FÜR INFORMATIONSTECHNIK
BERLIN

# Projektsite

Home » Forschung » Numerische Mathematik » Visualisierung und Datenanalyse » Tensor Visualization

# Visualization and Analysis of Tensorfields

This project is concerned with the visualization and analysis of three-dimensional tensor fields. Due to the complexity of tensor data, visualization methods have to be chosen carefully. This is especially true for three-dimensional fields. In a pre-processing step filter methods have to be applied to reduce the field to relevant features. A challenging question in this context is the question: "What are relevant features?".

# Introduction

Tensors provide a powerful mathematical language to describe physical phenomena.
Consequently, they have a long tradition in physics and appear in various application
areas, either as intermediate product or as output of simulations or measurements. Examples are medicine, astrophysics, continuum mechanics, image processing, and many more. The potential of tensors to describe complex anisotropic behavior, however, concurrently complicates their interpretation. Scientific visualization can provide insight into the processes that are described by tensors. The goal of this project is the development of methods that effectively communicate the complex information contained in three-dimensional tensor fields.

# Background

The focus of this work is on 3D stress  tensor fields. Important application areas and their interest in such data are:

• In material science, a material's behavior under pressure is observed to examine its stability.
• In geoscience, rock fractures caused by tension or compression are analyzed.
• In  medicine, the simulation of an implant design's impact on the  distribution of physiological stress inside a bone is analyzed.

Common to most of these areas is the goal of finding regions where the inspected material tends to crack. Various failure models exist, but in general they are based on the analysis of large shear stresses. Besides understanding a physical phenomenon, tensor analysis can help to detect failures in simulations where tensors appear as intermediate product.

# Basic Idea

The basic idea of our approach is to provide various perspectives onto the data via linking of well-known and novel visualization methods. Therefore, we combine attribute-space views and three-dimensional spatial visualizations (Figure 2). A particular challenge in this context arises if we have no a-priori knowledge about the data. In that case, automatic segmentation algorithms to reduce the data to relevant features are not applicable. In this project, we, therefore, focus on explorative visualization.

# Publications

• Andrea Kratz, Cornelia Auer, Markus Stommel, Ingrid Hotz. Visualization and Analysis of Second-Order Tensors: Moving Beyond the Symmetric Positive-Definite Case. Computer Graphics Forum - State of the Art Reports, 2012.
• Andrea Kratz, Björn Meyer, Ingrid Hotz. A Visual Approach To Analysis of Stress Tensor Fields. Scientific Visualization: Interactions, Features, Metaphors, Dagstuhl Follow-ups (2), 188-211, 2011.
• Andrea Kratz, Markus Hadwiger, Ingrid Hotz. Improved Visual Exploration and Hybrid Rendering of Stress Tensor Fields via Shape-Space Clustering. Poster presentation at the IEEE VisWeek 2011, Providence.