# Partial Matching in the Space of Varifolds

arXiv: https://arxiv.org/abs/2103.12441 · HTML: https://mlsanity.com/paper/2103.12441/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 23 Mar 2021.

## Builds on (most cited first, 6 of 6)

- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (2020)
- [Partial Functional Correspondence](https://mlsanity.com/paper/1506.05274/) (2015)
- [Optimal Transport for Diffeomorphic Registration](https://mlsanity.com/paper/1706.05218/) (2017)
- [The varifold representation of non-oriented shapes for diffeomorphic registration](https://mlsanity.com/paper/1304.6108/) (2013)
- [The Whole Is Greater Than the Sum of Its Nonrigid Parts](https://mlsanity.com/paper/2001.09650/) (2020)
- [The fshape framework for the variability analysis of functional shapes](https://mlsanity.com/paper/1404.6039/) (2014)

## Built on by (most cited first, 3 of 3)

- [How to Register a Live onto a Liver ? Partial Matching in the Space of Varifolds](https://mlsanity.com/paper/2204.05665/) (2022)
- [Feature-based morphological analysis of shape graph data](https://mlsanity.com/paper/2602.16120/) (2026)
- [Varifold Moment Invariants for Sustainable and Explainable Contour Feature Extraction](https://mlsanity.com/paper/2606.07333/) (2026)

## Abstract (arXiv)

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.