Two View Geometry Estimation with Outliers

Estimating the relative orientation of two cameras is a classical problem in vision. Probably the most well-known method is the eight-point algorithm introduced by Longuet-Higgins in 1981 [5], and modified by Hartley [3] to include normalization. Although normalization made the algorithm more robust, there are still algorithmic degeneracies and the algorithm breaks down in the presence of outliers. For calibrated cameras a guaranteed optimal algorithm minimizing reprojection errors appeared just recently in [2] but it cannot handle outliers in the correspondence set. Thus, heuristic methods like hypothesizeand-test approaches are normally used to remove outliers, [1, 4]. In this paper we address the problem of uncertain correspondences by formulating it as a mathematical optimization problem. For calibrated cameras, we provide both necessary and sufficient geometric constraints for an optimal solution. Based on this analysis, we propose an algorithm to find the optimal set of correspondences as well as the optimal relative orientation. To make this more precise, we say that a correspondence (x, x̄) is consistent with a relative orientation (R, t) if there exists a 3D point X such that its angular reprojection errors satisfy