Capturing. Reality The Art of Solving Minimal Problems Tricks: Problem Formulation Zuzana Kukelova, Martin Bujnak, Tomas Pajdla Microsoft Research Cambridge Czech Technical University in Prague Capturing Reality s. r. o.
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
The formulation of the problem may significantly influence • Complexity of the final “online” solver
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 • Easy with automatic solver generators one have to try many formulations & solvers
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