General search algorithms for energy minimization problems

Abstract

We describe a scheme for solving Energy Minimization problems, which is based on the A* algorithm accomplished with appropriately chosen LP-relaxations as heuristic functions. The proposed scheme is quite general and therefore can not be applied directly for real computer vision tasks. It is rather a framework, which allows to study some properties of Energy Minimization tasks and related LP-relaxations. However, it is possible to simplify it in such a way, that it can be used as a stop criterion for LP based iterative algorithms. Its main advantage is that it is exact - i.e. it never produces a discrete solution that is not globally optimal. In practice it is often able to find the optimal discrete solution even if the used LP-solver does not reach the global optimum of the corresponding LP-relaxation. Consequently, for many Energy Minimization problems it is not necessary to solve the corresponding LP-relaxations exactly. © 2009 Springer.