Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces (1903.03545v2)

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.

• The paper introduces a probabilistic generative model that combines CNNs with classical registration, ensuring efficient and topology-preserving deformations.
• The method employs variational inference with diffeomorphic integration layers to learn continuous deformation fields for both images and surfaces.
• Extensive experiments on over 3,500 brain scans demonstrate rapid registration (under 1 second) with minimal folding, ensuring high anatomical fidelity.

An Overview of Unsupervised Learning for Probabilistic Diffeomorphic Registration of Images and Surfaces

The paper presents a comprehensive paper on the integration of classical deformable registration techniques with recent advancements in machine learning to address the challenges of probabilistic diffeomorphic registration for images and surfaces. Diffeomorphic registration is crucial in medical image analysis, where it is essential to maintain topology-preserving transformations. While traditional methods provide a robust theoretical framework, they are limited by their computational demands. Recent machine learning approaches, although computationally efficient, often lack rigorous theoretical treatment and assurances of topology preservation.

Key Contributions

1. Probabilistic Generative Model: The authors propose a probabilistic model that assimilates the strengths of traditional probablisitc models with convolutional neural networks (CNNs). This model facilitates the learning of spatial deformation functions in an unsupervised manner, connecting classical and learning-based registration methods.
2. Diffeomorphic Guarantees: A critical advancement in this work is the derivation of unsupervised learning-based inference algorithms that preserve diffeomorphism. These guarantees are crucial for maintaining the topology of the structures during registration, ensuring transformations remain invertible and orientation-preserving.
3. Integration of Surfaces: The method extends naturally to surface alignment, allowing for the incorporation of anatomical segmentations. Through the use of a single cohesive framework, the approach enhances registration accuracy without sacrificing computational efficiency.

Methodology

The proposed framework employs a variational inference on a probabilistic generative model. It uses a convolutional neural network to learn the deformation field by mapping pairs of input images to deformations via end-to-end training. The network also incorporates diffeomorphic integration layers and a spatial transform layer, allowing for the computation of the deformation field in a differentiable manner.

Numerical Results

The empirical results in the paper demonstrate state-of-the-art registration accuracy with substantially reduced runtimes. For example, the method achieves image registration in under a second using a GPU. The research also confirms diffeomorphic properties with minimal folding in the deformation field, which is a significant advancement over existing methods that often exhibit folds, indicating possible topology violations.

The approach was validated using a large multi-paper dataset of over 3,500 brain scans, highlighting its applicability across different registration tasks. The inclusion of surface models delivered improved accuracy in regions associated with the given anatomical structures, reinforcing the model's potential in practical usage scenarios.

Implications and Future Prospects

From a theoretical standpoint, the proposed method bridges the gap between classical and learning-based registration approaches, offering a model that is both rigorous in its probabilistic formulation and efficient in its computation. Practically, this work opens doors to rapid and accurate deformable registration, particularly in medical imaging, where it can significantly impact clinical workflows by reducing computation times while ensuring high accuracy and maintaining anatomical fidelity.

Future advancements may explore further extensions to multi-modal registration and expansion to more complex anatomical surfaces. With increasing computational capacities, integrating more sophisticated deep learning architectures could yield even more refined registration solutions. Additionally, leveraging this framework’s probabilistic aspect could provide richer insights into the uncertainties associated with registration, thus enhancing its utility in robust clinical decision-making.

Overall, the paper's contribution lies in developing a fast, accurate, and theoretically sound approach to image and surface registration, aligning well with the ongoing advancements in machine learning and medical imaging technologies.