Capacity Scaling for Graph Cuts in Vision

Capacity scaling is a hierarchical approach to graph representation that can improve theoretical complexity and practical efficiency of max-flow/min-cut algorithms. Introduced by Edmonds, Karp, and Dinic [7, 6] in 1972, capacity scaling is well known in the combinatorial optimization community. Surprisingly, this major performance improving technique is overlooked in computer vision where graph cut methods typically solve energy minimization problems on huge N-D grids and algorithms' efficiency is a widely studied issue [3, 12, 16, 10]. Unlike some earlier hierarchical methods addressing efficiency of graph cuts in imaging, e.g. [16], capacity scaling preserves global optimality of the solution. This is the main motivation for our work studying capacity scaling in the context of vision. We show that capacity scaling significantly reduces non-polynomial theoretical time complexity of the max-flow algorithm in [3] to weakly polynomial O(m2 n2 log(U)) where U is the largest edge wei...

• Type: Conference
• Year: 2007
• Where: ICCV
• Authors: Olivier Juan, Yuri Boykov
• Keywords: Capacity Scaling, Capacity Scaling Preserves, Computer Vision, Graph Cut Methods, ICCV 2007, Methods Addressing Efficiency, Work Studying Capacity