Ebook: New Developments in the Visualization and Processing of Tensor Fields

Bringing together key researchers in disciplines ranging from visualization and image processing to applications in structural mechanics, fluid dynamics, elastography, and numerical mathematics, the workshop that generated this edited volume was the third in the successful Dagstuhl series. Its aim, reflected in the quality and relevance of the papers presented, was to foster collaboration and fresh lines of inquiry in the analysis and visualization of tensor fields, which offer a concise model for numerous physical phenomena. Despite their utility, there remains a dearth of methods for studying all but the simplest ones, a shortage the workshops aim to address.

Documenting the latest progress and open research questions in tensor field analysis, the chapters reflect the excitement and inspiration generated by this latest Dagstuhl workshop, held in July 2009. The topics they address range from applications of the analysis of tensor fields to purer research into their mathematical and analytical properties. They show how cooperation and the sharing of ideas and data between those engaged in pure and applied research can open new vistas in the study of tensor fields.

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Bringing together key researchers in disciplines ranging from visualization and image processing to applications in structural mechanics, fluid dynamics, elastography, and numerical mathematics, the workshop that generated this edited volume was the third in the successful Dagstuhl series. Its aim, reflected in the quality and relevance of the papers presented, was to foster collaboration and fresh lines of inquiry in the analysis and visualization of tensor fields, which offer a concise model for numerous physical phenomena. Despite their utility, there remains a dearth of methods for studying all but the simplest ones, a shortage the workshops aim to address.

Documenting the latest progress and open research questions in tensor field analysis, the chapters reflect the excitement and inspiration generated by this latest Dagstuhl workshop, held in July 2009. The topics they address range from applications of the analysis of tensor fields to purer research into their mathematical and analytical properties. They show how cooperation and the sharing of ideas and data between those engaged in pure and applied research can open new vistas in the study of tensor fields.

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Bringing together key researchers in disciplines ranging from visualization and image processing to applications in structural mechanics, fluid dynamics, elastography, and numerical mathematics, the workshop that generated this edited volume was the third in the successful Dagstuhl series. Its aim, reflected in the quality and relevance of the papers presented, was to foster collaboration and fresh lines of inquiry in the analysis and visualization of tensor fields, which offer a concise model for numerous physical phenomena. Despite their utility, there remains a dearth of methods for studying all but the simplest ones, a shortage the workshops aim to address.

Documenting the latest progress and open research questions in tensor field analysis, the chapters reflect the excitement and inspiration generated by this latest Dagstuhl workshop, held in July 2009. The topics they address range from applications of the analysis of tensor fields to purer research into their mathematical and analytical properties. They show how cooperation and the sharing of ideas and data between those engaged in pure and applied research can open new vistas in the study of tensor fields.

Content:
Front Matter....Pages i-xxi
Front Matter....Pages 1-1
Structure Tensor Estimation: Introducing Monomial Quadrature Filter Sets....Pages 3-28
Adaptation of Tensor Voting to Image Structure Estimation....Pages 29-50
Edge-Enhancing Diffusion Filtering for Matrix Fields....Pages 51-67
Front Matter....Pages 69-69
Fabric-Like Visualization of Tensor Field Data on Arbitrary Surfaces in Image Space....Pages 71-92
Beyond Topology: A Lagrangian Metaphor to Visualize the Structure of 3D Tensor Fields....Pages 93-109
Tensor Field Design: Algorithms and Applications....Pages 111-133
Front Matter....Pages 135-135
Interactive Exploration of Stress Tensors Used in Computational Turbulent Combustion....Pages 137-156
Shear Wave Diffusion Observed by Magnetic Resonance Elastography....Pages 157-168
Front Matter....Pages 169-169
A Comparative Analysis of Dimension Reduction Techniques for Representing DTI Fibers as 2D/3D Points....Pages 171-185
Exploring Brain Connectivity with Two-Dimensional Maps....Pages 187-207
Uncertainty Propagation in DT-MRI Anisotropy Isosurface Extraction....Pages 209-225
Front Matter....Pages 227-227
Classification Study of DTI and HARDI Anisotropy Measures for HARDI Data Simplification....Pages 229-251
Towards Resolving Fiber Crossings with Higher Order Tensor Inpainting....Pages 253-265
Representation and Estimation of Tensor-Pairs....Pages 267-280
Front Matter....Pages 281-281
On the Choice of a Tensor Distance for DTI White Matter Segmentation....Pages 283-306
Divergence Measures and Means of Symmetric Positive-Definite Matrices....Pages 307-321
Metric Selection and Diffusion Tensor Swelling....Pages 323-336
Front Matter....Pages 337-337
${mathcal{H}}^{2}$ -Matrix Compression....Pages 339-362
Harmonic Field Analysis....Pages 363-379
Back Matter....Pages 381-384

