Improving the robustness and accuracy of the marching cubes algorithm for isosurfacing

Lopes, Adriano; Brodlie, Ken

doi:10.1109/tvcg.2003.1175094

Cited by 126 publications

(96 citation statements)

References 14 publications

(23 reference statements)

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“…In order to overcome such shortcomings of MC, several extensions are discussed in the literature [3], [4], [5], [16], [21], [23], [24], [33], [34], [35]. To obtain a high-quality triangle mesh from MC, postprocessing steps are typically applied directly to the triangle mesh [10].…”

Section: Related Workmentioning

confidence: 99%

Edge Transformations for Improving Mesh Quality of Marching Cubes

Dietrich¹,

Scheidegger

Schreiner

et al. 2009

IEEE Trans. Visual. Comput. Graphics

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Abstract-Marching Cubes is a popular choice for isosurface extraction from regular grids due to its simplicity, robustness, and efficiency. One of the key shortcomings of this approach is the quality of the resulting meshes, which tend to have many poorly shaped and degenerate triangles. This issue is often addressed through postprocessing operations such as smoothing. As we demonstrate in experiments with several data sets, while these improve the mesh, they do not remove all degeneracies and incur an increased and unbounded error between the resulting mesh and the original isosurface. Rather than modifying the resulting mesh, we propose a method to modify the grid on which Marching Cubes operates. This modification greatly increases the quality of the extracted mesh. In our experiments, our method did not create a single degenerate triangle, unlike any other method we experimented with. Our method incurs minimal computational overhead, requiring at most twice the execution time of the original Marching Cubes algorithm in our experiments. Most importantly, it can be readily integrated in existing Marching Cubes implementations and is orthogonal to many Marching Cubes enhancements (particularly, performance enhancements such as out-of-core and acceleration structures).

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Section: Related Workmentioning

confidence: 99%

Edge Transformations for Improving Mesh Quality of Marching Cubes

Dietrich¹,

Scheidegger

Schreiner

et al. 2009

IEEE Trans. Visual. Comput. Graphics

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“…The function values of face and body saddles in the cell can be used to decide the correct topology and consistent triangulation of an isosurface in the cell [42]. Lopes and Brodlie [38] provided a more accurate triangulation.…”

Section: Previous Work Isosurface Extractionmentioning

confidence: 99%

“…Several cases may have more than one local topology, and are termed ambiguous. We refer to [38] for all the cases of different local topology of an isosurface in a cube. When a case is ambiguous, the standard dual contouring method causes a non-manifold at the minimizing vertex in the cube.…”

Section: Mesh Topologymentioning

confidence: 99%

3D finite element meshing from imaging data

Zhang

Bajaj

Sohn

2005

Computer Methods in Applied Mechanics and Engineering

165

134

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This paper describes an algorithm to extract adaptive and quality 3D meshes directly from volumetric imaging data. The extracted tetrahedral and hexahedral meshes are extensively used in the Finite Element Method (FEM). A top-down octree subdivision coupled with the dual contouring method is used to rapidly extract adaptive 3D finite element meshes with correct topology from volumetric imaging data. The edge contraction and smoothing methods are used to improve the mesh quality. The main contribution is extending the dual contouring method to crack-free interval volume 3D meshing with feature sensitive adaptation. Compared to other tetrahedral extraction methods from imaging data, our method generates adaptive and quality 3D meshes without introducing any hanging nodes. The algorithm has been successfully applied to constructing the geometric model of a biomolecule in finite element calculations.

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“…As algorithms and implementations become more complex, issues may be overlooked and remain hidden in the multitude of (pseudo-) lines of code. Throughout years of research, it has been shown that some supposedly topologically correct techniques, including MC33, have issues that prevent correctness [7,16,21]. In particular, the work of Etiene et al [7] shows that the MC33 implementation by Lewiner et al [14,15], fails to produce topologically correct isosurfaces.…”

Section: Introductionmentioning

confidence: 99%

Practical considerations on Marching Cubes 33 topological correctness

Custódio

Etiene

Pesco

et al. 2013

Computers & Graphics

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Chernyaev's Marching Cubes 33 is one of the first algorithms intended to preserve the topology of the trilinear interpolant. In this work, we address three issues with the Marching Cubes 33 algorithm, two of which are related to its original description and one that is related to its variant. In particular, we solve a problem with the core disambiguation procedure of Marching Cubes 33 that prevents the extraction of topologically correct isosurfaces for the ambiguous configuration 13.5. This work closes an existing gap in the topological correctness of Marching Cubes 33. Furthermore, we make our results reproducible, meaning that examples provided in this work can be easily explored and studied. Finally, as part of the philosophy of reproducibility, we provide a corrected version of the Marching Cubes 33 open-source implementation and access to datasets that can be used to verify the correctness of any available topologically correct isosurface extraction implementation that preserves the topology of the trilinear interpolant.

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Improving the robustness and accuracy of the marching cubes algorithm for isosurfacing

Cited by 126 publications

References 14 publications

Edge Transformations for Improving Mesh Quality of Marching Cubes

Edge Transformations for Improving Mesh Quality of Marching Cubes

3D finite element meshing from imaging data

Practical considerations on Marching Cubes 33 topological correctness

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