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Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration

E-BookPDF1 - PDF WatermarkE-Book
350 Seiten
Englisch
Springer Berlin Heidelbergerschienen am12.06.20092009
The goal of visualization is the accurate, interactive, and intuitive presentation of data. Complex numerical simulations, high-resolution imaging devices and incre- ingly common environment-embedded sensors are the primary generators of m- sive data sets. Being able to derive scienti?c insight from data increasingly depends on having mathematical and perceptual models to provide the necessary foundation for effective data analysis and comprehension. The peer-reviewed state-of-the-art research papers included in this book focus on continuous data models, such as is common in medical imaging or computational modeling. From the viewpoint of a visualization scientist, we typically collaborate with an application scientist or engineer who needs to visually explore or study an object which is given by a set of sample points, which originally may or may not have been connected by a mesh. At some point, one generally employs low-order piecewise polynomial approximationsof an object, using one or several dependent functions. In order to have an understanding of a higher-dimensional geometrical 'object' or function, ef?cient algorithms supporting real-time analysis and manipulation (- tation, zooming) are needed. Often, the data represents 3D or even time-varying 3D phenomena (such as medical data), and the access to different layers (slices) and structures (the underlying topology) comprising such data is needed.mehr
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Produkt

KlappentextThe goal of visualization is the accurate, interactive, and intuitive presentation of data. Complex numerical simulations, high-resolution imaging devices and incre- ingly common environment-embedded sensors are the primary generators of m- sive data sets. Being able to derive scienti?c insight from data increasingly depends on having mathematical and perceptual models to provide the necessary foundation for effective data analysis and comprehension. The peer-reviewed state-of-the-art research papers included in this book focus on continuous data models, such as is common in medical imaging or computational modeling. From the viewpoint of a visualization scientist, we typically collaborate with an application scientist or engineer who needs to visually explore or study an object which is given by a set of sample points, which originally may or may not have been connected by a mesh. At some point, one generally employs low-order piecewise polynomial approximationsof an object, using one or several dependent functions. In order to have an understanding of a higher-dimensional geometrical 'object' or function, ef?cient algorithms supporting real-time analysis and manipulation (- tation, zooming) are needed. Often, the data represents 3D or even time-varying 3D phenomena (such as medical data), and the access to different layers (slices) and structures (the underlying topology) comprising such data is needed.
Details
Weitere ISBN/GTIN9783540499268
ProduktartE-Book
EinbandartE-Book
FormatPDF
Format Hinweis1 - PDF Watermark
FormatE107
Erscheinungsjahr2009
Erscheinungsdatum12.06.2009
Auflage2009
ReiheMathematics and Visualization
Seiten350 Seiten
SpracheEnglisch
IllustrationenX, 350 p. 183 illus., 134 illus. in color.
Artikel-Nr.1441192
Rubriken
Genre9200

