Summer School on Tensors and Tensor Fields in Imaging

Location and Date: Marstal, Denmark, August 18-23, 2013

General Course Objectives:

Introduce the use of tensors and tensor fields as compact data representations, and illustrate with examples from computer vision and medical imaging. Demonstrate the novel aspects of such representations, and introduce the mathematical toolset required in order to be able to perform analysis of one's own data in these domains.

Learning Objectives:

After completion of the summer school, one should be able to:

  •  Understand the relevance and importance of being able to represent tensors and tensor fields as images
  •  Understand the relationship between tensor fields and manifolds
  •  Understand how computational geometry can be used to analyse manifolds and tensor fields
  •  Implement statistical measures on tensor fields
  •  Apply standard analytical methods to their own tensor data
  •  Describe the state-of-the-art use of tensors and tensor fields in various applications, including:
    1.  Tensors derived from scalar images (e.g. computer vision)
    2.  Inherently tensor-based images (e.g. diffusion MRI)


The course is based upon the differing approaches to tensors and tensor field imaging promoted by the various invited speakers, each of whom is internationally well-regarded for their research in this area. The format will be based upon a series of lectures by each speaker, first introducing the attendees to their own speciality before building up to a description of the latest developments. In addition, exercises will be provided to reinforce the principles presented in the lectures. Introductory lectures at the start of the week by local speakers will ensure that everyone has a chance to reach the same level before the invited speakers begin. Local speakers will also provide a selection of other example applications of the presented approaches.

By providing two differing viewpoints of how tensors and tensor fields can be applied to existing datasets, we aim to provide a diverse toolset of mathematical methods that will permit attendees to directly utilise these powerful approaches in their own research.


Course Credit:

2.5 (+2.5) ECTS
2.5 ECTS points are awarded for participation, an additional 2.5 points can be achieved by students who do a poster presentation and write a small report on how the topics covered by the summer school can be related to their own PhD project


For registration, please mail Dina Riis Johannessen at
Course fee is DKK 4000 and covers accommodation, food, bus and ferry transport from/to Copenhagen and social activities during the week. For more details on registration and payment, please visit here.