The critical issue in noise removal of diffusion tensor images is to remove noise without distroying the topological structure of the images, including information about nerve fibre bundles that cross each other inside a voxel. In diffusion tensor imaging, a tensor (positive-definite quadratic form) is observed in each voxel and the traditional approach is to use the eigenvector of the largest eigenvalue as a representative of the preferred direction of the nerve fibres in the voxel. This approach is not appropriate at voxels with crossing fibre bundles. Several other approaches are being investigated in a collaborative CSGB project between the KU and AU-math groups.

Work on defining metrics on tree-like geometric shapes with varying topology, see the illustration, has also been initiated leading to first potentially useful constructions.