Fast and Reliable Two-View Translation Estimation

Abstract

It has long been recognized that one of the fundamental difficulties in the estimation of two-view epipolar geometry is the capability of handling outliers. In this paper, we develop a fast and tractable algorithm that maximizes the number of inliers under the assumption of a purely translating camera. Compared to classical random sampling methods, our approach is guaranteed to compute the optimal solution of a cost function based on reprojection errors and it has better time complexity. The performance is in fact independent of the inlier/outlier ratio of the data.This opens up for a more reliable approach to robust ego-motion estimation. Our basic translation estimator can be embedded into a system that computes the full camera rotation. We demonstrate the applicability in several difficult settings with large amounts of outliers. It turns out to be particularly well-suited for small rotations and rotations around a known axis (which is the case for cellular phones where the gravitation axis can be measured). Experimental results show that compared to standard RANSAC methods based on minimal solvers, our algorithm produces more accurate estimates in the presence of large outlier ratios.

Practical robust two-view translation estimation

“…We show that the method outperforms RANSAC in terms of quality of the solution and can in some cases be faster, in particular if the portion of outliers is high. In addition, the approach outperforms [7] with orders of magnitude while providing the same optimality guarantees.…”

“…In this paper we present a branch and bound approach tailored for the two-view translation problem that outperforms Fredriksson et al [7]. The key to designing an effective formulation is to find strong bounding functions that can be evaluated efficiently.…”

“…In this paper we present a branch and bound approach that is significantly faster than [7] with the same kind of theoretical guarantees. The branch and bound methodology has been applied to a variety of geometry problems.…”

“…In [7], Fredriksson et al gave an optimal algorithm for the two-view translation problem in the presence of outliers. For a given error threshold the algorithm finds a translation with the maximal amount of inlier correspondences, with a theoretical time complexity of O(n 2 log n).…”

“…[8,7]. For spherical cameras the projections are formed by first applying a Euclidean transformation which takes the 3D-points to the camera's coordinate system followed by normalization.…”