Variational problems on flows of diffeomorphisms for image matching
Quarterly of Applied Mathematics
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
Deformable templates using large deformation kinematics
IEEE Transactions on Image Processing
SIAM Journal on Imaging Sciences
Sparse Multi-Scale Diffeomorphic Registration: The Kernel Bundle Framework
Journal of Mathematical Imaging and Vision
IDiff: irrotational diffeomorphisms for computational anatomy
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
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In the LDDMM framework, optimal warps for image registration are found as end-points of critical paths for an energy functional, and the EPDiff equations describe the evolution along such paths. The Large Deformation Diffeomorphic Kernel Bundle Mapping (LDDKBM) extension of LDDMM allows scale space information to be automatically incorporated in registrations and promises to improve the standard framework in several aspects. We present the mathematical foundations of LDDKBM and derive the KB-EPDiff evolution equations, which provide optimal warps in this new framework. To illustrate the resulting diffeomorphism paths, we give examples showing the decoupled evolution across scales and how the method automatically incorporates deformation at appropriate scales.