### 16.02.14 - 21.02.14, Seminar 14082

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

### Diese Seminarbeschreibung wurde vor dem Seminar auf unseren Webseiten veröffentlicht und bei der Einladung zum Seminar verwendet.

## Motivation

Higher-order descriptors, of which tensors are a special case, provide a natural language to describe phenomena in physics or image processing, e.g. medical imaging, fluid dynamics, or structural mechanics. The diversity of the application areas might explain why systematic and interdisciplinary investigations are still relatively rare. Many useful results are scattered throughout the scientific literature, and often researchers are only aware of articles in their own field, missing potentially valuable information in other areas. However, there are many shared challenges associated with this highly complex data, which can profit from a multidisciplinary approach. The idea of this Dagstuhl seminar is to bring together key researchers for disciplines ranging from visualization and image processing to applications in structural mechanics, fluid dynamics, and numerical mathematics. Thereby, the goal is to instigate solution-oriented research producing theoretical insight as well as practical algorithms applied to real-world problems. We will lay stress on the following issues:

Fundamental questions concerned with the processing of higher-order tensors dealing with

- Mathematical models to support a proper handling of higher-order tensors as elements of some adequate geometric space.
- The definition of useful decompositions, moving beyond spectral analysis.
- The investigation of high-level operations, e.g., generalization of mathematical morphology to higher-order descriptors.
- Interpolation, extrapolation and smoothing schemas that preserve important data characteristics.
- Statistics on higher-order descriptors to facilitate comparisons and parameter studies, e.g. to compare healthy and pathology groups.
- Sophisticated segmentation techniques for tensor fields:
- - Topological analysis of tensor fields.
- - Generalization of algorithms for scalar images to images using tensors or higher-order descriptors.
- Uncertainty analysis and visualization to generate reliable results. There is a large degree of uncertainty that accumulates throughout the processing pipeline. This concerns noise in the data acquisition process as well as parameter choices in multi-run simulations.

Analysis and visualization of higher order descriptors in applications

- Development of robust, scalable, and efficient algorithms and data structures capable to handle very large data sets.
- Development of visualization standards for diagnostic or analysis tools.
- Definition of intuitive visual abstractions carrying the most important tensor characteristics.
- Transfer of successful methods from one application to another.
- Development of standard use cases, e.g., to support the design process of construction pieces in structural mechanics.
- Definition of benchmarks and to foster the generation of data repositories.

This Dagstuhl seminar is the fifth in a series of stimulating, highly interdisciplinary Dagstuhl seminars. Previous seminars resulted in various collaborations and books that reflect the excitement and inspiration generated by these seminars. The charming atmosphere of Schloss Dagstuhl will prove once more to be a powerful catalyst that initiates vivid discussions, fruitful exchange of expertise, and lasting scientific relations between the participating researchers.