Learning a Probabilistic Model for Diffeomorphic Registration (1812.07460v2)

Abstract: We propose to learn a low-dimensional probabilistic deformation model from data which can be used for registration and the analysis of deformations. The latent variable model maps similar deformations close to each other in an encoding space. It enables to compare deformations, generate normal or pathological deformations for any new image or to transport deformations from one image pair to any other image. Our unsupervised method is based on variational inference. In particular, we use a conditional variational autoencoder (CVAE) network and constrain transformations to be symmetric and diffeomorphic by applying a differentiable exponentiation layer with a symmetric loss function. We also present a formulation that includes spatial regularization such as diffusion-based filters. Additionally, our framework provides multi-scale velocity field estimations. We evaluated our method on 3-D intra-subject registration using 334 cardiac cine-MRIs. On this dataset, our method showed state-of-the-art performance with a mean DICE score of 81.2% and a mean Hausdorff distance of 7.3mm using 32 latent dimensions compared to three state-of-the-art methods while also demonstrating more regular deformation fields. The average time per registration was 0.32s. Besides, we visualized the learned latent space and show that the encoded deformations can be used to transport deformations and to cluster diseases with a classification accuracy of 83% after applying a linear projection.

Overview of "Learning a Probabilistic Model for Diffeomorphic Registration"

The paper by Julian Krebs et al., "Learning a Probabilistic Model for Diffeomorphic Registration," introduces a novel approach for deformable image registration in medical imaging, particularly focusing on cardiac cine-MRI. This technique learns a probabilistic deformation model using a conditional variational autoencoder (CVAE), aiming to facilitate both accurate registration and analysis of deformations.

Framework and Methodology

The authors propose an unsupervised deep learning method that integrates a CVAE to capture a low-dimensional probabilistic model of deformations. In contrast to traditional numerical optimization approaches for registration, this method directly learns from data, encoding deformations in a latent space where similar deformations are closely located. The model is generative, allowing the synthesis of deformations, facilitating deformation transport across different image pairs, and enabling clustering of pathological states through learned encodings.

The methodological core includes:

• Variational Inference: Application of a CVAE framework, aiming to disentangle deformation from appearance through learning a low-dimensional latent representation.
• Symmetric and Diffeomorphic Constraints: Enforcement of transformation properties via a differentiable exponentiation layer alongside a symmetric loss function.
• Spatial Regularization: Integration of diffusion-based filters within the framework to ensure smooth deformation fields.
• Multi-Scale Velocity Field Estimations: Capability for velocity estimations at multiple scales, aiding in refined registration outcomes.

Experimental Validation and Results

The method was benchmarked on a dataset of 334 cardiac cine-MRIs. Key performance metrics were the mean DICE score and Hausdorff distance, with this approach achieving 81.2% DICE and 7.3mm Hausdorff on average, outperforming several state-of-the-art methods.

Further, the learned latent space allowed the authors to visualize and cluster disease categories with a classification accuracy of 83%, achieved through a linear projection of the latent codes.

Implications and Future Directions

This work presents significant advances in the field of medical image registration. By offering a probabilistic framework, it introduces a mechanism for the generation and transport of deformations, which is critical for pathological analysis and simulation. The seamless integration of generative modeling within the registration task represents a step forward in employing deep learning for flexible, accurate, and scalable deformable registration.

Looking ahead, the methodology showcases potential applications in longitudinal studies for disease progression tracking, uncertainty quantification, and augmentation in training datasets. The generative aspect could facilitate the development of more robust models for synthetic data generation, improving the adaptability of models to various pathological and anatomical variations.

The research opens paths for further exploration into different probabilistic priors and latent space configurations that could enhance model interpretability and efficiency, potentially extending its utility across broader medical imaging and computer vision applications.