# Unsupervised Diffeomorphic Surface Registration and Non-Linear Modelling

arXiv: https://arxiv.org/abs/2109.13630 · HTML: https://mlsanity.com/paper/2109.13630/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 28 Sep 2021.

## Builds on (most cited first, 13 of 13)

- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [FlowNet3D: Learning Scene Flow in 3D Point Clouds](https://mlsanity.com/paper/1806.01411/) (2018)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration](https://mlsanity.com/paper/1805.04605/) (2018)
- [Optimal Transport for Diffeomorphic Registration](https://mlsanity.com/paper/1706.05218/) (2017)
- [Unsupervised Probabilistic Deformation Modeling for Robust Diffeomorphic Registration](https://mlsanity.com/paper/1804.07172/) (2018)
- [Fast Predictive Image Registration](https://mlsanity.com/paper/1607.02504/) (2016)
- [Shape My Face: Registering 3D Face Scans by Surface-to-Surface Translation](https://mlsanity.com/paper/2012.09235/) (2020)
- [ResNet-LDDMM: Advancing the LDDMM Framework using Deep Residual Networks](https://mlsanity.com/paper/2102.07951/) (2021)
- [Fast GPU 3D Diffeomorphic Image Registration](https://mlsanity.com/paper/2004.08893/) (2020)

## Built on by (most cited first, 8 of 8)

- [A survey on deep learning in medical image registration: new technologies, uncertainty, evaluation metrics, and beyond](https://mlsanity.com/paper/2307.15615/) (2023)
- [ScanTalk: 3D Talking Heads from Unregistered Scans](https://mlsanity.com/paper/2403.10942/) (2024)
- [Toward Mesh-Invariant 3D Generative Deep Learning with Geometric Measures](https://mlsanity.com/paper/2306.15762/) (2023)
- [Beyond Fixed Topologies: Unregistered Training and Comprehensive Evaluation Metrics for 3D Talking Heads](https://mlsanity.com/paper/2410.11041/) (2024)
- [Deformable registration and generative modelling of aortic anatomies by auto-decoders and neural ODEs](https://mlsanity.com/paper/2506.00947/) (2025)
- [DefTransNet: A Transformer-based Method for Non-Rigid Point Cloud Registration in the Simulation of Soft Tissue Deformation](https://mlsanity.com/paper/2502.06336/) (2025)
- [FalconBC: Flow matching for Amortized inference of Latent-CONditioned physiologic Boundary Conditions](https://mlsanity.com/paper/2603.19331/) (2026)
- [FreeTalk: Emotional Topology-Free 3D Talking Heads](https://mlsanity.com/paper/2603.15512/) (2026)

## Abstract (arXiv)

Registration is an essential tool in image analysis. Deep learning based alternatives have recently become popular, achieving competitive performance at a faster speed. However, many contemporary techniques are limited to volumetric representations, despite increased popularity of 3D surface and shape data in medical image analysis. We propose a one-step registration model for 3D surfaces that internalises a lower dimensional probabilistic deformation model (PDM) using conditional variational autoencoders (CVAE). The deformations are constrained to be diffeomorphic using an exponentiation layer. The one-step registration model is benchmarked against iterative techniques, trading in a slightly lower performance in terms of shape fit for a higher compactness. We experiment with two distance metrics, Chamfer distance (CD) and Sinkhorn divergence (SD), as specific distance functions for surface data in real-world registration scenarios. The internalised deformation model is benchmarked against linear principal component analysis (PCA) achieving competitive results and improved generalisability from lower dimensions.