Interleaving Delaunay refinement and optimization for practical isotropic tetrahedron mesh generation

Tournois, Jane; Wormser, Camille; Alliez, Pierre; Desbrun, Mathieu

doi:10.1145/1576246.1531381

Cited by 26 publications

(44 citation statements)

References 24 publications

(30 reference statements)

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“…As previously mentioned, one of our future works will concern mesh optimization based on the method presented in [TWAD09]. We also plan to make our code available very soon and we hope that it will be useful in fields which require realistic geometric models.…”

Section: Resultsmentioning

confidence: 99%

“…Note that these meshes have been generated from segmented images without any time-consuming preprocessings of the input data. However, if the target application requires smoother geometric representations, the resulting meshes can be optimized using the method presented in [ACSYD05,TWAD09]. Figure 6 displays the mesh of a liver adjacent to a right kidney and their 1-junction edge defined at the intersection of these two objects and the background.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Feature preserving Delaunay mesh generation from 3D multi‐material images

Boltcheva

Yvinec

Boissonnat

2009

Computer Graphics Forum

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Generating realistic geometric models from 3D segmented images is an important task in many biomedical applications. Segmented 3D images impose particular challenges for meshing algorithms because they contain multimaterial junctions forming features such as surface patches, edges and corners. The resulting meshes should preserve these features to ensure the visual quality and the mechanical soundness of the models. We present a feature preserving Delaunay refinement algorithm which can be used to generate high-quality tetrahedral meshes from segmented images. The idea is to explicitly sample corners and edges from the input image and to constrain the Delaunay refinement algorithm to preserve these features in addition to the surface patches. Our experimental results on segmented medical images have shown that, within a few seconds, the algorithm outputs a tetrahedral mesh in which each material is represented as a consistent submesh without gaps and overlaps. The optimization property of the Delaunay triangulation makes these meshes suitable for the purpose of realistic visualization or finite element simulations.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Feature preserving Delaunay mesh generation from 3D multi‐material images

Boltcheva

Yvinec

Boissonnat

2009

Computer Graphics Forum

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“…The comparison among different methods has been carried out for triangle meshing. Specifically, we analyze the performance of four algorithms, the isosurface stuffing [97], TetGen [72], NetGen [98], and Delaunay refinement and interleaved mesh optimization [100] for the volumetric meshing of biomolecules. TetGen and NetGen both perform well, while the last one is very suitable for quality improvement, capable of remeshing the surface from possibly low-quality surface mesh inputs.…”

Section: Resultsmentioning

confidence: 99%

“…Another recent algorithm using interleaved Delaunay refinement and mesh optimization [100] can generate quality meshes that satisfy a set of user-defined criteria, which can be useful, for example, when importance of the sampling density is determined by the local chemical structure. In the Delaunay refinement step, sample points are inserted to satisfy the user-specified quality requirements.…”

Section: Volumetric Meshingmentioning

confidence: 99%

Geometric modeling of subcellular structures, organelles, and multiprotein complexes

Feng

Xia

Tong

et al. 2012

Numer Methods Biomed Eng

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SUMMARY Recently, the structure, function, stability, and dynamics of subcellular structures, organelles, and multi-protein complexes have emerged as a leading interest in structural biology. Geometric modeling not only provides visualizations of shapes for large biomolecular complexes but also fills the gap between structural information and theoretical modeling, and enables the understanding of function, stability, and dynamics. This paper introduces a suite of computational tools for volumetric data processing, information extraction, surface mesh rendering, geometric measurement, and curvature estimation of biomolecular complexes. Particular emphasis is given to the modeling of cryo-electron microscopy data. Lagrangian-triangle meshes are employed for the surface presentation. On the basis of this representation, algorithms are developed for surface area and surface-enclosed volume calculation, and curvature estimation. Methods for volumetric meshing have also been presented. Because the technological development in computer science and mathematics has led to multiple choices at each stage of the geometric modeling, we discuss the rationales in the design and selection of various algorithms. Analytical models are designed to test the computational accuracy and convergence of proposed algorithms. Finally, we select a set of six cryo-electron microscopy data representing typical subcellular complexes to demonstrate the efficacy of the proposed algorithms in handling biomolecular surfaces and explore their capability of geometric characterization of binding targets. This paper offers a comprehensive protocol for the geometric modeling of subcellular structures, organelles, and multiprotein complexes.

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“…Although local subdivision schemes have already been proposed for mesh generation (e.g. [TAD07,TWAD09] for 2D triangle and tetrahedral meshes, respectively), we do not know of a previous global hierarchical approach for CVT computation. In addition to the acceleration of the convergence speed, which is well known in many fields (a hierarchical sampling approach is for instance described for quantization in [GG91]), such an approach gives guarantees about the CVT regularity.…”

Section: Hierarchical Cvtmentioning

confidence: 99%

A Hierarchical Approach for Regular Centroidal Voronoi Tessellations

Wang

Hétroy-Wheeler

Boyer

2015

Computer Graphics Forum

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International audienceIn this paper we consider Centroidal Voronoi Tessellations (CVTs) and study their regularity. CVTs are geometric structures that enable regular tessellations of geometric objects and are widely used in shape modeling and analysis. While several efficient iterative schemes, with defined local convergence properties, have been proposed to compute CVTs, little attention has been paid to the evaluation of the resulting cell decompositions. In this paper, we propose a regularity criterion that allows us to evaluate and compare CVTs independently of their sizes and of their cell numbers. This criterion allows us to compare CVTs on a common basis. It builds on earlier theoretical work showing that second moments of cells converge to a lower bound when optimising CVTs. In addition to proposing a regularity criterion, this paper also considers computational strategies to determine regular CVTs. We introduce a hierarchical framework that propagates regularity over decomposition levels and hence provides CVTs with provably better regularities than existing methods. We illustrate these principles with a wide range of experiments on synthetic and real models

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Interleaving Delaunay refinement and optimization for practical isotropic tetrahedron mesh generation

Cited by 26 publications

References 24 publications

Feature preserving Delaunay mesh generation from 3D multi‐material images

Feature preserving Delaunay mesh generation from 3D multi‐material images

Geometric modeling of subcellular structures, organelles, and multiprotein complexes

A Hierarchical Approach for Regular Centroidal Voronoi Tessellations

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