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 non-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.
CITATION STYLE
Schmah, T., Risser, L., & Vialard, F. X. (2015). Diffeomorphic image matching with left-invariant metrics. Fields Institute Communications, 73, 373–392. https://doi.org/10.1007/978-1-4939-2441-7_16
Mendeley helps you to discover research relevant for your work.