IPMI 2021 oral

Partial Matching in the Space of Varifolds

Authors: Pierre-Louis A Antonsanti (GE Healthcare)*; Joan Glaunès (Université Paris 5); Thomas Benseghir (GE Healthcare); Vincent Jugnon (GE Healthcare); Irene Kaltenmark (MAP5 – Université de Paris)



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 geometric shapes like curves, sets of curves or surfaces. This term is based on the Varifold shape representation and assess the embedding of a shape into another without relying on correspondences between points. It is designed as data attachment for the Large Deformation Diffeomorphic Metric Mapping (LDDMM), 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 these data dissimilarity terms lead to coherent partial matching despite the topological differences.