Large Structures Seminar: Alfred Kume

Shape spaces of configurations are defined as quotient spaces of matrices after the actions of location, rotation and/or scale are filtered out.

The corresponding spaces equipped with certain metrics give rise to the Riemannian manifolds of shape spaces. Therefore the shape data are points on these manifolds and the statistical modelling is essentially addressing the inferential issues in such spaces.

For example the concept of mean is generalised to that of the Frechet mean which unlike Euclidean spaces is not generally unique. In the talk we mention some of the statistical models which are defined either directly in the shape spaces or in the original matrix spaces of landmark configurations. These approaches pose computational challenging problems which we are trying to address in the talk. The examples will taken from Biology and the focus will be on both 2 and 3 dimensional objects.