On computing metric upgrades of projective reconstructions under the rectangular pixel assumption

Abstract

This paper shows how to upgrade the projective reconstruction of a scene to a metric one in the case where the only assumption made about thecameras observing that scene is that they have rectangular pixels (zero-skew cameras).The proposed approach is based on a simple characterization of zero-skewprojection matrices in terms of line geometry, and it handles zero-skew cameras with arbitrary or known aspect ratios in a unified framework. The metric upgradecomputation is decomposed into a sequence of linear operations, including linearleast-squares parameter estimation and eigenvalue-based symmetric matrix factorization, followed by an optional non-linear least-squares refinement step. Afew classes of critical motions for which a unique solution cannot be found are spelled out. A MATLAB implementation has been constructed and preliminary experiments with real data are presented.