DK9: Algebraic Equations in Multiview Geometry

The structure-and-motion problem is the problem of obtaining information about a three-dimensional configuration - consisting of points, lines, or more complicated geometric figures - from its two-dimensional projections. The "motion"-aspect arised when we want to compute the position of the camera in relation to the spatial configuration. The question can be reduced to systems of polynomial equations.

The goal of the proposed PhD project is to study instances of such problems from a theoretical and practical point of view. Relevant questions are: how much information is needed so that the solution is determined uniquely or at least such that there are only finitely many solutions? In the second case, how many solutions do exists? Can we exploit special structure of the arising systems in order to solve them faster?

Supervisor: Prof. Josef Schicho