Saarland University |
Mathematical Image Analysis Group

Wintersemester 2005 / 2006

### Seminar on

# Visualization and Processing of Tensor Fields

### The registration is closed!

### Further applications are no longer possible!

### 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 /
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