On the Instability of Relative Pose Estimation and RANSAC's Role
This addresses a fundamental problem in computer vision for researchers and practitioners by providing insights into the conditioning of minimal problems, with incremental implications for improving RANSAC efficiency.
The paper tackles the numerical instabilities in relative pose estimation for multiview geometry, characterizing ill-posed scenes where condition numbers become infinite, and reveals that RANSAC in Structure-from-Motion not only filters outliers but also selects well-conditioned image data.
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.