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Graph Cuts via $\ell_1$ Norm Minimization
October 2008 (vol. 30 no. 10)
pp. 1866-1871
Arvind Bhusnurmath, GRASP Laboratory, Philadelphia
Camillo J. Taylor, GRASP Laboratory, Philadelphia
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 $\ell_1$ norm minimization which can be solved effectively using interior point methods. This reformulation exposes connections between the 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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Index Terms:
Continuous optimization, Graph-theoretic methods
Citation:
Arvind Bhusnurmath, Camillo J. Taylor, "Graph Cuts via $\ell_1$ Norm Minimization," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 30, no. 10, pp. 1866-1871, Oct. 2008, doi:10.1109/TPAMI.2008.82
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