Thank you !