February 16 – 21 , 2014, Dagstuhl Seminar 14082

Visualization and Processing of Higher Order Descriptors for Multi-Valued Data


Bernhard Burgeth (Universität des Saarlandes, DE)
Ingrid Hotz (DLR – Braunschweig, DE)
Anna Vilanova Bartroli (TU Delft, NL)
Carl-Fredrik Westin (Harvard Medical School – Boston, US)

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Higher Order Descriptors for Multi-Valued Data

This seminar is the 5th in a series of Dagstuhl Seminars devoted to the visualization and processing of higher-order descriptors, of which tensors are a special case. They provide a natural language to describe phenomena in physics or image processing, e.g. medical imaging, fluid dynamics, or structural mechanics. Due to the increasing complexity of data generated in the engineering industry and the rapid advances in medical imaging, multi-valued data have gained significant importance in scientific visualization and image processing. Compared to their importance analysis and processing tools are still relatively rare.

In many scientific and engineering applications, as modern product development processes, simulations are an essential part of the advancement of the field. The results are large and complex data sets often comprising multi-filed data of various kind. Thereby, the tensor concept is essential for the description of physical phenomena related to anisotropic behavior. Examples for second-order tensors are stress and strain fields, inertia tensors, and orientation distribution tensors. Higher-order tensors occur when multiple vector fields or second-order tensors are set into relation, e.g., the stiffness tensor relating stress and strain. The field of engineering faces many open problems in tensor field analysis and visualization.

In medical imaging, multi-valued data include diffusion-weighted magnetic resonance imaging (dMRI), a medical imaging modality that allows the measurement of water diffusion in tissue (e.g., white matter or muscle) in vivo. Simple models approximate the diffusion in fibrous tissue by a second-order diffusion tensor (i.e., a positive semi-definite 3 X 3 matrix). But, often the acquired data is more complex and cannot be sufficiently described by the second-order tensor model and requires higher-order descriptors (i.e., higher-order tensors or spherical harmonics).

Even though these applications are very different in their nature they face many shared challenges associated with this highly complex data, which can profit from a multidisciplinary approach. The idea of this Dagstuhl Seminar was to bring together key researchers for disciplines ranging from visualization and image processing to applications in structural mechanics, fluid dynamics, and numerical mathematics.

Seminar Topics and Breakout Sessions

The seminar has been organized in presentation and breakout sessions. The presentation sessions gave the participants the possibility to presented recent developments in the multidisciplinary field. The talks covered a broad variety of topics related to both theoretical and practical issues. They served as basis for inspiring discussions across the application areas, which demonstrated that there are many shared issues related to analyzing and visualizing fields of tensors and higher-order descriptors. Besides the presentations, we put an emphasis on breakout sessions, which were very successful already in the previous meeting. They were targeted at fostering focused discussions in smaller groups. During a first session the group defined some driving objectives that partially already emerged in preparatory discussions:

  • Statistics on higher-order descriptors and visualization of uncertainty
  • Generalization of mathematical framework to higher-order descriptors
  • Features on tensor visualization
  • Next generation diffusion MRI

Most issues identified in the call have been discussed. Subjects that found special attention can be summarized as: Fundamental general topics, as tensor interpolation, statistics, morphology, and topology; Questions related to pattern description and detection; More specific issues like the analysis of ensembles, the visualization and measurement of differences and anomalies for engineering as well as for medical data sets. Further, there has been much interest in double pulse field gradient methods that have been discussed as possible next generation diffusion MRI. The outcome of the sessions can also be seen at

The breakout sessions again turned out to be very successful. The format of the breakout sessions fits very well in the Dagstuhl environment promoting discussions and interactions. We could also observe that, for some topics, it is not easy to go beyond a list of challenges in such a short time frame. This motivates to strengthen these sessions by pre-defining topics in preparation of the meeting and asking selected participants for related statements.


The participants all agreed that the meeting was successful and stimulating. Seminar participants are already collaborating on a Springer book summarizing the results of the meeting. The Springer book will have about seventeen chapters authored by the meeting participants. It is also planned to summarize the results of two breakout sessions as a chapter of the book. The participants Thomas Schultz and Ingrid Hotz agreed on taking the lead for the collection of the contributions and the assembly of the book. We expect the book to be published in 2015.

It was voted that the group will apply for another meeting in this series, and that in addition to the current organizer (Ingrid Hotz) there will be two new organizers (Thomas Schultz, University Bonn Germany and Evren Özarslan, Harvard Medical School -- Boston, US) for the next event.


The organizers thank all the attendees for their contributions and extend special thanks to the team of Schloss Dagstuhl for helping to make this seminar a success. As always, we enjoyed the warm atmosphere of the Schloss, which supports both formal presentations as well as informal exchanges of ideas.

  Creative Commons BY 3.0 Unported license
  Bernhard Burgeth, Ingrid Hotz, Anna Vilanova Bartroli, and Carl-Fredrik Westin

Dagstuhl Seminar Series


  • Bioinformatics
  • Computer Graphics / Computer Vision


  • Visualization
  • Image processing
  • Tensor fields
  • Diffusion tensor imaging
  • High angular resolution diffusion imaging (HARDI)
  • Data analysis
  • Feature extraction
  • Fiber tracking
  • Structural mechanics
  • Fluid dynamics

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