Variational problems on flows of diffeomorphisms for image matching
Quarterly of Applied Mathematics
Geodesic Interpolating Splines
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
libMesh: a C++ library for parallel adaptive mesh refinement/coarsening simulations
Engineering with Computers
Large Deformation Diffeomorphic Metric Curve Mapping
International Journal of Computer Vision
Adaptive Mesh Refinement for Nonparametric Image Registration
SIAM Journal on Scientific Computing
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part II
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Landmark matching via large deformation diffeomorphisms
IEEE Transactions on Image Processing
Adaptive Numerical Solution of PDEs
Adaptive Numerical Solution of PDEs
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The Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework acting on currents is a conceptually powerful tool for matching highly varying shapes. In the classical approach, the numerical treatment is based on currents representing individual particles, and couples the discretization of shape and deformation. This design restricts the capabilities of LDDMM. In this work, we propose to decouple current and deformation discretization by using conforming adaptive finite elements. We show how to efficiently (a) compute the temporal evolution of discrete $$m$$-current attributes for any $$m$$, and (b) incorporate multiple scales into the matching process. This effectively leads to more flexibility, which is demonstrated in several numerical experiments on anatomical shapes.