# zbMATH — the first resource for mathematics

Spatially adaptive metrics for diffeomorphic image matching in LDDMM. (English) Zbl 07274051
Pennec, Xavier (ed.) et al., Riemannian geometric statistics in medical image analysis. Amsterdam: Elsevier/Academic Press (ISBN 978-0-12-814725-2/pbk; 978-0-12-814726-9/ebook). The Elsevier and Miccai Society Book Series, 533-556 (2020).
Summary: The construction of the large deformation diffeomorphic metric mapping (LDDMM) framework is based on a variational setting and the choice of a Riemannian metric. Its goal is to estimate optimal smooth and invertible maps (diffeomorphisms) of the ambient space that represent a mapping between the points of a source image $$I_S$$ and those of a target image $$I_T$$. This diffeomorphic image registration formalism is particularly adapted to the registration of most 3D medical images, where the hypothesis that organ deformations are smooth is reasonable, and the topology of the represented organs is preserved. Note that this second property is mainly due to the fact that there is no occlusion or out-of-slice motion in such images. Image registration thus takes the form of an infinite-dimensional optimal control problem.
For the entire collection see [Zbl 1428.92004].
##### MSC:
 92C55 Biomedical imaging and signal processing 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds
Full Text: