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SIAM Review, 1999
The author considers numerical methods for solving the nonlinear eikonal equation \[ |\nabla u(x)|= F(x)\quad\text{in }\Omega\subset \mathbb{R}^2\quad\text{or }\mathbb{R}^3,\tag{1} \] under given boundary conditions \(u=g\) on some prescribed curve or surface \(\Gamma\) in \(\Omega\).
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The author considers numerical methods for solving the nonlinear eikonal equation \[ |\nabla u(x)|= F(x)\quad\text{in }\Omega\subset \mathbb{R}^2\quad\text{or }\mathbb{R}^3,\tag{1} \] under given boundary conditions \(u=g\) on some prescribed curve or surface \(\Gamma\) in \(\Omega\).
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Some Improvements of the Fast Marching Method
SIAM Journal on Scientific Computing, 2001Summary: The fast marching method published by \textit{J. A. Sethian} [Proc. Natl. Acad. Sci. USA 93, No. 4, 1591-1595 (1996; Zbl 0852.65055)] is an optimally efficient algorithm for solving problems of front evolution where the front speed is monotonic. It has been used in a wide variety of applications such as robotic path planning [\textit{R. Kimmel}
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Fast Marching Adaptive Sampling
IEEE Robotics and Automation Letters, 2017A challenging problem for autonomous exploration is estimating the utility of future samples. In this paper, we consider the problem of placing observations over an initially unknown continuous cost field to find the least-cost path from a fixed start to a fixed goal position.
Nicholas R. J. Lawrance +2 more
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Distributed fast marching methods
Proceedings of the 15th ACM Mardi Gras conference: From lightweight mash-ups to lambda grids: Understanding the spectrum of distributed computing requirements, applications, tools, infrastructures, interoperability, and the incremental adoption of key capabilities, 2008Fast Marching represents a very efficient technique for solving the front propagation problems which can be formulated as boundary value partial differential equations |∇T(x, y)| = 1/F(x, y) on Ω, with Dirichlet boundary condition T(x, y) = 0 on ∂Ω. We show that the problem of computing the distance map across a smooth sampling domain can be posed in ...
Maria Cristina Tugurlan, Blaise Bourdin
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GO solutions with Fast Marching
2016 10th European Conference on Antennas and Propagation (EuCAP), 2016We develop an approach for a fast and accurate determination of the Geometrical Optics solutions to Maxwell's equations based on the determination of the eikonal function. The approach, here presented for a 3D problem, is devised to handle scenarios involving complex spatially varying refraction indices.
CAPOZZOLI, AMEDEO +3 more
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Fast marching for hybrid control
Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design (Cat. No.99TH8404), 2003This paper describes an approach to solving optimal hybrid control problems using level set methods. Level set methods are a powerful set of techniques for generating equipotential contours with applications in the realm of fluid mechanics, computer vision, material science, robotics and geometry.
M.S. Branicky, R. Hebbar
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Fast Marching farthest point sampling
2003Using Fast Marching for the incremental computation of distance maps across the sampling domain, we obtain an efficient farthest point sampling technique (FastFPS). The method is based on that of Eldar et al. (1992, 1997) but extends more naturally to the case of non-uniform sampling and is more widely applicable. Furthermore, it can be applied to both
Carsten Moenning, Neil A. Dodgson
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2004
The fast marching method was introduced by Sethian [190, 191, 192] as a computationally efficient solution to eikonal equations on flat domains. A related method was presented by Tsitsiklis in [205]. The fast marching method was extended to triangulated surfaces by Kimmel and Sethian in [112].
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The fast marching method was introduced by Sethian [190, 191, 192] as a computationally efficient solution to eikonal equations on flat domains. A related method was presented by Tsitsiklis in [205]. The fast marching method was extended to triangulated surfaces by Kimmel and Sethian in [112].
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Fast Marching Based Superpixels Generation
2019In this article, we present a fast-marching based algorithm for generating superpixel (FMS) partitions of images. The idea behind the algorithm is to draw an analogy between waves propagating in an heterogeneous medium and regions growing on an image at a rate depending on the local color and texture.
Chang, Kaiwen, Figliuzzi, Bruno
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