ETH Zurich - D-INFK - IVC - CVG - Research - Toroidal Constraints for Localization

Toroidal Constraints for Two-Point Localization Under High Outlier Ratios

Federico Camposeco (1)      Torsten Sattler (1)      Andrea Cohen (1)     
Andreas Geiger (1,2)      Marc Pollefeys(1)

(1) CVG ETH Zurich, Switzerland
(2) Autonomous Vision Group, MPI for Intelligent Systems Tübingen,,,,

Our method utilizes previously unused latent geometric information in the 2D-3D image matching process (a). From the initial direction of triangulation (q0) we can get a rough estimate of the camera position on the surface of the torus (b). Since only two 2D-3D matches are needed for this computation, we develop a novel outlier filter based on this rough camera positions.


Localizing a query image against a 3D model at large scale is a hard problem, since 2D-3D matches become more and more ambiguous as the model size increases. This creates a need for pose estimation strategies that can handle very low inlier ratios. In this paper, we draw new insights on the geometric information available from the 2D-3D matching process. As modern descriptors are not invariant against large variations in viewpoint, we are able to find the rays in space used to triangulate a given point that are closest to a query descriptor. It is well known that two correspondences constrain the camera to lie on the surface of a torus. Adding the knowledge of direction of triangulation, we are able to approximate the position of the camera from two matches alone. We derive a geometric solver that can compute this position in under 1 microsecond. Using this solver, we propose a simple yet powerful outlier filter which scales quadratically in the number of matches. We validate the accuracy of our solver and demonstrate the usefulness of our method in real world settings.


  • Toroidal Constraints for Two-Point Localization under High Outlier Ratios
    Federico Camposeco, Torsten Sattler, Andrea Cohen, Andreas Geiger and Marc Pollefeys.
    to appear in CVPR 2017.

Code for Geometric Solver

Coming soon.

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