A linear method for camera pair self-calibration

Abstract

We examine 3D reconstruction in unordered sets of uncalibrated images. We introduce a linear method to self-calibrate and find the metric reconstruction of a camera pair. We assume unknown and varying focal lengths but otherwise known internal camera parameters and a known projective reconstruction of the camera pair. We recover two possible camera configurations in space and use the Cheirality condition, that all 3D scene points are in front of both cameras, to disambiguate the solution. Towards identifying camera configurations that would perplex solution disambiguation, we show in two Theorems, first that the two solutions are in mirror positions and then the relations between their viewing directions. We validate our approach in synthetic and real scenes. In camera pair self-calibration and metric reconstruction, our method performs on par (median rotation error ΔR=3.49°) with the standard approach of Kruppa equations followed by 5P algorithm (ΔR=3.77°). We get realistic multi-view reconstructions, using numerous camera pair metric reconstructions generated by our linear method, rotation-averaging algorithms and a novel method to average focal length estimates.