Invariant Fitting of Two View Geometry
Philip Torr and Andrew Fitzgibbon
Abstract
This paper describes the adaptation the Bookstein method for fitting conics
to determination of epipolar geometry. The new method has the advantage
that it exhibits the improved stability of previous methods for estimating
the epipolar geometry, such as the preconditioning method of Hartley,
whilst also being invariant to equiform transformations. Within this paper
it is proven that there is only one invariant norm to the set of Euclidean
transformations of the image, and that this norm gives rise to a quadratic
form allowing eigenvector methods to be used to find the essential matrix
E, the fundamental matrix F, or an arbitrary homography
H. This is a surprising result, as previously it had been thought
that there was no more to say on the matter of linear estimation of
epipolar geometry. The improved performance is justified by theory and
verified by experiments on real images.
PDF
Torr03.pdf
Code
fm_linear_trace22.m