Partial Matching in the Space of Varifolds
This addresses the challenge of partial shape matching in computer vision and medical imaging, where data from different modalities or anatomies may not fully align, offering a method for applications like automatic annotation and data reconstruction.
The paper tackles the problem of matching geometric structures like curves or surfaces that only partially correspond due to topological differences, by introducing a new asymmetric dissimilarity term based on Varifold representation, which enables coherent partial matching in experiments on synthetic and real data such as vascular trees and liver surfaces.
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.