Fast Marching Methods

By Ron Kimmel. 2004

747 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/d8ac53a5825fe625ed31069d4f61add24bfadd83

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In Artificial Intelligence

In Computer Graphics and Computer-Aided Design

In Computer Vision and Pattern Recognition

Citations in the corpus

A new multi-material level set topology optimization method with the length scale control capability (2018, neutral): “(30) can be efficiently solved through the highly efficient fast marching method [63].”
PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab (2012, neutral): “…a signed distance function can be obtained from the level sets of a given implicit function by solving a nonlinear system of equations (cf. Persson and Strang 2004) or more generally using marching algorithms (see, for example, (Sussman et al. 1998; Sethian 1999; Osher and Fedkiw 2003; Zhao 2004)).”
Computer Methods and Programs in Biomedicine (neutral): “During the evolution, the vessel centerline is iteratively computed with the Fast Marching Method (FMM) [173] .”
Meshless methods with application to metal forming (2006, methodology): “Level set and fast marching methods (FMM) [18] are well-known interface-capturing techniques in which the interface is represented as the zero level contour of a function (level set) of one higher-dimension.”
Spatially adaptive techniques for level set methods and incompressible flow (2006, methodology): “Although this method is only first order accurate, it is straightforward to extend it to higher order accuracy as was done in [80] using an equivalent finite difference formulation of the method (i.”
GeoS: Geodesic Image Segmentation (2008, methodology): “Instead, wave-front algorithms such as Fast Marching Methods (FMM) [17] are based on the iterative propagation of a pixel front with velocity F .”
3D distance fields: a survey of techniques and applications (2006, methodology): “This has motivated another version (FMMHA) of the method which is more precise by virtue of the fact that second order finite difference approximations to the partial derivatives are used [106].”
Three‐dimensional non‐planar crack growth by a coupled extended finite element and fast marching method (2008, methodology): “In this case, because we want the distance function, the FMM is used to solve the Eikonal equation: ‖∇ρ‖ = 1.”
An image-based modeling framework for patient-specific computational hemodynamics (2008, methodology): “The wavefronts travel with speed proportional to local image intensity, following the so-called eikonal equation [25] jrTj 1⁄4 I 1 ð2Þ”
A geometric mass‐preserving redistancing scheme for the level set function (2011, methodology): “Later, Tsitsiklis [23] proposed in a completely different framework, a method that can be used for the construction of distance functions, and therefore for reinitialization, known as the fast marching method, further popularized by Sethian (see [24] and [ 25 ]).”
Curve-Skeleton Properties, Applications, and Algorithms (2007, methodology): “Adistancefieldcanalsobeapproximated using fast marching methods [103], [111], [123], [124].”
A hybrid particle level set method for improved interface capturing (2002, background): “(2) to steady state via fast marching methods are discussed in [31, 32].”
An algorithm for Mean Curvature Motion (2004, neutral): “We follow [52].”
A hybrid extended finite element/level set method for modeling phase transformations (2002, methodology): “4.1. The fast marching method In the context of the Level Set method, the Fast Marching Method was introduced in Reference [36], and later improved in References [ 37 ; 35].”
Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method (2003, methodology): “Expressions for D− y , D + y , s − 2 , s + 2 are similar (see [33]).”
A fast and accurate semi-Lagrangian particle level set method (2005, methodology): “O(N log N ), first order accurate marching technique first proposed by Tsitsiklis [26] and later popularized by Sethian and co-workers, see e.g. [17].”
Transport and diffusion of material quantities on propagating interfaces via level set methods (2003, methodology): “The Fast Marching Method has been extended to higher order finite difference approximations by Sethian in [20], first order unstructured meshes by Kimmel and Sethian [8], and higher order unstructured meshes by Sethian and Vladimirsky [23].”