Multi-Resolutional Parallel Isosurface Extraction based on Tetrahedral Bisection

Gerstner, Thomas; Rumpf, Martin

doi:10.1007/978-1-4471-0737-8_17

Cited by 26 publications

(29 citation statements)

References 10 publications

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“…not uniformly) it can happen that the extracted isosurface contains holes (cracks) at transition zones where the mesh resolution changes. Different solutions have been devised for this problem, including remeshing [4,8], point insertion [20], filling, adaptive projection [17], and saturation of the error indicator [6,7].…”

Section: Related Workmentioning

confidence: 99%

Topology preserving and controlled topology simplifying multiresolution isosurface extraction

Gerstner

Pajarola

Proceedings Visualization 2000. VIS 2000 (Cat. No.00CH37145)

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Multiresolution methods are becoming increasingly important tools for the interactive visualization of very large data sets. Multiresolution isosurface visualization allows the user to explore volume data using simplified and coarse representations of the isosurface for overview images, and finer resolution in areas of high interest or when zooming into the data. Ideally, a coarse isosurface should have the same topological structure as the original. The topological genus of the isosurface is one important property which is often neglected in multiresolution algorithms. This results in uncontrolled topological changes which can occur whenever the level-of-detail is changed. The scope of this paper is to propose an efficient technique which allows preservation of topology as well as controlled topology simplification in multiresolution isosurface extraction.

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Section: Related Workmentioning

confidence: 99%

Topology preserving and controlled topology simplifying multiresolution isosurface extraction

Gerstner

Pajarola

Proceedings Visualization 2000. VIS 2000 (Cat. No.00CH37145)

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“…Nested tetrahedral meshes based on the Longest Edge Bisection (LEB) operation were originally introduced for domain decomposition in finite element analysis [20,23,34], and have since then been applied in many different contexts, including scientific computing [46,13,14], surface reconstruction [24] and volume segmentation [21]. A recent survey on nested simplicial meshes based on bisection can be found in [44].…”

Section: Multi-resolution Modelingmentioning

confidence: 99%

“…The LEB operation is defined by bisecting a tetrahedron t along the plane defined by the midpoint of its longest edge e and the two vertices of t not incident to e. The containment relation among the tetrahedra generated by successive LEB operations naturally defines a binary tree, where the two tetrahedra generated by bisecting a parent tetrahedron t are the children of t. When a full binary tree is stored, this representation can be efficiently encoded as a linear array, and the parent-child relation can be implicitly determined from the array indices [13,22,46]. A forest of six such tetrahedral binary trees, whose roots share a common cube diagonal can thus decompose a cubic region of space.…”

Section: Multi-resolution Modelingmentioning

confidence: 99%

Discrete Distortion for 3D Data Analysis

Floriani

Iuricich

Magillo

et al. 2012

Mathematics and Visualization

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Summary. We investigate a morphological approach to the analysis and understanding of three-dimensional scalar fields, and we consider applications to 3D medical and molecular images as examples. We consider a discrete model of the scalar field obtained by discretizing its 3D domain into a tetrahedral mesh. In particular, our meshes correspond to approximations at uniform or variable resolution extracted from a multi-resolution model of the 3D scalar field, that we call a hierarchy of diamonds. We analyze the images based on the concept of discrete distortion, that we have introduced in [26], and on segmentations based on Morse theory. Discrete distortion is defined by considering the graph of the discrete 3D field, which is a tetrahedral hypersurface in R 4 , and measuring the distortion of the transformation which maps the tetrahedral mesh discretizing the scalar field domain into the mesh representing its graph in R 4 . We describe a segmentation algorithm to produce Morse decompositions of a 3D scalar field which uses a watershed approach and we apply it to 3D images by using as scalar field both intensity and discrete distortion. We present experimental results by considering the influence of resolution on distortion computation. In particular, we show that the salient features of the distortion field appear prominently in lower resolution approximations to the dataset.

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“…For this problem, different solutions have been devised such as remeshing [8], point insertion [24], projection [19], blending [10], and saturation [5][6][7]32]. …”

Section: Related Workmentioning

confidence: 99%

“…η(T ) = η(x ref (T )), and choosing η(T ) < ε as a stopping criterion for some user specified threshold value ε. If the error indicator values are saturated [5][6][7]32], no hanging nodes can occur for all possible values of ε. This way, the extraction algorithm is completely local and information from neighboring tetrahedra is never required.…”

Section: Multiresolution Isosurface Extractionmentioning

confidence: 99%

Fast Multiresolution Extraction of Multiple Transparent Isosurfaces

Gerstner

2001

Eurographics

Self Cite

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Abstract. In this paper, we present a multiresolution algorithm which is capable to render multiple transparent isosurfaces under real-time constraints. To this end, the underlying 3D data set is covered with a hierarchical tetrahedral grid. The multiresolution extraction algorithm is then based on an adaptive traversal of the tetrahedral grid with the help of error indicators. The display of transparent isosurfaces using alpha blending requires a back-to-front rendering of the isosurface triangles. This is achieved by a hierarchical sorting procedure of the tetrahedra and the hierarchical computation of data gradients. We will also comment on the automated selection of suitable isovalues for visualization applications.

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Multi-Resolutional Parallel Isosurface Extraction based on Tetrahedral Bisection

Cited by 26 publications

References 10 publications

Topology preserving and controlled topology simplifying multiresolution isosurface extraction

Topology preserving and controlled topology simplifying multiresolution isosurface extraction

Discrete Distortion for 3D Data Analysis

Fast Multiresolution Extraction of Multiple Transparent Isosurfaces

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