About: Level-set method

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Level-set method Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : el.dbpedia.org associated with source document(s)

Level-set methods (LSM) are a conceptual framework for using level sets as a tool for numerical analysis of surfaces and shapes. The advantage of the level-set model is that one can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these objects (this is called the Eulerian approach). Also, the level-set method makes it very easy to follow shapes that change topology, for example, when a shape splits in two, develops holes, or the reverse of these operations. All these make the level-set method a great tool for modeling time-varying objects, like inflation of an airbag, or a drop of oil floating in water.

Attributes	Values
rdfs:label	Level-set method (en)
rdfs:comment	Level-set methods (LSM) are a conceptual framework for using level sets as a tool for numerical analysis of surfaces and shapes. The advantage of the level-set model is that one can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these objects (this is called the Eulerian approach). Also, the level-set method makes it very easy to follow shapes that change topology, for example, when a shape splits in two, develops holes, or the reverse of these operations. All these make the level-set method a great tool for modeling time-varying objects, like inflation of an airbag, or a drop of oil floating in water. (en)
dbp:wikiPageUsesTemplate	dbt:Cleanup dbt:Div_col dbt:Div_col_end dbt:NumBlk dbt:Reflist dbt:EquationNote dbt:Numerical_PDE dbt:EquationRef
Subject	Articles containing video clips Computational fluid dynamics Computer graphics algorithms Image processing Optimization algorithms and methods
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Level-set_method?oldid=1052134992&ns=0
Wikipage page ID	1203063 (xsd:integer)
page length (characters) of wiki page	12640 (xsd:nonNegativeInteger)
Wikipage revision ID	1052134992 (xsd:integer)
Link from a Wikipage to another Wikipage	Numerical analysis Ronald Fedkiw Advanced Simulation Library Airbag Upwind scheme Volume of fluid method Articles containing video clips Computational fluid dynamics Computer graphics algorithms Godunov's scheme James Sethian Image processing Optimization algorithms and methods Digital image processing Surface (topology) Zebra striping (computer graphics) Curve Shape Combustion Computational biology Computational fluid dynamics Computational geometry Computer graphics ENO methods Eikonal equation Parametric surface Partial differential equation Finite difference G equation Image segmentation Immersed boundary method Hamilton–Jacobi equation Euclidean space Stanley Osher Stochastic Eulerian Lagrangian method Topology Level set Level set (data structures) Mathematical optimization Regular grid dbr:VISPACK dbr:B:Fractals/Iterations_in_the_complex_plane/Mandelbrot_set dbr:File:Levelset-mean-curvature-spiral.ogv dbr:B:Fractals/Iterations_in_the_complex_plane/Julia_set
has abstract	Level-set methods (LSM) are a conceptual framework for using level sets as a tool for numerical analysis of surfaces and shapes. The advantage of the level-set model is that one can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these objects (this is called the Eulerian approach). Also, the level-set method makes it very easy to follow shapes that change topology, for example, when a shape splits in two, develops holes, or the reverse of these operations. All these make the level-set method a great tool for modeling time-varying objects, like inflation of an airbag, or a drop of oil floating in water. The figure on the right illustrates several important ideas about the level-set method. In the upper-left corner we see a shape; that is, a bounded region with a well-behaved boundary. Below it, the red surface is the graph of a level set function determining this shape, and the flat blue region represents the xy plane. The boundary of the shape is then the zero-level set of , while the shape itself is the set of points in the plane for which is positive (interior of the shape) or zero (at the boundary). In the top row we see the shape changing its topology by splitting in two. It would be quite hard to describe this transformation numerically by parameterizing the boundary of the shape and following its evolution. One would need an algorithm able to detect the moment the shape splits in two, and then construct parameterizations for the two newly obtained curves. On the other hand, if we look at the bottom row, we see that the level set function merely translated downward. This is an example of when it can be much easier to work with a shape through its level-set function than with the shape directly, where using the shape directly would need to consider and handle all the possible deformations the shape might undergo. Thus, in two dimensions, the level-set method amounts to representing a closed curve (such as the shape boundary in our example) using an auxiliary function , called the level-set function. is represented as the zero-level set of by and the level-set method manipulates implicitly, through the function . This function is assumed to take positive values inside the region delimited by the curve and negative values outside. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Level-set_method
is Wikipage redirect of	Level set method Level set methods
is Link from a Wikipage to another Wikipage of	Fluid animation Marker-and-cell method Active contour model Advanced Simulation Library Free-surface modelling General-purpose computing on graphics processing units Geometric design James Sethian Curve-shortening flow List of mathematics-based methods List of numerical analysis topics List of numerical computational geometry topics Closest point method Computational fluid dynamics Computational geometry Contour line Homicidal chauffeur problem Joel Spruck List of algorithms G equation Granular material ITK-SNAP Image segmentation Immersed boundary method Index of physics articles (L) Fast marching method Gunilla Kreiss Institute for Liquid Atomization and Spray Systems LSM Luminița Vese Level set Level set (data structures)

Faceted Search & Find service v1.17_git151 as of Feb 20 2025

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Nov 11 2024, on Linux (x86_64-ubuntu_focal-linux-gnu), Single-Server Edition (72 GB total memory, 1 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software