Combinatorial optimization method for a family of functions of discrete variables
Graph cut optimization is a combinatorial optimization method applicable to a family of functions of discrete variables, named after the concept of cut in the theory of flow networks. Thanks to the max-flow min-cut theorem, determining the minimum cut over a graph representing a flow network is equivalent to computing the maximum flow over the network. Given a pseudo-Boolean function , if it is possible to construct a flow network with positive weights such that
each cut of the network can be mapped to an assignment of variables to (and vice versa), and
the cost of equals (up to an additive constant)
then it is possible to find the global optimum of in polynomial time by computing a minimum cut of the graph. The mapping between cuts and variable assignments is done by representing each variable with one node in the graph and, given a cut, each variable will have a value of 0 if the corresponding node belongs to the component connected to the source, or 1 if it belong to the component connected to the sink.
Not all pseudo-Boolean functions can be represented by a flow network, and in the general case the global optimization problem is NP-hard. There exist sufficient conditions to characterise families of functions that can be optimised through graph cuts, such as submodular quadratic functions. Graph cut optimization can be extended to functions of discrete variables with a finite number of values, that can be approached with iterative algorithms with strong optimality properties, computing one graph cut at each iteration.
Graph cut optimization is an important tool for inference over graphical models such as Markov random fields or conditional random fields, and it has applications in computer vision problems such as image segmentation,[1][2] denoising,[3] registration[4][5] and stereo matching.[6][7]
^Cite error: The named reference peng was invoked but never defined (see the help page).
^Cite error: The named reference grabcut was invoked but never defined (see the help page).
^Cite error: The named reference lombaert was invoked but never defined (see the help page).
^Cite error: The named reference so was invoked but never defined (see the help page).
^Cite error: The named reference tang was invoked but never defined (see the help page).
^Cite error: The named reference kim was invoked but never defined (see the help page).
^Cite error: The named reference hong was invoked but never defined (see the help page).
and 22 Related for: Graph cut optimization information
Graphcutoptimization is a combinatorial optimization method applicable to a family of functions of discrete variables, named after the concept of cut...
As applied in the field of computer vision, graphcutoptimization can be employed to efficiently solve a wide variety of low-level computer vision problems...
In graph theory, a minimum cut or min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some...
In a graph, a maximum cut is a cut whose size is at least the size of any other cut. That is, it is a partition of the graph's vertices into two complementary...
Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the...
numerous optimization tasks involving some sort of graph, e.g., vehicle routing and internet routing. As an example, ant colony optimization is a class...
al. (2013). Two common examples of graph partitioning are minimum cut and maximum cut problems. Typically, graph partition problems fall under the category...
Three notable branches of discrete optimization are: combinatorial optimization, which refers to problems on graphs, matroids and other discrete structures...
Branch and cut is a method of combinatorial optimization for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some...
Combinatorial Optimization, IPCO The Aussois Combinatorial Optimization Workshop Bosscher, Steven; and Novillo, Diego. GCC gets a new Optimizer Framework...
prefers connected regions having the same label, and running a graphcut based optimization to infer their values. As this estimate is likely to be more...
An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must...
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers...
In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function...
Bayesian optimization is a sequential design strategy for global optimization of black-box functions that does not assume any functional forms. It is usually...
unconstrained binary optimization (QUBO), also known as unconstrained binary quadratic programming (UBQP), is a combinatorial optimization problem with a wide...
optimization is a feature of many relational database management systems and other databases such as NoSQL and graph databases. The query optimizer attempts...
Quantum optimization algorithms are quantum algorithms that are used to solve optimization problems. Mathematical optimization deals with finding the best...
assumptions about the optimization problem being solved and so may be usable for a variety of problems. Compared to optimization algorithms and iterative...
mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each...
an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function. An optimization problem...
Global Information
