# Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces

## TL;DR

This paper introduces an unsupervised, probabilistic learning framework for diffeomorphic registration of images and surfaces, combining classical and modern CNN-based methods to achieve fast, accurate, and topology-preserving registration with uncertainty estimates.

## Contribution

It presents a novel probabilistic generative model and inference algorithm that unites classical registration principles with deep learning, enabling unsupervised, diffeomorphic registration with uncertainty quantification.

## Key findings

- Achieves state-of-the-art accuracy in 3D brain registration
- Provides very fast registration runtimes
- Guarantees topology preservation through diffeomorphic constraints

## Abstract

Classical deformable registration techniques achieve impressive results and offer a rigorous theoretical treatment, but are computationally intensive since they solve an optimization problem for each image pair. Recently, learning-based methods have facilitated fast registration by learning spatial deformation functions. However, these approaches use restricted deformation models, require supervised labels, or do not guarantee a diffeomorphic (topology-preserving) registration. Furthermore, learning-based registration tools have not been derived from a probabilistic framework that can offer uncertainty estimates. In this paper, we build a connection between classical and learning-based methods. We present a probabilistic generative model and derive an unsupervised learning-based inference algorithm that uses insights from classical registration methods and makes use of recent developments in convolutional neural networks (CNNs). We demonstrate our method on a 3D brain registration task for both images and anatomical surfaces, and provide extensive empirical analyses. Our principled approach results in state of the art accuracy and very fast runtimes, while providing diffeomorphic guarantees. Our implementation is available at http://voxelmorph.csail.mit.edu.