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Fast approximate energy minimization with label costs
, 2010
"... The αexpansion algorithm [7] has had a significant impact in computer vision due to its generality, effectiveness, and speed. Thus far it can only minimize energies that involve unary, pairwise, and specialized higherorder terms. Our main contribution is to extend αexpansion so that it can simult ..."
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Cited by 108 (9 self)
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The αexpansion algorithm [7] has had a significant impact in computer vision due to its generality, effectiveness, and speed. Thus far it can only minimize energies that involve unary, pairwise, and specialized higherorder terms. Our main contribution is to extend αexpansion so that it can simultaneously optimize “label costs ” as well. An energy with label costs can penalize a solution based on the set of labels that appear in it. The simplest special case is to penalize the number of labels in the solution. Our energy is quite general, and we prove optimality bounds for our algorithm. A natural application of label costs is multimodel fitting, and we demonstrate several such applications in vision: homography detection, motion segmentation, and unsupervised image segmentation. Our C++/MATLAB implementation is publicly available.
Submodular Function Maximization
, 2012
"... Submodularity is a property of set functions with deep theoretical consequences and far–reaching applications. At first glance it appears very similar to concavity, in other ways it resembles convexity. It appears in a wide variety of applications: in Computer Science it has recently been identifie ..."
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Cited by 19 (5 self)
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Submodularity is a property of set functions with deep theoretical consequences and far–reaching applications. At first glance it appears very similar to concavity, in other ways it resembles convexity. It appears in a wide variety of applications: in Computer Science it has recently been identified and utilized in domains such as viral marketing (Kempe et al., 2003), information gathering (Krause and Guestrin, 2007), image segmentation (Boykov and
Bumi l LEE
"... A branchandbound algorithm for the multilevel uncapacitated facility location problem ..."
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A branchandbound algorithm for the multilevel uncapacitated facility location problem
Maximization of NonMonotone Submodular Functions
"... A litany of questions from a wide variety of scientific disciplines can be cast as nonmonotone submodular maximization problems. Since this class of problems includes maxcut, it is NPhard. Thus, generalpurpose algorithms for the class tend to be approximation algorithms. For unconstrained probl ..."
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A litany of questions from a wide variety of scientific disciplines can be cast as nonmonotone submodular maximization problems. Since this class of problems includes maxcut, it is NPhard. Thus, generalpurpose algorithms for the class tend to be approximation algorithms. For unconstrained problem instances, one recent innovation in this vein includes an algorithm of Buchbinder et al. (2012) that guarantees a 1 2approximation to the maximum. Building on this, for problems subject to cardinality constraints, Buchbinder et al. (2014) offer guarantees in the range [0.356, 12 + o(1)]. Earlier work has the best approximation factors for more complex constraints and settings. For constraints that can be characterized as a solvable polytope, Chekuri et al. (2011) provide guarantees. For the online secretary setting, Gupta et al. (2010) provide guarantees. In sum, the current body of work on nonmonotone submodular maximization lays