Kernel Bundle EPDiff: Evolution Equations for Multi-Scale Diffeomorphic Image Registration

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.