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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.
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
Bhusnurmath, Arvind and Taylor, Camillo J., "Graph Cuts via l1 Norm Minimization" (2008). Lab Papers (GRASP). Paper 47.
Date Posted: 07 October 2009
This document has been peer reviewed.