Compatibility of Fundamental and Essential Matrix Triples

Abstract: The fundamental matrix of a pair of pinhole cameras lies at the core of systems that reconstruct 3D scenes from 2D images. However, for more than two cameras, the relations between the various fundamental matrices of camera pairs are not yet completely understood. In joint work with Viktor Korotynskiy, Anton Leykin, and Tomas Pajdla, we characterize all polynomial constraints that hold for an arbitrary triple of fundamental matrices. Unlike most constraints in previous works, our constraints hold independently of the relative scaling of the fundamental matrices, which is unknown in practice. We also provide a partial characterization for essential matrix triples arising from calibrated cameras.

Computer sciencealgebraic geometry

Audience: learners

Tropical mathematics and machine learning

Series comments: Besides ML and tropical math, anything tech+math is welcome.