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Topic: Level set method

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	Fast Marching Methods and Level Set Methods: A Fast Introduction ------------------------------------------- Level Set ... (Site not responding. Last check: 2007-10-11)
		Level Set Methods are designed for problems in which the speed function can be positive in some places are negative in others, so that the front can move forwards in some places and backwards in others.
		The motion of the interface is matched with the zero level set of the level set function, and the resulting initial value partial differential equation for the evolution of the level set function resembles a Hamilton-Jacobi equation.
		In this setting, curvatures and normals may be easily evaluated, topological changes occur in a natural manner, and the technique extends trivially to three dimensions.
	math.berkeley.edu /~sethian/Explanations/level_set_explain.html (1075 words)

	Level set method - Wikipedia, the free encyclopedia
		Also, the level set method makes it very easy to follow shapes which change topology, for example when a shape splits in two, develops holes, or the reverse of these operations.
		The level set method was developed in the 1980s by the American mathematicians Stanley Osher and James Sethian.
		A number of level set data structures have been developed to facilitate the use of the level set method in computer applications.
	en.wikipedia.org /wiki/Level_set_method (632 words)

	Level set - Wikipedia, the free encyclopedia
		In mathematics, a level set of a real-valued function f of n variables is a set of the form
		When the number of variables is two, this is a level curve (contour line), if it is three this is a level surface, and for higher values of n the level set is a level hypersurface.
		The gradient of f at a point is perpendicular to the level set of f at that point.
	en.wikipedia.org /wiki/Level_set (367 words)

	2.1 Level Set Method (Site not responding. Last check: 2007-10-11)
		The level set method advects the free surface variable using the SEM method and then reinitialises the level sets so that they represent the distance from the interface.
		During this stage the zero level set, which represents the position of the interface, does not move but all other sets are recalculated.
		In most cases it is sufficient to use the upwind advection method as the reinitialisation stage overcomes the smearing of the interface associated with upwinding.
	www.gre.ac.uk /~physica/phy2.12/release/node6.htm (211 words)

	A Fast Marching Method of Computing Closest Points
		The zero set is made by first constructing a thin band of points in the zero set grid that surrounds the CSG model surface.
		Given a point p in the zero set that is closest to the grid point (i,j,k) in the zero band, one can determine all the points in the zero set that lie in a neighborhood of p by determining all the points in the zero band in a neighborhood of (i,j,k).
		The error in the distance using Sethian's level set method is proportional to the spacing of the distance grid.
	www.cco.caltech.edu /~sean/closestpoint/closept.html (2115 words)

	Level set Method for Shape Optimization
		We study a level set method for numerical shape optimization of elastic structures.
		The level set method, based on the classical shape derivative, is seen to easily handle boundary propagation with topological changes.
		For this reason, we couple the level set method with another approach, known as the bubble or topological gradient method, which is precisely designed for introducing new holes in the optimization process.
	www.cmap.polytechnique.fr /~optopo/level_en.html (275 words)

	Level Set Method Toolbox
		Level set methods are a class of numerical algorithms for simulation of dynamic implicit surfaces and approximation of solutions to the Hamilton-Jacobi (HJ) partial differential equation (PDE).
		Compared to their competitors, level set methods can be relatively easy to implement.
		Note that numerical instability (the level set function blows up) is usually caused by incorrect driver code (initialization, boundary conditions, dynamics or CFL choice), not by kernel code.
	www.cs.ubc.ca /~mitchell/ToolboxLS (892 words)

	Amazon.com: Level Set Methods and Dynamic Implicit Surfaces: Books: Stanley J. Osher,Ronald P. Fedkiw (Site not responding. Last check: 2007-10-11)
		Topics include the level set equation itself, Hamilton-Jacobi equations, motion of a surface normal to itself, re-initialization to a signed distance function, extrapolation in the normal direction, the particle level set method and the motion of co-dimension two (and higher) objects.
		Level sets and many of their various applications are covered in relative detail for a book of this size.
		Not all of the details are given (such as smoothing of the level set when computing curvature), but this will probably be addressed in a future volume.
	www.amazon.com /Level-Methods-Dynamic-Implicit-Surfaces/dp/0387954821 (1848 words)

	Parameter identification using the level set method
		This study describes an inverse approach for efficiently identifying the spatial shapes of zones of low (or high) permeability using the level set method, given a set of spatially distributed head measurements.
		By this method, the boundaries of zones are characterized by a level set function.
		From an initial setting, the unknown regions of zones are determined by evolving the boundaries in artificial time using a pseudo velocity field that is related to the sensitivity of head to permeability and the residual between the measured head and modeled head at the current time.
	www.agu.org /pubs/crossref/2006/2005GL025541.shtml (222 words)

	SSRN-The Level Set Method of Joo and its Use in Minimax Theory by J.B.G. (Hans) Frenk, G. Kassay
		In this paper we discuss the level set method of Joo and how to use it to give an elementary proof of the well-known Sion's minimax result.
		Although this proof technique is initiated by Joo and based on the inter-section of upper level sets and a clever use of the topological notion of connectedness, it is not very well known and accessible for researchers in optimization.
		Frenk, J.B.G. and Kassay, G., "The Level Set Method of Joo and its Use in Minimax Theory" (June 2004).
	papers.ssrn.com /sol3/papers.cfm?abstract_id=611842 (328 words)

