is a 3×3 matrix which relates corresponding points in stereo images.
Its seven parameters represent the only geometric information about cameras that can be obtained through point correspondences alone.
The term "fundamental matrix" was coined by QT Luong in his influential PhD thesis.
The above relation which defines the fundamental matrix was published in 1992 by both Olivier Faugeras and Richard Hartley.
Although H. Christopher Longuet-Higgins' essential matrix satisfies a similar relationship, the essential matrix is a metric object pertaining to calibrated cameras, while the fundamental matrix describes the correspondence in more general and fundamental terms of projective geometry.
Given the projection of a scene point into one of the images the corresponding point in the other image is constrained to a line, helping the search, and allowing for the detection of wrong correspondences.
The fundamental matrix can be determined by a set of point correspondences.
Additionally, these corresponding image points may be triangulated to world points with the help of camera matrices derived directly from this fundamental matrix.
The cameras then transform as The fundamental matrix can also be derived using the coplanarity condition.
[2] The fundamental matrix expresses the epipolar geometry in stereo images.
The epipolar geometry in images taken with perspective cameras appears as straight lines.