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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Part 1. Structure-Tensor Computation -- Structure Tensor Estimation: Introducing Monomial Quadrature Filter Sets / Hans Knutsson, Carl-Fredrik Westin and Mats Andersson -- Adaptation of Tensor Voting to Image Structure Estimation / Rodrigo Moreno, Luis Pizarro, Bernhard Burgeth, Joachim Weickert and Miguel Angel Garcia, et al. -- Edge-Enhancing Diffusion Filtering for Matrix Fields / Bernhard Burgeth, Luis Pizarro and Stephan Didas. Part 2. Tensor-Field Visualization -- Fabric-Like Visualization of Tensor Field Data on Arbitrary Surfaces in Image Space / Sebastian Eichelbaum, Mario Hlawitschka, Bernd Hamann and Gerik Scheuermann -- Beyond Topology: A Lagrangian Metaphor to Visualize the Structure of 3D Tensor Fields / Xavier Tricoche, Mario Hlawitschka, Samer Barakat and Christoph Garth -- Tensor Field Design: Algorithms and Applications / Eugene Zhang. Part 3. Applications of Tensor-Field Analysis and Visualization -- Interactive Exploration of Stress Tensors Used in Computational Turbulent Combustion / Adrian Maries, Abedul Haque, S. Levent Yilmaz, Mehdi B. Nik and G. Elisabeta Marai -- Shear Wave Diffusion Observed by Magnetic Resonance Elastography / Sebastian Papazoglou, Jürgen Braun, Dieter Klatt and Ingolf Sack. Part 4. DiffusionWeighted MRI Visualization -- A Comparative Analysis of Dimension Reduction Techniques for Representing DTI Fibers as 2D/3D Points / Xiaoyong Yang, Ruiyi Wu, Ziáng Ding, Wei Chen and Song Zhang -- Exploring Brain Connectivity with Two-Dimensional Maps / Çağatay Demiralp, Radu Jianu and David H. Laidlaw -- Uncertainty Propagation in DT-MRI Anisotropy Isosurface Extraction / Kai Pöthkow and Hans-Christian Hege. Part 5. Beyond Second-Order Diffusion Tensor MRI -- Classification Study of DTI and HARDI Anisotropy Measures for HARDI Data Simplification / Vesna Prčkovska, Maxime Descoteaux, Cyril Poupon, Bart M. ter Haar Romeny and Anna Vilanova -- Towards Resolving Fiber Crossings with Higher Order Tensor Inpainting / Thomas Schultz -- Representation and Estimation of Tensor-Pairs / Carl-Fredrik Westin and Hans Knutsson. Part 6. Tensor Metrics -- On the Choice of a Tensor Distance for DTI White Matter Segmentation / Rodrigo de Luis-García, Carlos Alberola-López and Carl-Fredrik Westin -- Divergence Measures and Means of Symmetric Positive-Definite Matrices / Maher Moakher -- Metric Selection and Diffusion Tensor Swelling / Ofer Pasternak, Nir Sochen and Peter J. Basser. Part 7. Tensor Analysis -- H²-Matrix Compression / Steffen Börm -- Harmonic Field Analysis / Christian Wagner, Christoph Garth and Hans Hagen