Memory Efficient Max Flow for Multi-label Submodular MRFs
This work addresses a memory bottleneck for researchers and practitioners in computer vision and related fields, though it is incremental as it builds on existing Ishikawa encoding.
The paper tackles the excessive memory requirement of max-flow algorithms for multi-label submodular MRFs by introducing a variant that reduces storage needs, enabling optimal solutions for large-scale problems on standard computers.
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 $\ell$ nodes (where $\ell$ is the number of labels) arranged in a column. However, this method in general requires $2\,\ell^2$ 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.