A Fast Level Set Method for Propagating Interfaces

Adalsteinsson, David; Sethian, James A.

doi:10.1006/jcph.1995.1098

Cited by 1,132 publications

(813 citation statements)

References 7 publications

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“…The computational issue was first addressed with the introduction of the narrow-band schemes [1], [29], [38], which restrict the computations to a small vicinity around the zero level set representing the deforming interface. However, narrowband methods still need to explicitly store a full grid and additional data structures.…”

Section: A Efficient Level Set Methods On the Cpumentioning

confidence: 99%

Fast Sparse Level Sets on Graphics Hardware

Jalba

Laan

Roerdink

2013

IEEE Trans. Visual. Comput. Graphics

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Abstract-The level set method is one of the most popular techniques for capturing and tracking deformable interfaces. Although level sets have demonstrated great potential in visualization and computer graphics applications, such as surface editing and physically-based modeling, their use for interactive simulations has been limited due to the high computational demands involved. In this paper we address this computational challenge by leveraging the increased computing power of graphics processors, to achieve fast simulations based on level sets. Our efficient, sparse GPU level set method is substantially faster than other state-of-the-art, parallel approaches on both CPU and GPU hardware. We further investigate its performance through a method for surface reconstruction, based on GPU level sets. Our novel multi-resolution method for surface reconstruction from unorganized point clouds compares favorably with recent, existing techniques and other parallel implementations. Finally, we point out that both level set computations and rendering of level-set surfaces can be performed at interactive rates, even on large volumetric grids. Therefore, many applications based on level sets can benefit from our sparse level set method.

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Section: A Efficient Level Set Methods On the Cpumentioning

confidence: 99%

Fast Sparse Level Sets on Graphics Hardware

Jalba

Laan

Roerdink

2013

IEEE Trans. Visual. Comput. Graphics

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“…The velocity can be used in the appropriate differential equation to track the interface according to time. Interface tracking algorithms are usually based on the phase-field method [20][21][22], cellular automata [23] or the Level Set Method [24][25][26][27][28]. The main idea of the phase-field method is to introduce a phase-field variable that varies smoothly from zero to unity between the solid and liquid phases over the region, which is narrow but it has numerically resolvable thickness.…”

Section: Introductionmentioning

confidence: 99%

Effect Of Natural Convection On Directional Solidification Of Pure Metal

Skrzypczak

Węgrzyn-Skrzypczak

Winczek

2015

Archives of Metallurgy and Materials

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The paper is focused on the modeling of the directional solidification process of pure metal. During the process the solidification front is sharp in the shape of the surface separating liquid from solid in three dimensional space or a curve in 2D. The position and shape of the solid-liquid interface change according to time. The local velocity of the interface depends on the values of heat fluxes on the solid and liquid sides. Sharp interface solidification belongs to the phase transition problems which occur due to temperature changes, pressure, etc. Transition from one state to another is discontinuous from the mathematical point of view. Such process can be identified during water freezing, evaporation, melting and solidification of metals and alloys, etc.The influence of natural convection on the temperature distribution and the solid-liquid interface motion during solidification of pure copper is studied. The mathematical model of the process is based on the differential equations of heat transfer with convection, Navier-Stokes equation and the motion of the interface. This system of equations is supplemented by the appropriate initial and boundary conditions. In addition the continuity conditions at the solidification interface must be properly formulated. The solution involves the determination of the temporary temperature and velocity fields and the position of the interface. Typically, it is impossible to obtain the exact solution of such problem. The numerical model of solidification of pure copper in a closed cavity is presented, the influence of the natural convection on the phase change is investigated. Mathematical formulation of the problem is based on the Stefan problem with moving internal boundaries. The equations are spatially discretized with the use of fixed grid by means of the Finite Element Method (FEM). Front advancing technique uses the Level Set Method (LSM). Chorin's projection method is used to solve Navier-Stokes equation. Such approach makes possible to uncouple velocities and pressure. The Petrov-Galerkin formulation is employed to stabilize numerical solutions of the equations. The results of numerical simulations in the 2D region are discussed and compared to the results obtained from the simulation where movement of the liquid phase was neglected.Keywords: Pure Metal, Solidification, Sharp Interface, Natural Convection, Finite Element Method, Level Set Method Praca porusza problematykę modelowania kierunkowego krzepnięcia czystego metalu. Podczas tego procesu obserwuje się formowanie ostrego frontu krzepnięcia w postaci powierzchni separującej ciecz i ciało stałe w przypadku trójwymiarowym lub krzywej w przypadku płaskim. Położenie oraz kształt interfejsu krzepnięcia zmieniają się w czasie a wartości prędkości lokalnych zależą od różnicy intensywności strumieni ciepła po stronie ciała stałego i cieczy. Krzepnięcie z ostrym frontem należy do grupy procesów z przemianami fazowymi, które warunkowane są zmianami temperatury, ciśnienia, itp. Przejście fazowe z jednego stanu w drugi...

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“…This way, the well known Osher-Sethian [19] level-set method can be employed to implement the surface propagation toward its optimal location. Efficient solutions for the resulting evolution equations can use either AOS [16,22] or ADI methods, coupled with a narrow band approach [7,1], as first introduced in [11] for the geodesic active contour.…”

Section: Lemma 6 the Robust Minimal Total Deviation Criterion Is Givementioning

confidence: 99%

Geometric segmentation of 3D structures

Kimmel

Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429)

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Segmentation in volumetric images deals with separating 'objects' from their 'background' in a given 3D data. Usually, one starts with 'edge detectors' that give binary clues on the locations of the objects boundaries. Classical edge detectors that can be adopted from 2D are the Marr-Hildreth, and Haralick or Canny edge detectors. Next, usually one integrates these clues into meaningful contours or surfaces that indicate the boundaries of the objects.We use our recent variational explanation for the MarrHildreth and the Haralick-Canny like edge detectors to extend these classical operators. We combine these operators with a minimal deviation measure that can be tuned to the problem at hand. Finally, an improved 'geometric active surface model' is defined.

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A Fast Level Set Method for Propagating Interfaces

Cited by 1,132 publications

References 7 publications

Fast Sparse Level Sets on Graphics Hardware

Fast Sparse Level Sets on Graphics Hardware

Effect Of Natural Convection On Directional Solidification Of Pure Metal

Geometric segmentation of 3D structures

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