Inhalt/Kritik

Inhaltsverzeichnis
1;Preface;5
2;Contents;8
3;Maximizing Adaptivity in Hierarchical Topological Models Using Cancellation Trees;10
3.1;1 Introduction;10
3.2;2 Morse-Smale Complex;12
3.3;3 Cancellation Forest;14
3.4;4 Hierarchy;17
3.5;5 Results;21
3.6;6 Conclusions and Future Research;26
3.7;References;26
4;The Toporrery: Computation and Presentation of Multiresolution Topology;28
4.1;1 Introduction;28
4.2;2 Multiresolution Contour Trees;31
4.3;3 Hierarchical Morse Functions;36
4.4;4 Multiresolution Contour Trees;39
4.5;5 Output Sensitive Visualization;44
4.6;6 Conclusions;47
5;Isocontour Based Visualization of Time-Varying Scalar Fields;50
5.1;1 Introduction;50
5.2;2 Isocontour Extraction;52
5.3;3 Topological Structures for Supporting Visualization;57
5.4;4 Conclusions;72
5.5;References;74
6;DeBruijn Counting for Visualization Algorithms;78
6.1;1 Introduction;78
6.2;2 History and Literature;80
6.3;3 Permuting the Colors: The Power Group;83
6.4;4 Summary;96
6.5;References;96
7;Topological Methods for Visualizing Vortical Flows;98
7.1;1 Introduction;98
7.2;2 Related Work;100
7.3;3 Theoretical Aspects of (Parametric) Topology;100
7.4;4 Topology Tracking;104
7.5;5 Planar Topology Tracking for Volume Exploration;109
7.6;6 Results;111
7.7;7 Conclusion;115
7.8;References;116
8;Stability and Computation of Medial Axes: A State-of-the-Art Report;117
8.1;1 Introduction;117
8.2;2 Medial Axis and Skeleton;118
8.3;3 Finiteness Properties;119
8.4;4 Homotopy Equivalence;120
8.5;5 Instability and Semi-continuity;121
8.6;6 Stability Under C2-Perturbations;122
8.7;7 Exact Computation of Medial Axes;122
8.8;8 Approximation Paradigm for Medial Axes;123
8.9;9 Punctured Euclidean Spaces;124
8.10;10 Voronoi Graph and Medial Axis;124
8.11;11 Pruning in the Presence of Noise;126
8.12;12 Stability of the .-Medial Axis;128
8.13;13 What Now?;129
8.14;References;131
9;Local Geodesic Parametrization: An Ant s Perspective;134
9.1;1 Introduction;134
9.2;2 The Algorithm;136
9.3;3 Implementation;139
9.4;4 Sample Application;142
9.5;5 Conclusion and Future Work;143
9.6;References;144
10;Tensor-Fields Visualization Using a Fabric-like Texture Applied to Arbitrary Two-dimensional Surfaces;145
10.1;1 Introduction;145
10.2;2 Related Work;146
10.3;3 Mathematical Background and Notation;147
10.4;4 MethodOverview;148
10.5;5 Metric Definition;149
10.6;6 Surface Definition and Tensor Projection;150
10.7;7 Texture Generation;151
10.8;8 Results and Conclusions;157
10.9;References;160
11;Flow Visualization via Partial Differential Equations;162
11.1;1 Introduction;162
11.2;2 Review of Texture Based Flow Visualization;164
11.3;3 A Brief Introduction to Scale Space Methods in Image Processing;166
11.4;4 A Flow Aligned Differential Operator;168
11.5;5 Anisotropic Diffusion for Stationary Flow;168
11.6;6 Transport and Diffusion for Non-stationary Flow Fields;174
11.7;7 Continuous Clustering via Anisotropic Phase Separation;178
11.8;8 Remarks on the Finite Element Implementation;183
11.9;9 Clustering Based on Hierarchical Decomposition of a Differential Operator;184
11.10;10 Conclusions;191
11.11;References;192
12;Iterative Twofold Line Integral Convolution for Texture-Based Vector Field Visualization;195
12.1;1 Introduction;195
12.2;2 Previous Work;196
12.3;3 Continuous Twofold Convolution Along Straightened Lines;197
12.4;4 Discretization and Sampling;200
12.5;5 Extended Scenarios;202
12.6;6 Discussion of Costs and Quality;204
12.7;7 Implementation and Results;205
12.8;8 Conclusion;211
12.9;References;214
13;Constructing 3D Elliptical Gaussians for Irregular Data;216
13.1;1 Introduction;216
13.2;2 Previous Work;218
13.3;3 Creating 3D Elliptical Gaussian;219
13.4;4 Evaluation;223
13.5;5 Rendering;224
13.6;6 Implementation and Results;224
13.7;7 Conclusion and Future Work;227
13.8;References;228
14;From Sphere Packing to the Theory of Optimal Lattice Sampling;229
14.1;1 Introduction;229
14.2;2 Multidimensional Sampling Theory;230
14.3;3 The Optimal Lattice Sampling;235
14.4;4 The BCC Lattice;236
14.5;5 Reconstruction Filters;238
14.6;6 Implementation;245
14.7;7 Results and Discussion;247
14.8;8 Conclusion;253
14.9;9 Future Research;254
14.10;References;256
15;Reducing Interpolation Artifacts by Globally Fairing Contours;258
15.1;1 Introduction;258
15.2;2 Related Work;259
15.3;3 Fairing Contours of a Scalar Field;260
15.4;4 Numerical Examples;266
15.5;5 Conclusions and Future Work;269
15.6;References;270
16;Time- and Space-Efficient Error Calculation for Multiresolution Direct Volume Rendering;271
16.1;1 Introduction;271
16.2;2 Previous Work;272
16.3;3 Error Estimation;274
16.4;4 Multiresolution Representation;279
16.5;5 Rendering;279
16.6;6 Results and Discussion;280
16.7;7 Conclusions and Future Work;282
16.8;References;283
17;Massive Data Visualization: A Survey;284
17.1;1 Introduction;284
17.2;2 Driving Problems;285
17.3;3 How Do We Explore Massive Data?;287
17.4;4 Simplification Methods;288
17.5;5 Multiresolution Methods;290
17.6;6 External Memory Methods;292
17.7;7 Visual Scalability;294
17.8;8 Conclusions;296
17.9;References;296
18;Compression and Occlusion Culling for Fast Isosurface Extraction from Massive Datasets;302
18.1;1 Introduction;302
18.2;2 Related Work;304
18.3;3 Mesh Refinement and Preprocessing;306
18.4;4 Data Compression;308
18.5;5 Occlusion Culling;311
18.6;6 Results;313
18.7;7 Conclusions and Future Work;318
18.8;References;319
19;Volume Visualization of Multiple Alignment of Large Genomic DNA;323
19.1;1 Introduction;323
19.2;2 Our Approach;326
19.3;3 Implementation;330
19.4;4 Results;332
19.5;5 Conclusions;338
19.6;References;338
20;Model-Based Visualization: Computing Perceptually Optimal Visualizations;341
20.1;1 Introduction;341
20.2;2 Approach;342
20.3;3 Discussion;346
20.4;References;348mehr

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