Continuous Inference in Graphical Models with Polynomial Energies

In this paper, we tackle the problem of performing inference in graphical models whose energy is a polynomial function of continuous variables. Our energy minimization method follows a dual decomposition approach, where the global problem is split into subproblems defined over the graph cliques. The optimal solution to these subproblems is obtained by making use of a polynomial system solver. Our algorithm inherits the convergence guarantees of dual decomposition. To speed up optimization, we also introduce a variant of this algorithm based on the augmented Lagrangian method. Our experiments illustrate the diversity of computer vision problems that can be expressed with polynomial energies, and demonstrate the benefits of our approach over existing continuous inference methods.