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Bringing together key researchers in disciplines ranging from visualization and image processing to applications in structural mechanics, fluid dynamics, elastography, and numerical mathematics, the workshop that generated this edited volume was the third in the successful Dagstuhl series. Its aim, reflected in the quality and relevance of the papers presented, was to foster collaboration and fresh lines of inquiry in the analysis and visualization of tensor fields, which offer a concise model for numerous physical phenomena. Despite their utility, there remains a dearth of methods for studying all but the simplest ones, a shortage the workshops aim to address.

Documenting the latest progress and open research questions in tensor field analysis, the chapters reflect the excitement and inspiration generated by this latest Dagstuhl workshop, held in July 2009. The topics they address range from applications of the analysis of tensor fields to purer research into their mathematical and analytical properties. They show how cooperation and the sharing of ideas and data between those engaged in pure and applied research can open new vistas in the study of tensor fields.

Content:
Front Matter....Pages i-xxi
Front Matter....Pages 1-1
Structure Tensor Estimation: Introducing Monomial Quadrature Filter Sets....Pages 3-28
Adaptation of Tensor Voting to Image Structure Estimation....Pages 29-50
Edge-Enhancing Diffusion Filtering for Matrix Fields....Pages 51-67
Front Matter....Pages 69-69
Fabric-Like Visualization of Tensor Field Data on Arbitrary Surfaces in Image Space....Pages 71-92
Beyond Topology: A Lagrangian Metaphor to Visualize the Structure of 3D Tensor Fields....Pages 93-109
Tensor Field Design: Algorithms and Applications....Pages 111-133
Front Matter....Pages 135-135
Interactive Exploration of Stress Tensors Used in Computational Turbulent Combustion....Pages 137-156
Shear Wave Diffusion Observed by Magnetic Resonance Elastography....Pages 157-168
Front Matter....Pages 169-169
A Comparative Analysis of Dimension Reduction Techniques for Representing DTI Fibers as 2D/3D Points....Pages 171-185
Exploring Brain Connectivity with Two-Dimensional Maps....Pages 187-207
Uncertainty Propagation in DT-MRI Anisotropy Isosurface Extraction....Pages 209-225
Front Matter....Pages 227-227
Classification Study of DTI and HARDI Anisotropy Measures for HARDI Data Simplification....Pages 229-251
Towards Resolving Fiber Crossings with Higher Order Tensor Inpainting....Pages 253-265
Representation and Estimation of Tensor-Pairs....Pages 267-280
Front Matter....Pages 281-281
On the Choice of a Tensor Distance for DTI White Matter Segmentation....Pages 283-306
Divergence Measures and Means of Symmetric Positive-Definite Matrices....Pages 307-321
Metric Selection and Diffusion Tensor Swelling....Pages 323-336
Front Matter....Pages 337-337
${mathcal{H}}^{2}$ -Matrix Compression....Pages 339-362
Harmonic Field Analysis....Pages 363-379
Back Matter....Pages 381-384
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