A finite element method for the simulation of a Rayleigh-Taylor instability

Dervieux, Alain; Thomasset, François

doi:10.1007/bfb0086904

Cited by 150 publications

(107 citation statements)

References 5 publications

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“…Since the work introduced in [3], implementing a PDE on a surface is affordable in the implicit framework with the level set method [9,22].…”

Section: The Sobolev H 1 Gradient Flowmentioning

confidence: 99%

“…Moreover, the content of this paper is not specific to a particular implementation of the contour evolution. In our experiments, we have used the level set framework [9,22,28,20,21], motivated by its numerical stability and its ability to handle topological changes automatically. The implicit framework also offers an elegant formulation of the Laplace-Beltrami operator [2] and of the average of a quantity along the contour [25].…”

Section: Numerical Experiments With the New Inner Productsmentioning

confidence: 99%

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Generalized Gradients: Priors on Minimization Flows

Charpiat

Maurel

Pons

et al. 2006

Int J Comput Vision

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This paper tackles an important aspect of the variational problem underlying active contours: optimization by gradient flows. Classically, the definition of a gradient depends directly on the choice of an inner product structure. This consideration is largely absent from the active contours literature. Most authors, explicitely or implicitely, assume that the space of admissible deformations is ruled by the canonical L 2 inner product. The classical gradient flows reported in the literature are relative to this particular choice. Here, we investigate the relevance of using (i) other inner products, yielding other gradient descents, and (ii) other minimizing flows not deriving from any inner product. In particular, we show how to induce different degrees of spatial consistency into the minimizing flow, in order to decrease the probability of getting trapped into irrelevant local minima. We report numerical experiments indicating that the sensitivity of the active contours method to initial conditions, which seriously limits its applicability and efficiency, is alleviated by our application-specific spatially coherent minimizing flows. We show that the choice of the inner product can be seen as a prior on the deformation fields and we present an extension of the definition of the gradient toward more general priors.

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“…Since the work introduced in [3], implementing a PDE on a surface is affordable in the implicit framework with the level set method [9,22].…”

Section: The Sobolev H 1 Gradient Flowmentioning

confidence: 99%

Section: Numerical Experiments With the New Inner Productsmentioning

confidence: 99%

Generalized Gradients: Priors on Minimization Flows

Charpiat

Maurel

Pons

et al. 2006

Int J Comput Vision

View full text Add to dashboard Cite

show abstract

“…Our method is based on variational image segmentation with level sets [22,37,11,34,38,12], and in particular on the method described in [8,5]. Level set formulations of the image segmentation problem have several advantages in comparison to other contour extraction methods.…”

Section: Level Set Formulationmentioning

confidence: 99%

Three-Dimensional Shape Knowledge for Joint Image Segmentation and Pose Tracking

Rosenhahn¹,

Brox

Weickert

2006

Int J Comput Vision

119

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In this article we present the integration of 3-D shape knowledge into a variational model for level set based image segmentation and tracking. Given a 3-D surface model of an object that is visible in the image of one or multiple cameras calibrated to the same world coordinate system, the object contour extracted by the segmentation method is applied to estimate the 3-D pose parameters of the object. Vice-versa, the surface model projected to the image plane helps in a top-down manner to improve the extraction of the contour. While common alternative segmentation approaches, which integrate 2-D shape knowledge, face the problem that an object can look very differently from various viewpoints, a 3-D free form model ensures that for each view the model can fit the data in the image very well. Moreover, one additionally solves the higher level problem of determining the object pose in 3-D space. Due to the variational formulation, the approach clearly states all model assumptions in a single energy functional that is locally minimized by our method. Its performance is demonstrated by experiments with a monocular and a stereo camera system.

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“…Originally proposed in [1,2] as a means to propagate interfaces in time, the level set method has become increasingly popular as a framework for image segmentation. The key idea is to represent an interface Γ ⊂ Ω in the image domain Ω ⊂ R 3 implicitly as the zero level set of an embedding function φ : R 3 → Ω:…”

Section: Introductionmentioning

confidence: 99%

Efficient Kernel Density Estimation of Shape and Intensity Priors for Level Set Segmentation

Rousson

Cremers

2005

Lecture Notes in Computer Science

103

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We propose a nonlinear statistical shape model for level set segmentation that can be efficiently implemented. Given a set of training shapes, we perform a kernel density estimation in the low-dimensional subspace spanned by the training shapes. In this way, we are able to combine an accurate model of the statistical shape distribution with efficient optimization in a finite-dimensional subspace. In a Bayesian inference framework, we integrate the nonlinear shape model with a nonparametric intensity model and a set of pose parameters that are estimated in a more direct data-driven manner than in previously proposed level set methods. Quantitative results show superior performance (regarding runtime and segmentation accuracy) of the proposed nonparametric shape prior over existing approaches.

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A finite element method for the simulation of a Rayleigh-Taylor instability

Cited by 150 publications

References 5 publications

Generalized Gradients: Priors on Minimization Flows

Generalized Gradients: Priors on Minimization Flows

Three-Dimensional Shape Knowledge for Joint Image Segmentation and Pose Tracking

Efficient Kernel Density Estimation of Shape and Intensity Priors for Level Set Segmentation

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