Zuzana Kukelova, Martin Bujnak, Tomas Pajdla The Art of Solving Minimal Problems Tricks: Problem Formulation Microsoft Research Cambridge Czech Technical University in Prague Capturing Reality s.r.o. CapturingReality

How important is the problem formulation? “The mere formulation of a problem is often far more essential than its solution, which may be merely a matter of mathematical or experimental skills. ….” - Albert Einstein

Absolute pose of a camera with unknown focal length Over-constrained system – 3.5 points sufficient Different strategies for selecting equations

Different formulations Using distances Using ratios of distances Rotation matrix parametrized using quaternions DIAC – dual image of the absolute quadric

Performance of different solvers and different formulations

How important is the problem formulation? Success = good formulation + good solver Finding a good solution one have to try many formulations & solvers Easy with automatic solver generators

Using an automatic generator we can quite quickly test and evaluate different, formulations, different orderings of variables or monomials Polynomial system Evaluation Solver source code