Delete and insert operations in Voronoi/Delaunay methods and applications

Mostafavi, Mir Abolfazl; Gold, Christopher M.; Dakowicz, Maciej

doi:10.1016/s0098-3004(03)00017-7

Cited by 82 publications

(34 citation statements)

References 19 publications

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“…Moreover, for better visual effect, a surface reconstruction algorithm [16] is used to re-mesh the model after the tensor data is completed. Since deformation often exists on the surrounding region of the hole in medical images, leading to deformed result in recovered data, a point-deletion algorithm [17] is used to eliminate the influence by removing the deformed points from the surrounding region. The top two rows show the result of RSTD on a CT data and the bottom two rows show the results on a MRI data.…”

Section: Methodsmentioning

confidence: 99%

Hole-Filling by Rank Sparsity Tensor Decomposition for Medical Imaging

Guo

Yin

Yang

et al. 2011

IEICE Trans. Inf. & Syst.

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SUMMARYSurface integrity of 3D medical data is crucial for surgery simulation or virtual diagnoses. However, undesirable holes often exist due to external damage on bodies or accessibility limitation on scanners. To bridge the gap, hole-filling for medical imaging is a popular research topic in recent years [1]- [3]. Considering that a medical image, e.g. CT or MRI, has the natural form of a tensor, we recognize the problem of medical hole-filling as the extension of Principal Component Pursuit (PCP) problem from matrix case to tensor case. Since the new problem in the tensor case is much more difficult than the matrix case, an efficient algorithm for the extension is presented by relaxation technique. The most significant feature of our algorithm is that unlike traditional methods which follow a strictly local approach, our method fixes the hole by the global structure in the specific medical data. Another important difference from the previous algorithm [4] is that our algorithm is able to automatically separate the completed data from the hole in an implicit manner. Our experiments demonstrate that the proposed method can lead to satisfactory results.

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Section: Methodsmentioning

confidence: 99%

Hole-Filling by Rank Sparsity Tensor Decomposition for Medical Imaging

Guo

Yin

Yang

et al. 2011

IEICE Trans. Inf. & Syst.

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“…[16,17,37]. As has already been argued, there exist some fundamental differences between the two-dimensional and the higherdimensional case.…”

Section: Deletion Of Verticesmentioning

confidence: 99%

Kinetic and dynamic Delaunay tetrahedralizations in three dimensions

Schaller

Meyer‐Hermann

2004

Computer Physics Communications

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We describe the implementation of algorithms to construct and maintain threedimensional dynamic Delaunay triangulations with kinetic vertices using a threesimplex data structure. The code is capable of constructing the geometric dual, the Voronoi or Dirichlet tessellation. Initially, a given list of points is triangulated. Time evolution of the triangulation is not only governed by kinetic vertices but also by a changing number of vertices. We use three-dimensional simplex flip algorithms, a stochastic visibility walk algorithm for point location and in addition, we propose a new simple method of deleting vertices from an existing three-dimensional Delaunay triangulation while maintaining the Delaunay property. The dual Dirichlet tessellation can be used to solve differential equations on an irregular grid, to define partitions in cell tissue simulations, for collision detection etc.Key words: Delaunay triangulation, Dirichlet, Voronoi, flips, point location, vertex deletion, kinetic algorithm, dynamic algorithmIn nearly all aspects of science nowadays simulations of discrete objects underlying different interactions play a very important role. Such an interaction for example could be mediated by colliding grains of sand in an hourglass or -more abstract -the neighborhood question of influence regions. One general method to represent possible two-body interactions within a system of N objects is given by a network which can be described by an N × N adjacency matrix ν, with its matrix elements ν ij = ν ji (undirected graph) representing the interaction between the objects i and j. However, for most realistic systems the graph defined this way is not practical if one remembers that the typical size of a system of atoms in chemistry can be O (10 23 ), the human body consists of O (10 18 ) cells and even simple systems such as a grain-filled hourglass

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“…It decomposes the earth surface into "natural" cells rather than "regular" cells by the traditional Discrete Global Grid (DGG), such as Quadrangle Grid [Seong 2005], Quaternary Triangular Mesh [Chen et al 2003], or Hexagon Grid [Sahr 2008] and Voronoi/TIN grid [Mostafavi et al 2003]. In fact, GNG can directly reveal the topological structure information related to the level sets of the height function defined on the earth surface and supports a knowledge-based approach to analyze, visualize and understand the earth surface behavior (in space and time) through a global perspective.…”

Section: Introductionmentioning

confidence: 99%

A Global "Natural" Grid Modeling Method Based on Terrain Topological Structure

Wang

Zhao

Wang

et al. 2013

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:In this paper, a Global "Natural" Grid (GNG) modeling method based on the terrain topological structure is proposed. GNG partitions the earth surface into "natural" cells by using the natural terrain feature elements, which may be more suitable for exploring and understanding some natural phenomena in the environment monitoring, hydrological analysis, species distribution, etc. This modeling method mainly consists of three steps: firstly, a variable-resolution geometric representation of global DEMs based on the restricted quadtree is constructed; secondly, the feature elements are extracted and an original GNG model is built; finally, a multi-resolution representation of GNG is established by recursively applying topological simplification. In the end, an experiment is done to validate the correctness and feasibility of this modeling method.

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Delete and insert operations in Voronoi/Delaunay methods and applications

Cited by 82 publications

References 19 publications

Hole-Filling by Rank Sparsity Tensor Decomposition for Medical Imaging

Hole-Filling by Rank Sparsity Tensor Decomposition for Medical Imaging

Kinetic and dynamic Delaunay tetrahedralizations in three dimensions

A Global "Natural" Grid Modeling Method Based on Terrain Topological Structure

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