New Developments in the Visualization and Processing of Tensor Fields

  • David H. Laidlaw
  • Anna Vilanova
Conference proceedings

DOI: 10.1007/978-3-642-27343-8

Part of the Mathematics and Visualization book series (MATHVISUAL)

Table of contents (19 papers)

  1. Front Matter
    Pages i-xxi
  2. Structure-Tensor Computation

    1. Front Matter
      Pages 1-1
    2. Structure Tensor Estimation: Introducing Monomial Quadrature Filter Sets
      Hans Knutsson, Carl-Fredrik Westin, Mats Andersson
      Pages 3-28
    3. Adaptation of Tensor Voting to Image Structure Estimation
      Rodrigo Moreno, Luis Pizarro, Bernhard Burgeth, Joachim Weickert, Miguel Angel Garcia, Domenec Puig
      Pages 29-50
    4. Edge-Enhancing Diffusion Filtering for Matrix Fields
      Bernhard Burgeth, Luis Pizarro, Stephan Didas
      Pages 51-67
  3. Tensor-Field Visualization

    1. Front Matter
      Pages 69-69
    2. Fabric-Like Visualization of Tensor Field Data on Arbitrary Surfaces in Image Space
      Sebastian Eichelbaum, Mario Hlawitschka, Bernd Hamann, Gerik Scheuermann
      Pages 71-92
    3. Beyond Topology: A Lagrangian Metaphor to Visualize the Structure of 3D Tensor Fields
      Xavier Tricoche, Mario Hlawitschka, Samer Barakat, Christoph Garth
      Pages 93-109
  4. Applications of Tensor-Field Analysis and Visualization

    1. Front Matter
      Pages 135-135
    2. Interactive Exploration of Stress Tensors Used in Computational Turbulent Combustion
      Adrian Maries, Abedul Haque, S. Levent Yilmaz, Mehdi B. Nik, G. Elisabeta Marai
      Pages 137-156
    3. Shear Wave Diffusion Observed by Magnetic Resonance Elastography
      Sebastian Papazoglou, Jürgen Braun, Dieter Klatt, Ingolf Sack
      Pages 157-168
  5. Diffusion Weighted MRI Visualization

    1. Front Matter
      Pages 169-169
    2. A Comparative Analysis of Dimension Reduction Techniques for Representing DTI Fibers as 2D/3D Points
      Xiaoyong Yang, Ruiyi Wu, Ziáng Ding, Wei Chen, Song Zhang
      Pages 171-185
    3. Exploring Brain Connectivity with Two-Dimensional Maps
      Çağatay Demiralp, Radu Jianu, David H. Laidlaw
      Pages 187-207
    4. Uncertainty Propagation in DT-MRI Anisotropy Isosurface Extraction
      Kai Pöthkow, Hans-Christian Hege
      Pages 209-225
  6. Beyond Second-Order Diffusion Tensor MRI

    1. Front Matter
      Pages 227-227
    2. Classification Study of DTI and HARDI Anisotropy Measures for HARDI Data Simplification
      Vesna Prčkovska, Maxime Descoteaux, Cyril Poupon, Bart M. ter Haar Romeny, Anna Vilanova
      Pages 229-251
    3. Representation and Estimation of Tensor-Pairs
      Carl-Fredrik Westin, Hans Knutsson
      Pages 267-280

About these proceedings


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.


Diffusion MRI Image Processing Tensor Field Visualization

Editors and affiliations

  • David H. Laidlaw
    • 1
  • Anna Vilanova
    • 2
  1. 1.Dept. Computer ScienceBrown UniversityProvidenceUSA
  2. 2.Department of Biomedical EngineeringEinhoven University of TechnologyEindhovenNetherlands

Bibliographic information

  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-27342-1
  • Online ISBN 978-3-642-27343-8
  • Series Print ISSN 1612-3786