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3rd workshop on visualization and processing of tensor fields, 2009

ISBN: (纸本)9783642543005

The proceedings contain 19 papers. The special focus in this conference is on visualization and processing of tensor fields. The topics include: Classification study of DTI and HArdI anisotropy measures for HArdI data simplification;towards resolving fiber crossings with higher order tensor inpainting;representation and estimation of tensor-pairs;on the choice of a tensor distance for dti white matter segmentation;divergence measures and means of symmetric positive-definite matrices;metric selection and diffusion tensor swelling;h2-matrix compression;harmonic field analysis;adaptation of tensor voting to image structure estimation;edge-enhancing diffusion filtering for matrix fields;fabric-like visualization of tensor field data on arbitrary surfaces in image space;beyond topology: A lagrangian metaphor to visualize the structure of 3D tensor fields;tensor field design: Algorithms and applications;interactive exploration of stress tensors used in computational turbulent combustion;shear wave diffusion observed by magnetic resonance elastography;A comparative analysis of dimension reduction techniques for representing DTI fibers as 2D/3D points;preface.

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tensor field design: Algorithms and applications 3rd

Tensor field design: Algorithms and applications

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3rd workshop on visualization and processing of tensor fields, 2009

作者： Zhang, Eugene School of Electrical Engineering and Computer Science 2111 Kelley Engineering Center Oregon State University CorvallisOR97331 United States

tensor field design has found increasing applications in computer graphics, geometry processing, and scientific visualization. In this chapter, we review recent advances in tensor field design and discuss possible fut... 详细信息

ISBN: (纸本)9783642543005

关键词： tensors

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Beyond topology: A lagrangian metaphor to visualize the structure of 3D tensor fields 3rd

Beyond topology: A lagrangian metaphor to visualize the stru...

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3rd workshop on visualization and processing of tensor fields, 2009

作者： Tricoche, Xavier Hlawitschka, Mario Barakat, Samer Garth, Christoph Purdue University LafayetteIN United States University of California at Davis DavisCA United States

ISBN: (纸本)9783642543005

Topology was introduced in the visualization literature some 15 years ago as a mathematical language to describe and capture the salient structures of symmetric second-order tensor fields. Yet, despite significant theoretical and algorithmic advances, this approach has failed to gain wide acceptance in visualization practice over the last decade. In fact, the very idea of a versatile visualization methodology for tensor fields that could transcend application domains has been virtually abandoned in favor of problem-specific feature definitions and visual representations. We propose to revisit the basic idea underlying topology from a different perspective. To do so, we introduce a Lagrangian metaphor that transposes to the structural analysis of eigenvector fields a perspective that is commonly used in the study of fluid flows. Indeed, one can view eigenvector fields as the local superimposition of two vector fields, from which a bidirectional flow field can be defined. This allows us to analyze the structure of a tensor field through the behavior of fictitious particles advected by this flow. Specifically, we show that the separatrices of 3D tensor field topology can in fact be captured in a fuzzy and numerically more robust setting as ridges of a trajectory coherence measure. As a result, we propose an alternative structure characterization strategy for the visual analysis of practical 3D tensor fields, which we demonstrate on several synthetic and computational datasets. © Springer-Verlag Berlin Heidelberg 2012.

关键词： Topology

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Towards resolving fiber crossings with higher order tensor inpainting 3rd

Towards resolving fiber crossings with higher order tensor i...

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3rd workshop on visualization and processing of tensor fields, 2009

作者： Schultz, Thomas University of Chicago Computation Institute 5735 S. Ellis Ave #209A ChicagoIL60637 United States

ISBN: (纸本)9783642543005

The use of second-order tensors for the modeling of data from Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) is limited by their inability to represent more than one dominant direction in cases of crossing fiber bundles or partial voluming. Higher-order tensors have been used in High Angular Resolution Diffusion Imaging (HArdI) to overcome these problems, but their larger number of parameters leads to longer measurement times for data acquisition. In this work, we demonstrate that higher-order tensors that indicate likely fiber directions can be estimated from a small number of diffusion-weighted measurements by taking into account information from local neighborhoods. To this end, we generalize tensor voting, a method from computer vision, to higher-order tensors. We demonstrate that the resulting even-order tensor fields facilitate fiber reconstruction at crossings both in synthetic and in real DW-MRI data, and that the odd-order fields differentiate crossings from junctions. © Springer-Verlag Berlin Heidelberg 2012.

