  In this paper we study the numerical instabilities of the 5- and 7-point
problems for essential and fundamental matrix estimation in multiview geometry.
In both cases we characterize the ill-posed world scenes where the condition
number for epipolar estimation is infinite. We also characterize the ill-posed
instances in terms of the given image data. To arrive at these results, we
present a general framework for analyzing the conditioning of minimal problems
in multiview geometry, based on Riemannian manifolds. Experiments with
synthetic and real-world data then reveal a striking conclusion: that Random
Sample Consensus (RANSAC) in Structure-from-Motion (SfM) does not only serve to
filter out outliers, but RANSAC also selects for well-conditioned image data,
sufficiently separated from the ill-posed locus that our theory predicts. Our
findings suggest that, in future work, one could try to accelerate and increase
the success of RANSAC by testing only well-conditioned image data.
