Hagen, Hans

Visualization and Processing of Tensor Fields

Hagen, Hans - Visualization and Processing of Tensor Fields, ebook


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ISBN: 9783540312727
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Table of contents

1. An Introduction to Tensors
Hans Hagen, Christoph Garth

Part I. Feature Detection with Tensors

2. Adaptive Structure Tensors and their Applications
Thomas Brox, Rein Boomgaard, François Lauze, Joost Weijer, Joachim Weickert, Pavel Mrázek, Pierre Kornprobst

3. On the Concept of a Local Greyvalue Distribution and the Adaptive Estimation of a Structure Tensor
Hans-Hellmut Nagel

4. Low-level Feature Detection Using the Boundary Tensor
Ullrich Köthe

Part II. Diffusion Tensor Imaging

5. An Introduction to Computational Diffusion MRI: the Diffusion Tensor and Beyond
Daniel C. Alexander

6. Random Noise in Diffusion Tensor Imaging, its Destructive Impact and Some Corrections
Klaus R. Hahn, Sergej Prigarin, Susanne Heim, Khader Hasan

7. An Introduction to Visualization of Diffusion Tensor Imaging and Its Applications
A. Vilanova, S. Zhang, G. Kindlmann, D. Laidlaw

8. Anatomy-Based Visualizations of Diffusion Tensor Images of Brain White Matter
James C. Gee, Hui Zhang, Abraham Dubb, Brian B. Avants, Paul A. Yushkevich, Jeffrey T. Duda

9. Variational Regularization of Multiple Diffusion Tensor Fields
Ofer Pasternak, Nir Sochen, Yaniv Assaf

10. Higher Rank Tensors in Diffusion MRI
Evren Özarslan, Baba C. Vemuri, Thomas H. Mareci

Part III. Visualization of Tensor Fields

11. Strategies for Direct Visualization of Second-Rank Tensor Fields
Werner Benger, Hans-Christian Hege

12. Tensor Invariants and their Gradients
Gordon Kindlmann

13. Visualizing the Topology of Symmetric, Second-Order, Time-Varying Two-Dimensional Tensor Fields
Xavier Tricoche, Xiaoqiang Zheng, Alex Pang

14. Degenerate 3D Tensors
Xiaoqiang Zheng, Xavier Tricoche, Alex Pang

15. Locating Closed Hyperstreamlines in Second Order Tensor Fields
Thomas Wischgoll, Joerg Meyer

16. Tensor Field Visualization Using a Metric Interpretation
Ingrid Hotz, Louis Feng, Hans Hagen, Bernd Hamann, Kenneth Joy

Part IV. Tensor Field Transformations

17. Symmetric Positive-Definite Matrices: From Geometry to Applications and Visualization
Maher Moakher, Philipp G. Batchelor

18. Continuous Tensor Field Approximation of Diffusion Tensor MRI data
Sinisa Pajevic, Akram Aldroubi, Peter J. Basser

19. Tensor Field Interpolation with PDEs
Joachim Weickert, Martin Welk

20. Diffusion-Tensor Image Registration
James C. Gee, Daniel C. Alexander

Part V. Image Processing Methods for Tensor Fields

21. Tensor Median Filtering and M-Smoothing
Martin Welk, Christian Feddern, Bernhard Burgeth, Joachim Weickert

22. Mathematical Morphology on Tensor Data Using the Loewner Ordering
Bernhard Burgeth, Martin Welk, Christian Feddern, Joachim Weickert

23. A Local Structure Measure for Anisotropic Regularization of Tensor Fields
E. Suárez-Santana, M. A. Rodriguez-Florido, C. Castaño-Moraga, C.-F. Westin, J. Ruiz-Alzola

24. Tensor Field Regularization using Normalized Convolution and Markov Random Fields in a Bayesian Framework
Carl-Fredrik Westin, Marcos Martin-Fernandez, Carlos Alberola-Lopez, Juan Ruiz-Alzola, Hans Knutsson

25. PDEs for Tensor Image Processing
Joachim Weickert, Christian Feddern, Martin Welk, Bernhard Burgeth, Thomas Brox

Keywords: Mathematics, Visualization, Imaging / Radiology, Computer Imaging, Vision, Pattern Recognition and Graphics, Image Processing and Computer Vision, Differential Geometry, Statistics for Business/Economics/Mathematical Finance/Insurance

Publication year
Mathematics and Visualization
Page amount
496 pages
Natural Sciences

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