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The foundational theory of graph cuts was first applied in computer vision in the seminal paper by Greig, Porteous and Seheult [3] of Durham University.Allan Seheult and Bruce Porteous were members of Durham's lauded statistics group of the time, led by Julian Besag and Peter Green, with the optimisation expert Margaret Greig notable as the first ever female member of staff of the Durham ...
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]
The use of optimization software requires that the function f is defined in a suitable programming language and connected at compilation or run time to the optimization software. The optimization software will deliver input values in A , the software module realizing f will deliver the computed value f ( x ) and, in some cases, additional ...
The canonical optimization variant of the above decision problem is usually known as the Maximum-Cut Problem or Max-Cut and is defined as: Given a graph G, find a maximum cut. The optimization variant is known to be NP-Hard. The opposite problem, that of finding a minimum cut is known to be efficiently solvable via the Ford–Fulkerson algorithm.
A popular algebraic modeling language for linear, mixed-integer and nonlinear optimization. Student and AMPL for courses versions are available for free. APMonitor: Fortran, C++, Python, Matlab, Julia 0.6.2 / March 2016 Yes Yes Dual (Commercial, academic) A differential and algebraic modeling language for mixed-integer and nonlinear optimization.
Branch and cut [1] is a method of combinatorial optimization for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some or all the unknowns are restricted to integer values. [2] Branch and cut involves running a branch and bound algorithm and using cutting planes to tighten
In mathematics, the minimum k-cut is a combinatorial optimization problem that requires finding a set of edges whose removal would partition the graph to at least k connected components. These edges are referred to as k-cut. The goal is to find the minimum-weight k-cut.
Cutting-plane methods for general convex continuous optimization and variants are known under various names: Kelley's method, Kelley–Cheney–Goldstein method, and bundle methods. They are popularly used for non-differentiable convex minimization, where a convex objective function and its subgradient can be evaluated efficiently but usual ...