Proceedings Article10.1117/12.404839
Surface area estimation for digitized regular solids
Yukiko Kenmochi,Reinhard Klette +1 more
- 23 Oct 2000
- Vol. 4117, pp 100-111
TL;DR: The paper summarizes work on global polyhedrization techniques with experimental results pointing towards correct multigrid convergence and the class of general ellipsoids is suggested to be a test set for such multigrids convergence studies.
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Abstract: The problem of multigrid convergent surface area measurement came with the advent of computer-based image analysis. The paper proposes a classification scheme of local and global polyhedrization approaches which allows us to classify different surface area measurement techniques with respect to the underlying polyhedrization scheme. It is shown that a local polyhedrization technique such as marching cubes is not multigrid convergent towards the true value even for elementary convex regular solids such as cubes, spheres or cylinders. The paper summarizes work on global polyhedrization techniques with experimental results pointing towards correct multigrid convergence. The class of general ellipsoids is suggested to be a test set for such multigrid convergence studies.
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Citations
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Digital Geometry: Geometric Methods for Digital Picture Analysis
Reinhard Klette,Azriel Rosenfeld +1 more
- 16 Aug 2004
TL;DR: Curves and Surfaces: Topology, 3D Straightness and Planarity, and Surface and Area Curvature.
626
Minkowski tensor shape analysis of cellular, granular and porous structures.
Gerd E. Schröder-Turk,Walter Mickel,Walter Mickel,Sebastian C. Kapfer,Michael A. Klatt,Fabian M. Schaller,Matthias Hoffmann,N. Kleppmann,Patrick Armstrong,Amer Inayat,Daniel Hug,M. Reichelsdorfer,Wolfgang Peukert,Wilhelm Schwieger,Klaus Mecke +14 more
TL;DR: This article provides a practical overview of the different uses of Minkowski tensors to extract quantitative physically-relevant spatial structure information from experimental and simulated data, both in 2D and 3D.
186
Surface area estimation of digitized 3D objects using weighted local configurations
TL;DR: A Monte Carlo-based optimization of the estimator performance on the distribution of digitized balls of increasing radii is performed in order to uniquely determine optimal surface area weights.
107
PuMA: the Porous Microstructure Analysis software
TL;DR: The PuMA software has been developed in order to compute effective material properties and perform material response simulations on digitized microstructures of porous media and includes a time-dependent, particle-based model for the oxidation of fibrous materials.
74
Adaptive estimation of normals and surface area for discrete 3-D objects: application to snow binary data from X-ray tomography
Frédéric Flin,Jean-Bruno Brzoska,David Coeurjolly,Romeu André Pieritz,Bernard Lesaffre,Cécile Coléou,Pascal Lamboley,Olivier Teytaud,Gerard L. Vignoles,Jean-François Delesse +9 more
TL;DR: A new and simple computational method is proposed in order to obtain accurate results on all types of shapes, whatever their local convexity degree, based on the gradient vector field analysis of the object distance map.
67
References
Marching cubes: A high resolution 3D surface construction algorithm
William E. Lorensen,Harvey E. Cline +1 more
- 01 Aug 1987
TL;DR: In this paper, a divide-and-conquer approach is used to generate inter-slice connectivity, and then a case table is created to define triangle topology using linear interpolation.
Octrees for faster isosurface generation
Jane Wilhelms,Allen Van Gelder +1 more
- 01 Nov 1990
TL;DR: In this article, a branch-on-need octree (BONO) data structure is proposed to store summary information to prevent useless exploration of regions of little or no current interest within the volume.
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Exploiting triangulated surface extraction using tetrahedral decomposition
A. Gueziec,R. Hummel +1 more
TL;DR: Data structures based upon a new encoding of the tetrahedra that are at least four times more compact than the standard data structures using vertices and triangles are introduced.
220
Marching cubes method with connectivity
Yukiko Kenmochi,Kazunori Kotani,Atsushi Imiya +2 more
- 24 Oct 1999
TL;DR: This paper solves the topological problem of isosurfaces generated by the marching cubes method using the approach of combinatorial topology by modifying the polyhedral configurations with the connectivity and constructing polyhedral isOSurfaces with the correct topologies.
45
Polyhedrization of the Boundary of a Voxel Object
Jean Françon,Laurent Papier +1 more
- 17 Mar 1999
TL;DR: A polyhedrization algorithm is presented in this paper that uses a recent algorithm for recognizing standard arithmetic planes and is the 3D extension of the known polygonalization of 2D discrete curves.
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