Level set methods and dynamic implicit surfaces

By Stanley J. Osher, Ronald Fedkiw. Applied Mathematical Sciences, 2002

6,389 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/c896b6c0e8e6be8ba28142e096d705241ce94b9a

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Time-optimal path planning in dynamic flows using level set equations: theory and schemes (2014, methodology): “Furthermore, since we use an explicit time integration scheme, t is chosen to satisfy the CFL condition (Osher and Fedkiw 2003), making t inversely proportional to n.”
Phase-Field Models for Multi-Component Fluid Flows (2012, methodology): “In interface capturing methods such as level-set [24,78,79,85,91,92] and phase-field methods [4,6,13,29,46,47,54,56,74,86,90,102], the interface is implicitly captured by a contour of a particular scalar function.”
Reach-avoid problems with time-varying dynamics, targets and constraints (2014, methodology): “While computationally intensive, Hamilton-Jacobi approaches are practically appealing nowadays due to the availability of modern numerical tools such as [16, 17, 22], which allow solving the associated equations for problems with low dimensionality.”
Distance Regularized Level Set Evolution and Its Application to Image Segmentation (2010, methodology): “Reinitialization is performed by periodically stopping the evolution and reshaping the degraded LSF as a signed distance function [21], [20].”
Structural Shape and Topology Optimization Using an Implicit Free Boundary Parametrization Method (2006, methodology): “…and Sethian, 1988) have become popular recently for tracking, modeling and simulating the motion of dynamic interfaces (moving free boundaries) in fluid mechanics, combustion, computer animation, material science, crack propagation and image processing [Sethian (1999); Osher and Fedkiw (2002)].”
A path defense approach to the multiplayer reach-avoid game (2014, methodology): “Modern numerical tools such as [15], [16], [17] are able to solve the HJI PDE when the dimensionality of the problem is low.”
Shape optimization with a level set based mesh evolution method (2014, neutral): “Roughly speaking (see also [52, 59] for more details), let Ω(t) ⊂ R be a domain, whose motion over a time period [0, T ] is driven by a velocity field V : [R → R.”
Deep Level Sets for Salient Object Detection (2017, methodology): “The Level Set method (LSM) [38] is widely applied in image segmentation with active contour [37], due to its ability to automatically handle various topological changes.”
Spatially adaptive techniques for level set methods and incompressible flow (2006, background): “We refer the interested reader to the recent book [67] and the references therein.”
Piecewise constant level set method for structural topology optimization (2009, methodology): “Compared with the conventional level set method with the upwind numerical scheme [30], the proposed PCLS method does not involve any reinitialization for the level set function.”
Coupled minimum-cost flow cell tracking for high-throughput quantitative analysis (2011, methodology): “Contour evolution approaches, and in particular level sets [1, 18, 19], offer some advantages as they can easily handle changes in topology.”
Blending liquids (2014, methodology): “A popular class of surface tracking algorithms is based on level-sets [Osher and Fedkiw 2002], and particle level-sets [Enright et al.”
A level set method for structural topology optimization and its applications (2004, methodology): “The level set method is firstly introduced into the structural topology optimization by Sethian and Wiegmann [23].”
An augmented approach for Stokes equations with a discontinuous viscosity and singular forces (2007, methodology): “In order to apply the method for problems on multi-connected domains and moving interface problems, the level set method is preferred, see, for example, [24,27,32].”