	Level Set Method(LSM) (Site not responding. Last check: 2007-10-11)
		This is a different approach from advecting a discontinuous scalar field where the discontinuity represents the interface which is the approach used with the VOF method.
		In the LSM the scalar variable must be maintained as a distance function so that the interface stays at a constant depth which depends on grid size.
		Since the level set method does not necessarily preserve volume a volume reinitialisation is employed,
	www.gre.ac.uk /~wd15/lsm/node6.html (422 words)

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	www.w3.org /Protocols/rfc2616/rfc2616-sec14.html (14880 words)

	Amazon.com: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid ... (Site not responding. Last check: 2007-10-11)
		Level Set Methods and Dynamic Implicit Surfaces by Stanley J. Osher
		In this new edition of the successful book Level Set Methods, Professor Sethian incorporates the most recent advances in Fast Marching Methods, many of which appear here for the first time.
		The first six chapters are good for giving you a nice qualitative understanding of the method and the issues of implementing the method.
	www.amazon.com /Level-Methods-Fast-Marching-Computational/dp/0521645573 (1465 words)

	CiteULike: kutabar's levelset (Site not responding. Last check: 2007-10-11)
		A Pseudo-distance for shape priors in level set segmentation
		Level set methods for optimization problems involving geometry and constraints
		A framework for the construction of level set methods for shape optimization and reconstruction
	www.citeulike.org /user/kutabar/tag/levelset (532 words)

	Stanley Osher's Homepage
		Level Set Methods and Dynamic Implicit Surfaces by Stanley Osher and Ronald P. Fedkiw
		LSS 03-01 Shi Jin and Stanley Osher, A Level Set Method for the Computation of Multivalued Solutions to Quasi-Linear Hyperbolic PDEs and Hamilton-Jacobi Equations, Submitted to Comm.
		LSS 03-02 Li-Tien Cheng, Hailiang Liu, and Stanley Osher, High-Frequency Wave Propagation in Schrodinger Equations Using the Level Set Method, Submitted to Comm.
	www.levelset.com /sjo/sjo.html (543 words)

	Level Set Method for Active Contours CS 766: Project Report (Site not responding. Last check: 2007-10-11)
		Level Set Method for Active Contours CS 766: Project Report
		This report describes a level set approach to active contours developed by Ravikanth Malladi,James A. Sethian and Baba C. Vemuri.
		The discrete approximation uses entropy satisfying upwind difference schemes which result in a final contour that is able to model arbitrarily complex shapes.
	www.cs.wisc.edu /~saurabh/finalreport (129 words)

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	CiteULike: A level-set method for shape optimization (Site not responding. Last check: 2007-10-11)
		We study a level-set method for numerical shape optimization of elastic structures.
		Its cost is moderate since the shape is captured on a fixed Eulerian mesh.
		Although this method is not specifically designed for topology optimization, it can easily handle topology changes for a very large class of objective functions.
	www.citeulike.org /user/kutabar/article/300091 (233 words)

	Level Set Method Library (LSMLIB)
		The Level Set Method Library (LSMLIB) provides support for the serial and parallel simulation of implicit surface and curve dynamics in two- and three-dimensions (support for nodes in one-dimension is also provided).
		The underlying philosophy of SAMRAI is that an application developer should be able to migrate to a high-performance, parallel program with adaptive mesh capabilities with minimal effort once a satisfactory numerical algorithm has been developed for calculations on a single, simple rectangular mesh.
		If you are interested in working with level set methods, but are not familiar with level set methods, parallel computing, etc., we would be happy to collaborate with you on your research projects.
	www.princeton.edu /~ktchu/software/lsmlib (788 words)

	Chunming Li's Level Set Formulation (Site not responding. Last check: 2007-10-11)
		The initial level set function can be simply defined as a binary function: -c in R and c outside of R.
		As pointed out by Gomes and Faugeras [4], in the traditional level set methods, there is a disagreement between the theory and the implementation, due to the need for reinitialization.
		Fox, “Level Set Evolution Without Re-initialization: A New Variational Formulation”, IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), vol.
	www.engr.uconn.edu /~cmli/research/pals.html (232 words)

	Information Bridge: DOE Scientific and Technical Information - - Document #395612 (Site not responding. Last check: 2007-10-11)
		This thesis describes a new method for the numerical solution of partial differential equations of the parabolic type on an adaptively refined mesh in two or more spatial dimensions.
		The method is motivated and developed in the context of the level set formulation for the curvature dependent propagation of surfaces in three dimensions.
		In that setting, it realizes the multiple advantages of decreased computational effort, localized accuracy enhancement, and compatibility with problems containing a range of length scales.
	www.osti.gov /bridge/product.biblio.jsp?osti_id=395612 (156 words)

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	The Level Set Method for Modeling Epitaxial Growth
		We have developed an island dynamics model that employs the level-set technique to describe epitaxial growth.
		In this method, the surface morphology is described by defining the island boundaries as the set $\varphi = 0$ of the so-called level-set function.
		In this talk, we will present some new results obtained with this new modeling technique for growth on singular and vicinal surfaces.
	www.nsti.org /Nanotech2003/showabstract.html?absno=260 (87 words)

	Fast Marching Methods and Level Set Methods: J.A. Sethian
		Fast Marching Methods and Level Set Methods are numerical techniques which can follow the evolution of interfaces.
		A Quick Explanation of Fast Marching Methods and Level Set Methods
		Please use Back to return to the Level Set Web Page.
	math.berkeley.edu /~sethian (191 words)

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