Approximate Labeling via Graph Cuts Based on Linear Programming

A new framework is presented for both understanding and developing graph-cut based combinatorial algorithms suitable for the approximate optimization of a very wide class of MRFs that are frequently encountered in computer vision. The proposed framework utilizes tools from the duality theory of linear programming in order to provide an alternative and more general view of state-of-the-art techniques like the α-expansion algorithm, which is included merely as a special case. Moreover, contrary to αexpansion, the derived algorithms generate solutions with guaranteed optimality properties for a much wider class of problems, e.g. even for MRFs with non-metric potentials. In addition, they are capable of providing per-instance suboptimality bounds in all occasions, including discrete Markov Random Fields with an arbitrary potential function. These bounds prove to be very tight in practice (i.e. very close to 1), which means that the resulting solutions are almost optimal. Our algorithmsâ...

• Type: Journal
• Year: 2007
• Where: PAMI
• Authors: Nikos Komodakis, Georgios Tziritas
• Keywords: Algorithms, Arbitrary Potential Function, Markov Random Fields, PAMI 2007