Partial Matching in the Space of Varifolds

Abstract

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.

A new variational model for shape graph registration with partial matching constraints

“…airway vessels or brain arteries with distinct graph structure). Several works have attempted to address the issue of partial matching, in particular frameworks that build on the Gromov-Hausdorff distance [11], or functional maps [41] in the context of 3D surfaces, and very recently diffeomorphic models [29,3] in which asymmetric data attachment terms are introduced in the registration functional. In ESA, however, not much work has been achieved to date.…”