Matrix-valued data sets ¿ so-called second order tensor fields ¿ have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the first edited volume that presents the state of the art in the visualization and processing of tensor fields. It contains some longer chapters dedicated to surveys and tutorials of specific topics, as well as a great deal of original work by leading experts that has not been published before. It serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as as a textbook for specialized classes and seminars for graduate and doctoral students.

Joachim Weickert is Full Professor of Mathematics and Computer Science at
Saarland University (Saarbr\"ucken, Germany) where he heads the Mathematical
Image Analysis Group. He performs research in image processing, computer
vision and scientific computing, focusing on techniques based on partial
differential equations and variational methods.

Hans Hagen is heading the research group for Computer Graphics and
Computer Geometry at the University of Kaiserslautern, Germany, and is
Scientific Director of the research lab Intelligent Visualization and
Simulation at the German Research Center for Artificial Intelligence
(DFKI). His research domains are geometric modeling and scientific
visualization.