Lecture 1: Computational Anatomy - Methods and Mathematical Challenges

Computational anatomy uses the paradigm of pattern theory to study anatomical data obtained via medical imaging methods like CT and MRI. The complexity of this data, the high inter-patient variability and the presence of noise make this task mathematically very challenging. Beginning from the problem of registration - finding point-to-point correspondences between two sets of data - the methods of Riemannian geometry and statistics on manifolds are used to analyse, compare and classify data. This talk will give an overview of the questions studied in computational anatomy and how Riemannian geometry, the diffeomorphism group and geometric mechanics can help answering them.