On Computing Metric Upgrades of Projective Reconstructions Under the Rectangular Pixel Assumption

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 the cameras observing that scene is that they have rectangular pixels (zero-skew cameras). The proposed approach is based on a simple characterization of zero-skew projection matrices in terms of line geometry, and it handles zero-skew cameras with arbitrary or known aspect ratios in a uniied framework. The metric upgrade computation is decomposed into a sequence of linear operations, including linear least-squares parameter estimation and eigenvalue-based symmetric matrix factorization, followed by an optional non-linear least-squares reenement step. A few 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.