Visualization and Processing of Tensor Fields

Dr. Bernhard Burgeth, Prof. Joachim Weickert

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Synopsis

Matrix-valued data sets (so-called tensor fields) have gained significant importance in the fields of scientific visualization and image processing. This has been triggered by the following developments:

Novel medical imaging techniques such as diffusion tensor magnetic resonance imaging (DT-MRI) have been introduced. DT-MRI is a 3-D imaging method that yields a diffusion tensor in each voxel. This diffusion tensor describes the diffusive behaviour of water moluecules in the tissue. It can be represented by a positive semidefinite 3 x 3 matrix in each voxel.
Tensors have shown their use as a general tool in image analysis, segmentation and grouping. This also includes widespread applications of the so-called structure tensor in fields ranging from motion analysis to texture segmentation.
A number of scientific applications require to visualize tensor fields. The tensor concept is a common physical description of anisotropic behaviour, especially in solid mechanics and civil engineering (e.g. stress-strain relationships, inertia tensors, diffusion tensors, permittivity tensors).

In spring 2004 a workshop has taken place at Schloss Dagstuhl where leading experts have adressed problems of visualisation, processing and interpretation of matrix fields.
The Seminar is based on the book resulting from this meeting.

Prerequisites

Basic knowledge of mathematics
prior knowledge in image processing and computer vision is helpful but not necessary
The book is published in English, therfore a basic knowledge of english language is strongly recommended.
Transparencies should also be in English while the talk itself might be delivered in English or German, as the lecturer pleases.

The Seminar is intended for both mathematicians and computer scientists.

Preliminary Schedule

A .pdf-file containing a preliminary schedule can be found here !

Please check regularly for updates !

Literature

J. Weickert and H. Hagen
Visualization and Image Processing of Tensor Fields
Springer, Berlin, to appear.

Credit Points, Criteria:

Regular active participation
Professional talk
A short written summary of the talk

Written Summary:

The deadline for the submission of the written summary is Wednesday, February 1st , 2006.

The summary for one talk should not exceed three pages in length.

Accepted file formats are .ps or .pdf.

The file has to be sent as an attachement to Bernhard Burgeth using the following subject line: tensor_chapXX_familyname

Joachim Weickert / January 20, 2006 / back to MIA home.
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