关键词： Magnetic resonance imaging

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Parallel visualization of large-scale unstructured geophysical data for the Earth Simulator

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PURE AND APPLIED GEOPHYSICS 2004年第11-12期161卷 2245-2263页

作者： Chen, L Fujishiro, I Nakajima, K Res Org Informat Sci & Technol Meguro Ku Tokyo 1530061 Japan Ochanomizu Univ Bunkyo Ku Tokyo 1128610 Japan

A scalable and high-performance parallel visualization subsystem has been developed in GeoFEM for the Earth Simulator. As part of the Earth Simulator project in Japan, the proposed subsystem is effective for the visualization of large-scale geoscientific data, and can be concurrent with computation subsystems on the same high-performance parallel computer. Moreover, several parallel visualization methods are developed for large unstructured datasets, covering scalar, vector and tensor fields. Furthermore, a number of strategies are adopted in order to improve the parallel performance of the proposed subsystem for the Earth simulator, including the three-level hybrid parallelization and dynamic load balancing. Good visualization images and high parallel performance have been obtained on a Hitachi SR8000 for large unstructured geoscientific data sets, and thus demonstrating the feasibility and effectiveness of the proposed method for use on the Earth Simulator.

关键词： parallel visualization unstructured grid large-scale geoscientific dataset Earth Simulator parallel volume rendering hybrid parallelization

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Edge-enhancing diffusion filtering for matrix fields 3rd

Edge-enhancing diffusion filtering for matrix fields

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3rd workshop on visualization and processing of tensor fields, 2009

作者： Burgeth, Bernhard Pizarro, Luis Didas, Stephan Faculty of Mathematics and Computer Science Saarland University Building E2.4 Saarbrücken66041 Germany Department of Computing Imperial College London 180 Queen’s Gate LondonSW7 2AZ United Kingdom Abteilung Bildverarbeitung Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM Fraunhofer-Platz 1 Kaiserslautern67663 Germany

ISBN: (纸本)9783642543005

The elimination of noise and small details from an image while simultaneously preserving or enhancing the edge structures in an image is a ever-lasting task in image processing. Edge-enhancing anisotropic diffusion is known to tackle this problem successfully. The problem of noise removal and edge enhancement is also a major concern in diffusion tensor magnetic resonance imaging (DT-MRI). This medical image acquisition technique outputs a 3D matrix field of symmetric 3 ☓ 3-matrices, and it helps to visualise, for example, the nerve fibres in brain tissue. As any physical measurement DT-MRI is subjected to errors causing faulty representations of the tissue structure corrupted by noise. In this paper we address that problem by proposing a edge-enhancing diffusion filtering methodology for matrix fields. The approach is based on a generic structure tensor concept for matrix fields that relies on the operator-algebraic properties of symmetric matrices, rather than their channel-wise treatment of earlier proposals. Numerical experiments with artificial and real DT-MRI data confirm the noise-removing and edge-enhancing qualities of the technique presented. © Springer-Verlag Berlin Heidelberg 2012.

关键词： Matrix algebra

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3rd workshop on Topological Methods in Data Analysis and visualization, TopoInVis 2009

3rd Workshop on Topological Methods in Data Analysis and Vis...

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3rd workshop on Topological Methods in Data Analysis and visualization, TopoInVis 2009

ISBN: (纸本)9783642543005

The proceedings contain 20 papers. The special focus in this conference is on Topological Methods in Data Analysis and visualization. The topics include: Eigenvector-based interpolation and segmentation of 2D tensor fields;time-dependent visualization of lagrangian coherent structures by grid advection;topological extraction and tracking of defects in crystal structures;extracting and visualizing structural features in environmental point cloud lidar data sets;topological flow structures in a mathematical model for rotation-mediated cell aggregation;a categorical approach to contour, split and join trees with application to airway segmentation;complementary space for enhanced uncertainty and dynamics visualization;topological feature extraction for comparison of terascale combustion simulation data;stripe parameterization of tubular surfaces;feature tracking using reeb graphs;the stability of the apparent contour of an orientable 2-manifold;reconstructing cell complexes from cross-sections;substructure topology preserving simplification of tetrahedral meshes;practical considerations in morse-smale complex computation;modeling and simplifying morse complexes in arbitrary dimensions;simplification of jacobi sets;combinatorial 2D vector field topology extraction and simplification;preface.

