Diffeomorphic image matching with left-invariant metrics [article]

Tanya Schmah, Laurent Risser, François-Xavier Vialard
2014 arXiv   pre-print
The geometric approach to diffeomorphic image registration known as "large deformation by diffeomorphic metric mapping" (LDDMM) is based on a left action of diffeomorphisms on images, and a right-invariant metric on a diffeomorphism group, usually defined using a reproducing kernel. We explore the use of left-invariant metrics on diffeomorphism groups, based on reproducing kernels defined in the body coordinates of a source image. This perspective, which we call Left-LDM, allows us to consider
more » ... on-isotropic spatially-varying kernels, which can be interpreted as describing variable deformability of the source image. We also show a simple relationship between LDDMM and the new approach, implying that spatially-varying kernels are interpretable in the same way in LDDMM. We conclude with a discussion of a class of kernels that enforce a soft mirror-symmetry constraint, which we validate in numerical experiments on a model of a lesioned brain.
arXiv:1401.3609v1 fatcat:fiq64n7g55gd7csxp6xvddbkhu