Ebook: Visualization and Processing of Tensor Fields

Matrix-valued data sets - so-called second order tensor fields -
have gained significant importance in scientific visualization and
image processing due to recent developments such as diffusion tensor
imaging. This book is the first edited volume that presents the
state-of-the-art in the visualization and processing of tensor fields.
It contains some longer chapters dedicated to surveys and tutorials of
specific topics, as well as a great deal of original work by leading
experts that has not been published before. It serves as an overview
for the inquiring scientist, as a basic foundation for developers and
practitioners, and as as a textbook for specialized classes and seminars
for graduate and doctoral students.

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Matrix-valued data sets - so-called second order tensor fields -
have gained significant importance in scientific visualization and
image processing due to recent developments such as diffusion tensor
imaging. This book is the first edited volume that presents the
state-of-the-art in the visualization and processing of tensor fields.
It contains some longer chapters dedicated to surveys and tutorials of
specific topics, as well as a great deal of original work by leading
experts that has not been published before. It serves as an overview
for the inquiring scientist, as a basic foundation for developers and
practitioners, and as as a textbook for specialized classes and seminars
for graduate and doctoral students.

---

Matrix-valued data sets - so-called second order tensor fields -
have gained significant importance in scientific visualization and
image processing due to recent developments such as diffusion tensor
imaging. This book is the first edited volume that presents the
state-of-the-art in the visualization and processing of tensor fields.
It contains some longer chapters dedicated to surveys and tutorials of
specific topics, as well as a great deal of original work by leading
experts that has not been published before. It serves as an overview
for the inquiring scientist, as a basic foundation for developers and
practitioners, and as as a textbook for specialized classes and seminars
for graduate and doctoral students.

Content:
Front Matter....Pages I-XV
Front Matter....Pages 1-1
An Introduction to Tensors....Pages 3-13
Front Matter....Pages 15-15
Adaptive Structure Tensors and their Applications....Pages 17-47
On the Concept of a Local Greyvalue Distribution and the Adaptive Estimation of a Structure Tensor....Pages 49-61
Low-level Feature Detection Using the Boundary Tensor....Pages 63-79
Front Matter....Pages 81-81
An Introduction to Computational Diffusion MRI: the Diffusion Tensor and Beyond....Pages 83-106
Random Noise in Diffusion Tensor Imaging, its Destructive Impact and Some Corrections....Pages 107-119
An Introduction to Visualization of Diffusion Tensor Imaging and Its Applications....Pages 121-153
Anatomy-Based Visualizations of Diffusion Tensor Images of Brain White Matter....Pages 155-163
Variational Regularization of Multiple Diffusion Tensor Fields....Pages 165-176
Higher Rank Tensors in Diffusion MRI....Pages 177-187
Front Matter....Pages 189-189
Strategies for Direct Visualization of Second-Rank Tensor Fields....Pages 191-214
Tensor Invariants and their Gradients....Pages 215-224
Visualizing the Topology of Symmetric, Second-Order, Time-Varying Two-Dimensional Tensor Fields....Pages 225-240
Degenerate 3D Tensors....Pages 241-256
Locating Closed Hyperstreamlines in Second Order Tensor Fields....Pages 257-267
Tensor Field Visualization Using a Metric Interpretation....Pages 269-281
Front Matter....Pages 283-283
Symmetric Positive-Definite Matrices: From Geometry to Applications and Visualization....Pages 285-298
Continuous Tensor Field Approximation of Diffusion Tensor MRI data....Pages 299-314
Tensor Field Interpolation with PDEs....Pages 315-325
Diffusion-Tensor Image Registration....Pages 327-342
Front Matter....Pages 343-343
Tensor Median Filtering and M-Smoothing....Pages 345-356
Mathematical Morphology on Tensor Data Using the Loewner Ordering....Pages 357-368
A Local Structure Measure for Anisotropic Regularization of Tensor Fields....Pages 369-380
Tensor Field Regularization using Normalized Convolution and Markov Random Fields in a Bayesian Framework....Pages 381-398
PDEs for Tensor Image Processing....Pages 399-414
Back Matter....Pages 415-481

---

Matrix-valued data sets - so-called second order tensor fields -
have gained significant importance in scientific visualization and
image processing due to recent developments such as diffusion tensor
imaging. This book is the first edited volume that presents the
state-of-the-art in the visualization and processing of tensor fields.
It contains some longer chapters dedicated to surveys and tutorials of
specific topics, as well as a great deal of original work by leading
experts that has not been published before. It serves as an overview
for the inquiring scientist, as a basic foundation for developers and
practitioners, and as as a textbook for specialized classes and seminars
for graduate and doctoral students.

Content:
Front Matter....Pages I-XV
Front Matter....Pages 1-1
An Introduction to Tensors....Pages 3-13
Front Matter....Pages 15-15
Adaptive Structure Tensors and their Applications....Pages 17-47
On the Concept of a Local Greyvalue Distribution and the Adaptive Estimation of a Structure Tensor....Pages 49-61
Low-level Feature Detection Using the Boundary Tensor....Pages 63-79
Front Matter....Pages 81-81
An Introduction to Computational Diffusion MRI: the Diffusion Tensor and Beyond....Pages 83-106
Random Noise in Diffusion Tensor Imaging, its Destructive Impact and Some Corrections....Pages 107-119
An Introduction to Visualization of Diffusion Tensor Imaging and Its Applications....Pages 121-153
Anatomy-Based Visualizations of Diffusion Tensor Images of Brain White Matter....Pages 155-163
Variational Regularization of Multiple Diffusion Tensor Fields....Pages 165-176
Higher Rank Tensors in Diffusion MRI....Pages 177-187
Front Matter....Pages 189-189
Strategies for Direct Visualization of Second-Rank Tensor Fields....Pages 191-214
Tensor Invariants and their Gradients....Pages 215-224
Visualizing the Topology of Symmetric, Second-Order, Time-Varying Two-Dimensional Tensor Fields....Pages 225-240
Degenerate 3D Tensors....Pages 241-256
Locating Closed Hyperstreamlines in Second Order Tensor Fields....Pages 257-267
Tensor Field Visualization Using a Metric Interpretation....Pages 269-281
Front Matter....Pages 283-283
Symmetric Positive-Definite Matrices: From Geometry to Applications and Visualization....Pages 285-298
Continuous Tensor Field Approximation of Diffusion Tensor MRI data....Pages 299-314
Tensor Field Interpolation with PDEs....Pages 315-325
Diffusion-Tensor Image Registration....Pages 327-342
Front Matter....Pages 343-343
Tensor Median Filtering and M-Smoothing....Pages 345-356
Mathematical Morphology on Tensor Data Using the Loewner Ordering....Pages 357-368
A Local Structure Measure for Anisotropic Regularization of Tensor Fields....Pages 369-380
Tensor Field Regularization using Normalized Convolution and Markov Random Fields in a Bayesian Framework....Pages 381-398
PDEs for Tensor Image Processing....Pages 399-414
Back Matter....Pages 415-481
....