Healed marching cubes algorithm for non-manifold implicit surfaces

2016 ◽  
Author(s):  
Quoc Trong Nguyen ◽  
Abel J.P. Gomes
Keyword(s):  
Implicit Surfaces ◽  
Marching Cubes ◽  
Marching Cubes Algorithm

Dual-Primal Mesh Optimization for Polygonized Implicit Surfaces With Sharp Features

2002 ◽  
Vol 2 (4) ◽  
pp. 277-284 ◽  
Author(s):  
Yutaka Ohtake ◽  
Alexander G. Belyaev
Keyword(s):  
Adaptive Mesh ◽  
Implicit Surfaces ◽  
Marching Cubes ◽  
Triangle Mesh ◽  
Implicit Surface ◽  
Weighted Vertex ◽  
Visualization Toolkit ◽  
Object Oriented Approach ◽  
Speed And Accuracy ◽  
Dual Mesh

A new method for improving polygonizations of implicit surfaces with sharp features is proposed. The method is based on the observation that, given an implicit surface with sharp features, a triangle mesh whose triangles are tangent to the implicit surface at certain inner triangle points gives a better approximation of the implicit surface than the standard Marching Cubes mesh [Lorensen, W.E., and Cline, H.E., 1987, Computer Graphics (Proceedings of SIGGRAPH ’87), 21(3), pp. 163–169] (in our experiments we use VTK Marching Cubes [Schroeder, W., Martin, K., and Lorensen, W., 1998, The Visualization Toolkit: An Object-Oriented Approach to 3-D Graphics, Prentice Hall]). First, given an initial triangle mesh, its dual mesh composed of the triangle centroids is considered. Then the dual mesh is modified such that its vertices are placed on the implicit surface and the mesh dual to the modified dual mesh is considered. Finally the vertex positions of that “double dual” mesh are optimized by minimizing a quadratic energy measuring a deviation of the mesh normals from the implicit surface normals computed at the vertices of the modified dual mesh. In order to achieve an accurate approximation of fine surface features, these basic steps are combined with adaptive mesh subdivision and curvature-weighted vertex resampling. The proposed method outperforms approaches based on the mesh evolution paradigm in speed and accuracy.

Modification of the Marching Cubes Algorithm to Obtain a 3D Representation of a Planar Image

2021 ◽  
Vol 47 (3) ◽  
pp. 215-223
Author(s):  
Delia Irazú Hernández Farías ◽  
Rafael Guzmán Cabrera ◽  
Teodoro Cordova Fraga ◽  
José Zacarías Huamaní Luna ◽  
Jose Francisco Gomez Aguilar
Keyword(s):  
Marching Cubes ◽  
Planar Image ◽  
Marching Cubes Algorithm ◽  
3D Representation

Contouring Medial Surface of Thin-Plate Structures Using Local Marching Cubes

2005 ◽  
Vol 5 (2) ◽  
pp. 111-115 ◽  
Author(s):  
Tomoyuki Fujimori ◽  
Hiromasa Suzuki ◽  
Yohei Kobayashi ◽  
Kiwamu Kase
Keyword(s):  
Thin Plate ◽  
Computer Aided Design ◽  
Prototype System ◽  
Marching Cubes ◽  
Plate Structures ◽  
Medial Surface ◽  
Surface Models ◽  
Marching Cubes Algorithm ◽  
Computer Aided ◽  
Ct Data

This paper describes a new algorithm for contouring a medial surface from CT (computed tomography) data of a thin-plate structure. Thin-plate structures are common in mechanical structures, such as car body shells. When designing thin-plate structures in CAD (computer-aided design) and CAE (computer-aided engineering) systems, their shapes are usually represented as surface models associated with their thickness values. In this research, we are aiming at extracting medial surface models of thin-plate structures from their CT data for use in CAD and CAE systems. Commonly used isosurfacing methods, such as marching cubes, are not applicable to contour the medial surface. Therefore, we first extract medial cells (cubes comprising eight neighboring voxels) from the CT data using a skeletonization method to apply the marching cubes algorithm for extracting the medial surface. It is not, however, guaranteed that the marching cubes algorithm can contour those medial cells (in short, not “marching cubeable”). In this study, therefore we developed cell operations that correct topological connectivity to guarantee such marching cubeability. We then use this method to assign virtual signs to the voxels to apply the marching cubes algorithm to generate triangular meshes of a medial surface and map the thicknesses of thin-plate structures to the triangle meshes as textures. A prototype system was developed to verify some experimental results.

History of the Marching Cubes Algorithm

2020 ◽  
Vol 40 (2) ◽  
pp. 8-15 ◽  
Author(s):  
William E. Lorensen ◽  
Chris Johnson ◽  
Dave Kasik ◽  
Mary C. Whitton
Keyword(s):  
Marching Cubes ◽  
Marching Cubes Algorithm ◽  
History Of

Medical Image Segmentation and Reconstruction Based on Bayesian Level Set Method and Marching Cubes Algorithm

2011 ◽  
Vol 110-116 ◽  
pp. 4832-4836
Author(s):  
Yao Tien Chen
Keyword(s):  
Level Set Method ◽  
Surface Reconstruction ◽  
Level Set ◽  
Statistical Tests ◽  
Three Dimensional ◽  
Medical Image Segmentation ◽  
Tumor Segmentation ◽  
Marching Cubes ◽  
Appropriate Treatment ◽  
Marching Cubes Algorithm

We propose an approach, integrating Bayesian level set method with modified marching cubes algorithm for brain tissue and tumor segmentation and surface reconstruction. First, we extend the level set method based on the Bayesian risk to three-dimensional segmentation. Then, the three-dimensional Bayesian level set method is used to segment solid three-dimensional targets (e.g., tissue, whole brain, or tumor) from serial slice of medical images. Finally, the modified marching cubes algorithm is used to continuously reconstruct the surface of targets. Since each step can definitely obtain an appropriate treatment by statistical tests, the tissue and tumor segmentation and surface reconstruction are expected to be satisfied.

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