1309 eng reportzib 0 2011-06-14 2011-06-14 -- We consider Large Deformation Diffeomorphic Metric Mapping of general $m$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete $m$-current attributes. 11-22 urn:nbn:de:0297-zib-13090 10.1007/s11263-012-0599-3 An extended version appeared under the title "Flexible Shape Matching with Finite Element Based LDDMM" in: International Journal of Computer Vision November 2013, Volume 105, Issue 2, pp 128-143 Andreas Günther Andreas Günther Hans Lamecker Martin Weiser 11-22 eng uncontrolled Large Deformation eng uncontrolled Diffeomorphic Registration eng uncontrolled Matching eng uncontrolled Currents eng uncontrolled Adaptive Finite Elements Homeomorphisms and diffeomorphisms of planes and surfaces Optimal control problems involving partial differential equations Currents [See also 32C30, 53C65] Correspondences and other transformation methods (e.g. Lie- Bäcklund) [See also 35A22] Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods Numerical Mathematics Visual Data Analysis Computational Medicine Therapy Planning Lamecker, Hans Weiser, Martin MATHEON-F2 Visual and Data-centric Computing https://opus4.kobv.de/opus4-zib/files/1309/ZIB-Report11-22_GLW-LDDMMwithAFEM.pdf