Invariant Fitting of Two View Geometry
Philip Torr and Andrew Fitzgibbon


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.