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Fundamental Matrix

http://en.wikipedia.org/wiki/Fundamental_matrix_(computer_vision)
In computer vision, the fundamental matrix  \mathbf{F} is a  3 \times 3 matrix of rank 2 which relates corresponding points in stereo images. In epipolar geometry, with homogeneous image coordinates  \mathbf{y_1} and  \mathbf{y_2} of corresponding points in a stereo image pair,  \mathbf{F y_1} describes a line (an epipolar line) on which the corresponding point y2 on the other image must lie. That means, for all pairs of corresponding points holds

 \mathbf{ y_2^T  F y_1} = 0.

Being of rank two and determined only up to scale, the fundamental matrix can be estimated given at least seven point correspondences. Its seven parameters represent the only geometric information about cameras that can be obtained through point correspondences alone.



epipole
epipolar line
epipolar plane

http://en.wikipedia.org/wiki/Epipolar_geometry


RANdom SAmple Consensus
http://en.wikipedia.org/wiki/RANSAC



ref.
http://www.robots.ox.ac.uk/~vgg/hzbook/index.html

http://nonsense.danielwedge.com/2008/10/19/the-fundamental-matrix-song/


An Invitation to 3-D Vision
Yi Ma, Stefano Soatto, Jana Kosecka, Shankar Sastry
Springer Verlag, 2003

Learning Epipolar Geometry
The Java code for this page was created by Sylvain Bougnoux.

posted by maetel