Graph Cuts via l1 Norm Minimization

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Laplace equations
graph theory
linear programming
minimisation
sparse matrices
Laplacian
continuous optimization problems
graph cuts
image processing problems
sparse linear systems
unconstrained l1 norm minimization
Continuous optimization
Graph-theoretic methods
Algorithms
Artificial Intelligence
Image Enhancement
Image Interpretation
Computer-Assisted
Imaging
Three-Dimensional
Pattern Recognition
Automated
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Abstract

Graph cuts have become an increasingly important tool for solving a number of energy minimization problems in computer vision and other fields. In this paper, the graph cut problem is reformulated as an unconstrained l1 norm minimization that can be solved effectively using interior point methods. This reformulation exposes connections between graph cuts and other related continuous optimization problems. Eventually, the problem is reduced to solving a sequence of sparse linear systems involving the Laplacian of the underlying graph. The proposed procedure exploits the structure of these linear systems in a manner that is easily amenable to parallel implementations. Experimental results obtained by applying the procedure to graphs derived from image processing problems are provided.

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2008-10-01
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Copyright 2008 IEEE. Reprinted from: Bhusnurmath, A.; Taylor, C.J., "Graph Cuts via $ell_1$ Norm Minimization," Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol.30, no.10, pp.1866-1871, Oct. 2008 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4483514&isnumber=4601506 This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
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