  In computer vision and medical imaging, the problem of matching structures
finds numerous applications from automatic annotation to data reconstruction.
The data however, while corresponding to the same anatomy, are often very
different in topology or shape and might only partially match each other. We
introduce a new asymmetric data dissimilarity term for various geometric shapes
like sets of curves or surfaces. This term is based on the Varifold shape
representation and assesses the embedding of a shape into another one without
relying on correspondences between points. It is designed as data attachment
for the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework,
allowing to compute meaningful deformation of one shape onto a subset of the
other. Registrations are illustrated on sets of synthetic 3D curves, real
vascular trees and livers' surfaces from two different modalities: Computed
Tomography (CT) and Cone Beam Computed Tomography (CBCT). All experiments show
that this data dissimilarity term leads to coherent partial matching despite
the topological differences.
