Mathematics of Image Registration

Monday September 5th, 2005
School of Mathematics, University of Manchester

The workshop

This workshop focuses on the mathematical techniques for registering images. The aims are to bring together interested researchers for fruitful discussions of current challenges and future directions for mathematicians to contribute to imaging and registration problems, with special emphasis on medical images.

The five main speakers are

1. On non-rigid medical image registration. Bernd Fischer (Mathematics, Luebeck)

   Image registration is central to many challenges in medical imaging today and has a vast range of applications. The problem of registration arises whenever images acquired from different subjects, at different times, or from different scanners need to be combined for analysis or visualization.

   The purpose of this talk is to provide a unified, but extremely flexible framework for non-rigid image registration. We present a toolbox for intensity driven registration schemes, which may be adapted to a particular application. The building blocks of the toolbox resemble user demands and may be assembled in a consistent and intuitive fashion. Each individual block is given in a variational formulation. This not only allows for a unified treatment but also for fast and reliable implementations.

   Presentation

2. Applications of Medical Image Registration in Healthcare, Biomedical Research and Drug Discovery. Daniel Rueckert (Imperial)

   Imaging technologies are developing at a rapid pace allowing for in-vivo 3D and 4D imaging of the anatomy and physiology in humans and animals. This is opening up unprecedented opportunities for research and clinical applications ranging from imaging for drug discovery and delivery, over imaging for diagnosis and therapy, to imaging for basic research such as brain mapping. In this talk we will focus on how computational techniques based on non-rigid image registration can be used to address the image analysis challenges in healthcare, biomedical research and drug discovery.

   Presentation

3. Generalising Splines. Jeremy Levesley (Mathematics, Leicester)

   I will discuss how radial basis functions are a generalisation of splines via the minimisiation of some energy functional. There will be a discussion of some recent developments in theory and computational methods for approximation with RBFs. I will discuss applications in image reconstruction using interpolation of a wide range of functionals, including tomography.

   Presentation

4. Fluid Images: The Euler Equations and Image Registration. Stephen Marsland (Information Sciences, Massey University)

   An approach to diffeomorphic image registration using landmarks is to find solutions to the Euler equations in Diff(R^2) or Diff(R^3). This talk will comment on what this means for image registration, with respect to metrics, integration methods, and similarities to fluid mechanics methods such as point vortices. I'll demonstrate the behaviour of points particles and sheets moving in Diff(R^2) under different metrics.

   Presentation

5. Constrained image registration. Jan Modersitzki (Mathematics, Luebeck)

   Click here for abstract.

   Presentation 1. Presentation 2

Informal enquiries can be directed to Tony Shardlow (shardlow(at)maths.man.ac.uk; 0161-275-5821).

Organization and Sponsorship

The workshop is organized by the School of Mathematics, MIMS, and Imaging Science and Biomedical Engineering at the University of Manchester. It is supported by the EPSRC.

Organizing Committee

Tony Shardlow , David Silvester (School of Mathematics, University of Manchester), Stephen Marsland (Massey), Carole Twining (ISBE, University of Manchester)

Last updated, Sep 13 2005.