Evaluation of a First-Order Primal-Dual Algorithm for MRF Energy Minimization
We investigate the First-Order Primal-Dual (FPD) algorithm of Chambolle and Pock  in connection with MAP inference for general discrete graphical models. We provide a tight analytical upper bound of the stepsize parameter as a function of the underlying graphical structure (number of states, graph connectivity) and thus insight into the dependency of the convergence rate on the problem structure. Furthermore, we provide a method to compute efficiently primal and dual feasible solutions as part of the FPD iteration, which allows to obtain a sound termination criterion based on the primal-dual gap. An experimental comparison with Nesterov’s first-order method in connection with dual decomposition shows superiority of the latter one in optimizing the dual problem. However due to the direct optimization of the primal bound, for small-sized (e.g. 20x20 grid graphs) problems with a large number of states, FPD iterations lead to faster improvement of the primal bound and a resulting faster overall convergence.
Keywordsgraphical model MAP inference LP relaxation image labeling sparse convex programming
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- 1.Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging and Vision, 1–26 (2010)Google Scholar
- 4.Schlesinger, M.: Syntactic analysis of two-dimensional visual signals in the presence of noise. Kibernetika, 113–130 (1976)Google Scholar
- 5.Werner, T.: A linear programming approach to max-sum problem: A review. IEEE PAMI 29 (2007)Google Scholar
- 8.Komodakis, N., Paragios, N., Tziritas, G.: MRF optimization via dual decomposition: Message-passing revisited. In: ICCV (2007)Google Scholar
- 9.Schlesinger, M., Giginyak, V.: Solution to structural recognition (MAX,+)-problems by their equivalent transformations. In 2 parts. Control Systems and Computers (2007)Google Scholar
- 10.Savchynskyy, B., Kappes, J., Schmidt, S., Schnörr, C.: A study of Nesterov’s scheme for Lagrangian decomposition and MAP labeling. In: CVPR 2011 (2011)Google Scholar
- 12.Nesterov, Y.: Smooth minimization of non-smooth functions. Math. Program. Ser. A, 127–152 (2004)Google Scholar