On the Metric Geometry of General Lebesgue Spaces and Metrics in Medical Imaging Analysis

Watch a 21-minute mathematics lecture from the Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications" that explores the metric geometry of general Lebesgue spaces and their applications in medical imaging. Delve into how medical data signals often involve nonlinear spaces, such as SPD matrices in diffusion tensor imaging and probability simplexes in soft segmentation maps. Learn about a generalization of Lebesgue spaces where elements take values in arbitrary metric spaces, and discover the concept of pointwise absolutely continuous curves. Understand how these mathematical concepts can be applied to derive properties of metrics that account for Sobolev diffeomorphisms' action on general Lebesgue spaces, with practical applications in manifold-valued image matching.