Directional preference or anisotropy is encountered across many disciplines and spatial scales. For example, local anisotropies are imprinted in the cosmic microwave background radiation, the human brain contains elongated nerve fibers, etcetera. Such phenomena lead to physical quantities that take on different values along different directions. Compared to scalar or vector-valued data, it is much more challenging to model, process, and visualize anisotropic quantities.

Scientists encountering anisotropy in specific fields are often unaware of theoretical results and practical tools developed in other fields, while these might be relevant and adaptable to their needs. This Dagstuhl seminar will bring together researchers from three domains in which anisotropy plays an important role:

• Medical imaging, in which modalities such as diffusion-weighted magnetic resonance imaging (DW-MRI) and quantitative susceptibility mapping are used to probe structure-induced anisotropies, e.g., in the human brain.
• 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 environmental scans.
• Astronomy, where anisotropies in the cosmic microwave background (CMB) are present in the form of a polarization tensor field. Moreover, in the field of “cosmography”, anisotropies in the cosmic web are linked to the complex patterns traced by galaxies.

Currently, there is little interaction between scientists working in these disciplines. Progress made in one field is usually not transferred to others despite the connections that could make an exchange of ideas very rewarding:

• Tensor fields play an important role in the three domains, i.e., they all share a common mathematical language.
• Software tools originally developed for medical imaging have proven useful for 3D visualization of astronomical data.
• In recent years, differential geometry and topology have made an important contribution in modeling and understanding the structure of the brain from neuroimaging data.
• The concept of connectivity arises in both astronomy and brain imaging.
• We expect that advanced techniques for smoothing or feature extraction in tensor-valued images could be transferred to geometry processing.
• Much insight has been gained on tensor field analysis, especially tensor field topology, by the visualization community. Similar needs have arisen in geometry processing.

Creative Commons BY 3.0 DE

Andrea Fuster, Evren Özarslan, Thomas Schultz, and Eugene Zhang

• David Bommes (Universität Bern, CH) [dblp]
• Bernhard Burgeth (Universität des Saarlandes, DE) [dblp]
• Tom Dela Haije (University of Copenhagen, DK) [dblp]
• Ali Can Demiralp (RWTH Aachen, DE) [dblp]
• Aasa Feragen (University of Copenhagen, DK) [dblp]
• Luc Florack (TU Eindhoven, NL) [dblp]
• Andrea Fuster (TU Eindhoven, NL) [dblp]
• Shekoufeh Gorgi Zadeh (Universität Bonn, DE) [dblp]
• Hans Hagen (TU Kaiserslautern, DE) [dblp]
• Magnus Herberthson (Linköping University, SE) [dblp]
• Ingrid Hotz (Linköping University, SE) [dblp]
• Jana Hutter (King's College London, GB) [dblp]
• Daniel Jörgens (KTH Royal Institute of Technology - Stockholm, SE) [dblp]
• Andreas Kleefeld (Jülich Supercomputing Centre, DE) [dblp]
• Chunlei Liu (University of California at Berkeley, US) [dblp]
• Timothy Luciani (University of Illinois - Chicago, US) [dblp]
• Evren Özarslan (Linköping University, SE) [dblp]
• Renato Pajarola (Universität Zürich, CH) [dblp]
• Reynier Peletier (University of Groningen, NL) [dblp]
• Marco Pizzolato (EPFL - Lausanne, CH) [dblp]
• Gerik Scheuermann (Universität Leipzig, DE) [dblp]
• Thomas Schultz (Universität Bonn, DE) [dblp]
• Chantal Tax (Cardiff University, GB) [dblp]
• Donggang Wang (Leiden University, NL)
• Bei Wang Phillips (University of Utah - Salt Lake City, US) [dblp]
• Carl-Fredrik Westin (Harvard Medical School - Boston, US) [dblp]
• Hsiang-Yun Wu (TU Wien, AT) [dblp]
• Eugene Zhang (Oregon State University - Corvallis, US) [dblp]
• Yue Zhang (Oregon State University - Corvallis, US) [dblp]
• Jovisa Zunic (Mathematical Institute SANU, RS) [dblp]