28. Oktober – 02. November 2018, Dagstuhl-Seminar 18442

Visualization and Processing of Anisotropy in Imaging, Geometry, and Astronomy


Andrea Fuster (TU Eindhoven, NL)
Evren Özarslan (Linköping University, SE)
Thomas Schultz (Universität Bonn, DE)
Eugene Zhang (Oregon State University – Corvallis, US)

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Topics and Motivation

Directional preferences or anisotropies are encountered across many different disciplines and spatial scales. For example, local anisotropies are imprinted in the cosmic microwave background radiation, the human brain contains elongated nerve fibers, etc. Such anisotropies lead to (physical) orientation-dependent quantities, i.e., quantities that take on different values when considered along different directions. Compared to scalar or vector-valued data, it is much more challenging to model, process, and visualize anisotropic quantities. Suitable mathematical models often involve tensors and other higher-order descriptors, and pose specific research challenges in several areas of computer science, such as visualization, image analysis, and geometry processing.

In order to explore synergies between different fields, to inform computer scientists about open application challenges, and domain experts about existing solutions, this seminar brought together researchers from three different disciplines:

  • Medical imaging, where several modalities are now available to probe anisotropic behavior. In particular, Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) is based on measuring anisotropic diffusion. It makes it possible to visualize and quantify microstructural information in fibrous tissues such as white-matter and muscles, and to infer larger-scale structures, such as fiber tracts in the human brain.
  • Computer graphics and geometry processing, where tensor fields have a wide range of applications, such as quadrangular and hexahedral geometry remeshing, street network modeling, geometry synthesis, computational architecture, and path planning for environment scans.
  • Cosmology and astronomy, where anisotropy plays a crucial role. For example, anisotropies in the cosmic microwave background (CMB) consist of small temperature fluctuations in the blackbody radiation left over from the Big Bang. Anisotropies are also found in the CMB in the form of a polarization tensor field, and they arise in the field of "cosmography, where efforts are united to map (parts of) the cosmos, e.g. the large-scale distribution of matter in the Universe or cosmic web.

Organization of the Seminar

This seminar was the seventh in a series of Dagstuhl seminars that was started in 2004, and has been devoted to the visualization and processing of tensor fields and higher-order descriptors. This particular instance of the seminar series focused on anisotropy in the fields of imaging, geometry, and astronomy.

To ensure a steady inflow of new ideas and challenges, we put an emphasis on inviting researchers who previously did not have the opportunity to attend one of the meetings in this series. This was true for almost half the attendees in the final list of participants.

The seminar itself started with a round of introductions, in which all participants presented their area of work within 100 seconds with help of a single slide. This helped to create a basis for discussion early on during the week, and was particularly useful since participants came from different scientific communities, backgrounds, and countries. A substantial part of the week was devoted to presentations by 29 participants, who spent 20 minutes each on presenting recent advances, ongoing work, or open challenges, followed by ten minutes of discussion in the plenary, as well as in-depth discussions in the breaks and over lunch. Abstracts of the presentations are collected in this report. On Wednesday we held the traditional social event which was joined by almost all participants, and offered additional welcome opportunities for interaction.

A total of six breakout sessions were organized in the afternoons of Monday and Tuesday. Moderators summarized the respective discussion in the plenary on Thursday afternoon. The organizers came up with initial suggestions for session topics, which were refined further after discussion with the seminar participants. The session topics were as follows:

  • Astronomy
  • Time-varying anisotropy
  • Theoretical tools
  • Visualization
  • Diffusion MRI
  • Geometry

Notes were taken during all sessions, and the main points are summarized later in this report.


The participants all agreed that the meeting was inspiring and successful. It also stimulated new scientific collaborations and joint grant proposals. In addition we plan to publish another Springer book documenting the results of the meeting. Participants have pre-registered seventeen chapters already during the seminar, and we are in the process of collecting additional contributions both from participants and from researchers working on closely related topics who could not attend the meeting. We expect that the book will be ready for publication in 2020.


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

Summary text license
  Creative Commons BY 3.0 Unported license
  Andrea Fuster, Evren Özarslan, Thomas Schultz, and Eugene Zhang

Dagstuhl-Seminar Series


  • Computer Graphics / Computer Vision


  • Tensor fields
  • Anisotropy
  • Diffusion-weighted imaging (DWI)
  • Geometry
  • Astronomy


In der Reihe Dagstuhl Reports werden alle Dagstuhl-Seminare und Dagstuhl-Perspektiven-Workshops dokumentiert. Die Organisatoren stellen zusammen mit dem Collector des Seminars einen Bericht zusammen, der die Beiträge der Autoren zusammenfasst und um eine Zusammenfassung ergänzt.


Download Übersichtsflyer (PDF).

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