Unsupervised Diffeomorphic Surface Registration and Non-Linear Modelling

TL;DR

This paper introduces a one-step deep learning model for 3D surface registration that uses a probabilistic deformation model constrained to be diffeomorphic, offering a faster alternative to iterative methods with competitive accuracy.

Contribution

It presents a novel one-step registration approach for 3D surfaces using CVAE and diffeomorphic constraints, extending deep learning surface registration beyond volumetric data.

Findings

Competitive shape fit with iterative methods

Improved generalisability over PCA-based models

Effective use of Chamfer distance and Sinkhorn divergence

Abstract

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.