Variational models in image inpainting
 
Selim Esedoglu (University of Michigan, USA)
 
     Image inpainting is the process of automatically filling in damaged regions in digitized pictures with information gleaned from surrounding, undamaged areas. It has been a very active area of mathematical research in image processing. We will describe some of the variational and partial differential equations based models proposed for this application, and discuss efficient numerical methods for their solution. Topics will include some of the more recent non-local models.

Image segmentation
 
Sung Ha Kang (Georgia Institute of Technology, Atlanta, USA)

Image reconstruction in tomography
 
Alfred K. Louis (Saarland University, Germany)
 
     In imaging technologies, both in medicine and in non-destructive testing, the task is to reconstruct the desired information from measured data. In a first step, the forward problem has to be addressed, namely the development of mathematical models. The reconstruction then is the inverse problem. We study several imaging technologies as x-ray CT, MRI and ultrasound CT.
     As model case we consider the Radon transform as mathematical model for 2D CT. We derive inversion formulae and analyze the principles for constructing fast algorithms. We also consider question of uniqueness and resolution for a given data set. Finally we include the data analysis part into the reconstruction in order to determine features of the image in just one step. We discuss optimal filters and study the behavior for real data sets.
     We discuss extensions of the methods to 3D X-ray CT and ultrasound CT.

Flexible algorithms for image registration
 
Jan Modersitzki (McMaster University, Canada)
 
     A generic task in modern image processing is image registration, needed for integration and/or comparison of data obtained from different images. Particularly in a medical environment, there is a huge demand for comparing pre- and post-intervention images, integrating modalities like anatomy (obtained, e.g., from computer tomography) and functionality (obtained, e.g., from positron emission tomography), motion correction and/or reconstruction of two-dimensional projections from a three-dimensional volume (applies to all tomography techniques and histology). The problem is easily stated: given two images (a reference and a template image), and a transformation, such that the transformed image is similar to the reference image.
     In this course we present a general and unified approach to image registration. The course covers central problems arising in typical applications. The course covers theoretical as well as practical components. Implementation issues are discussed on the basis of the FAIR software, see http://www.cas.mcmaster.ca/fair/index.shtml for details.