Invariant fitting of two view geometry.

Abstract

This paper describes an extension of Bookstein's and Sampson's methods, for fitting conics, to the determination of epipolar geometry, both in the calibrated case, where the Essential matrix E is to be determined or in the uncalibrated case, where we seek the fundamental matrix F. We desire that the fitting of the relation be invariant to Euclidean transformations of the image, and show that there is only one suitable normalization of the coefficients and that this normalization gives rise to a quadratic form allowing eigenvector methods to be used to find E or F, or an arbitrary homography H. The resulting 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, while also being invariant to equiform transformations.