Publication

Memory Efficient Max Flow for Multi-Label Submodular MRFs

Mathieu Salzmann
2019
Journal Articles

Abstract

Multi-label submodular Markov Random Fields (MRFs) have been shown to be solvable using max-flow based on an encoding of the labels proposed by Ishikawa, in which each variable X-i is represented by l nodes (where l is the number of labels) arranged in a column. However, this method in general requires 2l(2) edges for each pair of neighbouring variables. This makes it inapplicable to realistic problems with many variables and labels, due to excessive memory requirement. In this paper, we introduce a variant of the max-flow algorithm that requires much less storage. Consequently, our algorithm makes it possible to optimally solve multi-label submodular problems involving large numbers of variables and labels on a standard computer.

Official source

https://infoscience.epfl.ch/entities/publication/cf814669-821e-4ea7-8b9e-5e2206a821c5

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Mathieu Salzmann
2019
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/cf814669-821e-4ea7-8b9e-5e2206a821c5

About this result

Related concepts (8)

Maximum flow problem

In optimization theory, maximum flow problems involve finding a feasible flow through a flow network that obtains the maximum possible flow rate. The maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem. The maximum value of an s-t flow (i.e., flow from source s to sink t) is equal to the minimum capacity of an s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem. The maximum flow problem was first formulated in 1954 by T.

Max-flow min-cut theorem

In computer science and optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source to the sink is equal to the total weight of the edges in a minimum cut, i.e., the smallest total weight of the edges which if removed would disconnect the source from the sink. This is a special case of the duality theorem for linear programs and can be used to derive Menger's theorem and the Kőnig–Egerváry theorem.

Flow network

In graph theory, a flow network (also known as a transportation network) is a directed graph where each edge has a capacity and each edge receives a flow. The amount of flow on an edge cannot exceed the capacity of the edge. Often in operations research, a directed graph is called a network, the vertices are called nodes and the edges are called arcs. A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, unless it is a source, which has only outgoing flow, or sink, which has only incoming flow.

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