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Metric selection and diffusion tensor swelling 3rd

Metric selection and diffusion tensor swelling

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3rd workshop on visualization and processing of tensor fields, 2009

作者： Pasternak, Ofer Sochen, Nir Basser, Peter J. Brigham and Women’s Hospital Harvard Medical School BostonMA United States Department of Applied Mathematics Tel Aviv University Tel Aviv Israel National Institutes of Health BethesdaMD United States

ISBN: (纸本)9783642543005

The measurement of the distance between diffusion tensors is the foundation on which any subsequent analysis or processing of these quantities, such as registration, regularization, interpolation, or statistical inference is based. Euclidean metrics were first used in the context of diffusion tensors;then geometric metrics, having the practical advantage of reducing the "swelling effect," were proposed instead. In this chapter we explore the physical roots of the swelling effect and relate it to acquisition noise. We find that Johnson noise causes shrinking of tensors, and suggest that in order to account for this shrinking, a metric should support swelling of tensors while averaging or interpolating. This interpretation of the swelling effect leads us to favor the Euclidean metric for diffusion tensor analysis. This is a surprising result considering the recent increase of interest in the geometric metrics. © Springer-Verlag Berlin Heidelberg 2012.

关键词： tensors

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Fabric-like visualization of tensor field data on arbitrary surfaces in image space 3rd

Fabric-like visualization of tensor field data on arbitrary ...

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3rd workshop on visualization and processing of tensor fields, 2009

作者： Eichelbaum, Sebastian Hlawitschka, Mario Hamann, Bernd Scheuermann, Gerik Abteilung für Bild- und Signalverarbeitung Institut für Informatik Universität Leipzig Leipzig Germany Scientific Visualization Group Institut für Informatik Universität Leipzig Leipzig Germany University of California DavisCA United States

ISBN: (纸本)9783642543005

tensors are of great interest to many applications in engineering and in medical imaging, but a proper analysis and visualization remains challenging. It already has been shown that, by employing the metaphor of a fabric structure, tensor data can be visualized precisely on surfaces where the two eigendirections in the plane are illustrated as thread-like structures. This leads to a continuous visualization of most salient features of the tensor data set. We introduce a novel approach to compute such a visualization from tensor field data that is motivated by image space line integral convolution (LIC). Although our approach can be applied to arbitrary, non-self-intersecting surfaces, the main focus lies on special surfaces following important features, such as surfaces aligned to the neural pathways in the human brain. By adding a postprocessing step, we are able to enhance the visual quality of the results, which improves perception of the major patterns. © Springer-Verlag Berlin Heidelberg 2012.

关键词： visualization

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Eigenvector-based Interpolation and Segmentation of 2D tensor fields 3rd

Eigenvector-based Interpolation and Segmentation of 2D Tenso...

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3rd workshop on Topological Methods in Data Analysis and visualization

作者： Sreevalsan-Nair, Jaya Auer, Cornelia Hamann, Bernd Hotz, Ingrid Univ Texas Austin Texas Adv Comp Ctr Austin TX 78712 USA

ISBN: (纸本)9783642150135

We propose a topology-based segmentation of 2D symmetric tensor fields, which results in cells bounded by tensorlines. We are particularly interested in the influence of the interpolation scheme on the topology, considering eigenvector-based and component-wise linear interpolation. When using eigenvector-based interpolation the most significant modification to the standard topology extraction algorithm is the insertion of additional vertices at degenerate points. A subsequent Delaunay re-triangulation leads to connections between close degenerate points. These new connections create degenerate edges and triangles. When comparing the resulting topology per triangle with the one obtained by component-wise linear interpolation the results are qualitatively similar, but our approach leads to a less "cluttered" segmentation.

关键词： Topology

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