Details of Grant 

EPSRC Reference:	EP/C523164/1
Title:	Mathematics of Image Registration
Principal Investigator:	Shardlow, Dr T
Other Investigators:	twining, Dr CJ Silvester, Professor DJ
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	University of Manchester, The
Scheme:	Mathematics Small Grant PreFEC
Starts:	05 September 2005	Ends:	04 September 2006	Value (£):	5,112
EPSRC Research Topic Classifications:	Numerical Analysis
EPSRC Industrial Sector Classifications:	Healthcare
Related Grants:
Panel History:
Summary on Grant Application Form
There are now many techniques for medical imaging, such as Magnetic Resonance Imaging (MRI), providing insight into the structure of the brain and other internal organs, and the increase in the use of these techniques is generating lots of data. To help help medics analyse this data, the images are warped or deformed onto standard templates to help identify similarities and differences between patients. This aids in identifying diseases, for example. The process of deforming an image to increases its similarity with a second image is known as image registration. This proposal concerns the mathematical techniques used in image registration, specifically the numerical methods used to compute a registration. We wish to bring three international leading researchers in the area of image registration to discuss to specific approaches to this problem. The first approach uses the numerical solution of a partial differential equation (PDE) known as the Euler Lagrange equation to find the deformation. The second approach, known as Geodesic Interpolating Splines (GIS), uses numerical optimisation to select a time dependent flow expressed using radial basis functions. The techniques both have their merits, with PDEs methods providing better resolution and the GIS approach giving smaller computational problems, and it is important for the two sets of researchers to compare notes on their work. We plan to run a one day meeting to introduce and discuss these techniques to a wider mathematical audience. We believe the UK mathematics community could have much to contribute to this area. We also plan to develop joint research projects in this area. Investigator Silvester has expertise on fast solvers in fluid dynamics, which will provide insight into PDE methods for image registration. Investigator Shardlow and recognised researcher Twining are involved developing the GIS.
Key Findings
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Potential use in non-academic contexts
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Organisation Website:	http://www.man.ac.uk