Globally Optimal 2D-3D Registration from Points or Lines without Correspondences

Abstract

An open access repository of Middlesex University research http://eprints.mdx.ac.uk Brown, Mark and Windridge, David and Guillemaut, Jean-Yves (2015) Globally optimal 2D-3D registration from points or lines without correspondences. Copyright and moral rights to this thesis/research project are retained by the author and/or other copyright owners. The work is supplied on the understanding that any use for commercial gain is strictly forbidden. A copy may be downloaded for personal, non-commercial, research or study without prior permission and without charge. Any use of the thesis/research project for private study or research must be properly acknowledged with reference to the work's full bibliographic details.This thesis/research project may not be reproduced in any format or medium, or extensive quotations taken from it, or its content changed in any way, without first obtaining permission in writing from the copyright holder(s).If you believe that any material held in the repository infringes copyright law, please contact the Repository Team at Middlesex University via the following email address:eprints@mdx.ac.ukThe item will be removed from the repository while any claim is being investigated. Globally Optimal 2D-3D Registration from Points or Lines Without Correspondences

Globally-Optimal Inlier Set Maximisation for Simultaneous Camera Pose and Feature Correspondence

“…While not optimal, Jurie [20] used an approach similar to BB for 2D-3D alignment with a linear approximation of perspective projection. Brown et al [5] proposed a global and -suboptimal method using BB. It finds a camera pose whose trimmed geometric error, the sum of angular distances between the bearings and their rotationally-closest 3D points, is within of the global minimum.…”

“…The translation bound from [5] encloses a translation cube with a sphere of radius ρ t = √ 3δ t and is given by…”

“…Hypothesise-and-test approaches such as RANSAC [13], when applied to the correspondence-free problem [15], are global methods that are not reliant on pose priors but quickly become computationally intractable as the number of points and outliers increase and do not provide an optimality guarantee. More recently, a global andsuboptimal method has been proposed [5], which uses a branch-and-bound approach to find a camera pose whose trimmed geometric error is within of the global minimum.…”

“…In addition, we also apply local optimisation whenever the algorithm finds a better transformation, to accelerate convergence without voiding the optimality guarantee. Cardinality maximisation allows an exact optimiser to be found, unlike the -suboptimality inherent to the continuous objective function used in [5]. More critically, cardinality maximisation is inherently robust to 2D and 3D outliers, while avoiding the problems associated with trimming.…”

“…If the inlier fraction is over-or under-estimated, this approach may converge to the wrong pose, without a means to detect failure. Figure 2 demonstrates how the global optimum of a trimmed objective function, as used by [5,49], may not occur at the true pose, a problem that is exacerbated when the inlier fraction is guessed incorrectly.…”