Graph cuts with interacting edge weights: examples, approximations, and algorithms

We study an extension of the classical graph cut problem, wherein we replace the modular (sum of edge weights) cost function by a submodular set function defined over graph edges. Special cases of this problem have appeared in different applications in signal processing, machine learning, and comput...

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Bibliographic Details
Published in:Mathematical programming Vol. 162; no. 1-2; pp. 241 - 282
Main Authors: Jegelka, Stefanie, Bilmes, Jeff A.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2017
Springer Nature B.V
Subjects:
Algorithms
Approximation
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Computer vision
Full Length Paper
Graph theory
Graphs
Joints
Linear programming
Machine learning
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Signal processing
Studies
Theoretical
Wireless networks
68T45
68R10
68Q25
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary:We study an extension of the classical graph cut problem, wherein we replace the modular (sum of edge weights) cost function by a submodular set function defined over graph edges. Special cases of this problem have appeared in different applications in signal processing, machine learning, and computer vision. In this paper, we connect these applications via the generic formulation of “cooperative graph cuts”, for which we study complexity, algorithms, and connections to polymatroidal network flows. Finally, we compare the proposed algorithms empirically.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-016-1038-y