A Riemannian approach to shape spaces with applications in medical imaging, computer vision and computer graphics is studied in this project. At the heart of the matter is a discrete geodesic calculus for which existence and convergence results are proven. A particular focus is on image models with a high-dimensional, local structure description using learned feature vectors or based on filter kernels weighted with sparse weight functions. The discrete calculus will be generalized to measure spaces and combined with optimal transport methods.
DFG Programme
Collaborative Research Centres
