Visualization and Processing of Tensor Fields

By: J. Weickert, Joachim Weickert (Editor), Hans Hagen (Editor)

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Hardcover | 1 December 2005

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500 Pages

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24.13 x 15.88 x 1.27

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"This timely Springer monograph collects a total of 25 survey and research articles on the analysis, processing, and visualization of tensor fields, an area with increasing impact and visibility in contemporary imaging and medical image analysis. Compared with many existing volumes of similar styles or missions, this collection has been carefully edited to yield a smooth and continuous flow of topics and techniques. The categorization into five self-contained parts has been enormously helpful for a generic reader to attain an organic view of the entire dynamic field. This volume will be an invaluable research tool or information source for all readers who are interested in tensor processing and visualization, including, e.g., image processing experts, graphic and visualization engineers, medical imaging scientists, and radiologists, as well as graduate students who are pursuing a degree in the related research subjects." (Jianhong Shen, Mathematical Reviews)

Industry Reviews

"This timely Springer monograph collects a total of 25 survey and research articles on the analysis, processing, and visualization of tensor fields, an area with increasing impact and visibility in contemporary imaging and medical image analysis.

Compared with many existing volumes of similar styles or missions, this collection has been carefully edited to yield a smooth and continuous flow of topics and techniques. The categorization into five self-contained parts has been enormously helpful for a generic reader to attain an organic view of the entire dynamic field.

This volume will be an invaluable research tool or information source for all readers who are interested in tensor processing and visualization, including, e.g., image processing experts, graphic and visualization engineers, medical imaging scientists, and radiologists, as well as graduate students who are pursuing a degree in the related research subjects." (Jianhong Shen, Mathematical Reviews)

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An introduction to tensors	p. 3
Adaptive structure tensors and their applications	p. 17
On the concept of a local greyvalue distribution and the adaptive estimation of a structure tensor	p. 49
Low-level feature detection using the boundary tensor	p. 63
An introduction to computational diffusion MRI : the diffusion tensor and beyond	p. 83
Random noise in diffusion tensor imaging, its destructive impact and some corrections	p. 107
An introduction to visualization of diffusion tensor imaging and its applications	p. 121
Anatomy-based visualizations of diffusion tensor images of brain white matter	p. 155
Variational regularization of multiple diffusion tensor fields	p. 165
Higher rank tensors in diffusion MRI	p. 177
Strategies for direct visualization of second-rank tensor fields	p. 191
Tensor invariants and their gradients	p. 215
Visualizing the topology of 2D tensor fields	p. 225
Degenerate 3D tensors	p. 241
Locating closed hyperstreamlines in second order tensor fields	p. 257
Tensor field visualization using a metric interpretation	p. 269
Symmetric positive-definite matrices : from geometry to applications and visualization	p. 285
Continuous tensor field approximation of DT-MRI data	p. 299
Tensor field interpolation with PDEs	p. 315
Diffusion-tensor image registration	p. 327
Tensor-valued median filtering and M-smoothing	p. 345
Mathematical morphology on tensor data using the Loewner ordering	p. 357
A local structure measure for anisotropic regularization of tensor fields	p. 369
Tensor field regularization using normalized convolution and Markov random fields in a Bayesian framework	p. 381
PDEs for tensor image processing	p. 399
Table of Contents provided by Blackwell. All Rights Reserved.

Visualization and Processing of Tensor Fields

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