Multidisciplinary Approaches to Multivalued Data: Modeling, Visualization, Analysis

Summary

Topics and Motivation

This seminar is the sixth in a series of Dagstuhl Seminars devoted to the use of tensor fields and other higher order descriptors, including higher-order tensors or Spherical Harmonics, to model intricate multivalued data that arises in modern medical imaging modalities, as well as in simulations in engineering and industry. Even though the literature on image analysis, visualization, as well as statistical hypothesis testing and machine learning is quite rich for scalar or vector-valued data, relatively little work has been performed on these disciplines for tensors and higher-order descriptors.

Applications wherein such descriptors can be employed to process multivalued data range from neuroimaging to image analysis and engineering. Diffusion Weighted Magnetic Resonance Imaging (DW-MRI), an MRI modality which makes it possible to visualize and quantify structural information about white matter pathways in the brain in vivo, is one of the driving technologies, but tensors have also shown their usefulness as feature descriptors for segmentation and grouping in image analysis, including structure tensors and tensor voting. Applications in solid mechanics, civil engineering, computational fluid dynamics and geology require the processing of tensor fields as part of domain-specific modeling, simulation, and analysis (e.g. stress-strain relationships, inertia tensors, permittivity tensor).

The Dagstuhl seminar provides a unique platform by facilitating scientific exchange between key researchers in seemingly diverse applications. Despite these disciplines' commonalities in terms of the tools employed, it would be very unlikely that these scientists would attend the same conference as the theme of most conferences is defined by a specific application. By bringing together specialists in visualization, image processing, statistics, and numerical mathematics, the Dagstuhl seminar provides new impulses for methodological work in those areas.

Organization of the Seminar

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 26 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. For the traditional social event on Wednesday, we went on a hike, which was joined by almost all participants, and offered additional welcome opportunities for interaction.

Three breakout sessions were organized in the afternoons, and another one in the evening, so that none of them took place in parallel, and everyone had the opportunity to visit all groups relevant to him or her. The topics of the four groups were formed by clustering topics brought up in the round of introductions, and were denoted as:

• Visual encodings and the interface between theory and applications
• Models and geometry
• Topological methods
• Multi-field and tensor group analysis

Depending on the interests of the participants, the breakout groups differed in nature, ranging from the collection of open questions and discussions on future directions of the field to spontaneous tutorial-style presentations. Notes taken during these sessions, and the main results of two of them are summarized in this report.

Outcomes

The participants all agreed that the meeting was successful and stimulating, and we plan to publish another Springer book documenting the results of the meeting. Participants have pre-registered thirteen 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 2017.

It was voted that the group will apply for another meeting in this series. In addition to the current organizers Thomas Schultz (University of Bonn, Germany) and Evren Özarslan (Linköpings Universitet, Sweden), Andrea Fuster (TU Eindhoven, The Netherlands) and Eugene Zhang (Oregon State University, USA) agreed to help apply for the next event.

Acknowledgments

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, which supports formal presentations as well as informal exchange of ideas.