# Diffeomorphic 3D Image Registration via Geodesic Shooting Using an Efficient Adjoint Calculation

@article{Vialard2011Diffeomorphic3I, title={Diffeomorphic 3D Image Registration via Geodesic Shooting Using an Efficient Adjoint Calculation}, author={François-Xavier Vialard and Laurent Risser and Daniel Rueckert and Colin J. Cotter}, journal={International Journal of Computer Vision}, year={2011}, volume={97}, pages={229-241} }

In the context of large deformations by diffeomorphisms, we propose a new diffeomorphic registration algorithm for 3D images that performs the optimization directly on the set of geodesic flows. The key contribution of this work is to provide an accurate estimation of the so-called initial momentum, which is a scalar function encoding the optimal deformation between two images through the Hamiltonian equations of geodesics. Since the initial momentum has proven to be a key tool for statistics…

## 163 Citations

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A novel finite-dimensional Lie algebra structure on the space of bandlimited velocity fields is introduced that can effectively represent initial velocities for diffeomorphic image registration at much lower dimensions than typically used, with little to no loss in registration accuracy.

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