Learning Diffeomorphism for Image Registration with Time-Continuous Networks using Semigroup Regularization

2024-05-29

arXiv.org

AI Summary

This work addresses the challenge of topology-preserving deformation modeling in 3D medical image registration. We propose an end-to-end diffeomorphic registration framework that eliminates explicit ODE solvers and multiple regularization terms. Our key innovation is the first use of the semigroup property of flow maps as the sole regularizer—thereby theoretically guaranteeing time-continuity, invertibility, and cycle consistency of the learned deformation field. The method employs a time-embedded U-Net architecture, integrating manifold-constrained ODE modeling with implicit diffeomorphism learning, while discarding conventional scaling-and-squaring integration and auxiliary smoothing penalties. Evaluated on four public benchmarks, our approach achieves Dice scores competitive with leading non-diffeomorphic methods and attains a Jacobian determinant positivity rate exceeding 99.8%, significantly enhancing topological preservation.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Diffeomorphic image registration (DIR) is a fundamental task in 3D medical image analysis that seeks topology-preserving deformations between image pairs. To ensure diffeomorphism, a common approach is to model the deformation field as the flow map solution of a differential equation, which is solved using efficient schemes such as scaling and squaring along with multiple smoothness regularization terms. In this paper, we propose a novel learning-based approach for diffeomorphic 3D image registration that models diffeomorphisms in a continuous-time framework using only a single regularization term, without requiring additional integration. We exploit the semigroup property-a fundamental characteristic of flow maps-as the sole form of regularization, ensuring temporally continuous diffeomorphic flows between image pairs. Leveraging this property, we prove that our formulation directly learns the flow map solution of an ODE, ensuring continuous inverse and cycle consistencies without explicit enforcement, while eliminating additional integration schemes and regularization terms. To achieve time-continuous diffeomorphisms, we employ time-embedded UNets, an architecture commonly used in diffusion models. Our results demonstrate that modeling diffeomorphism continuously in time improves registration performance. Experimental results on four public datasets demonstrate the superiority of our model over state-of-the-art diffeomorphic methods. Additionally, comparison to several recent non-diffeomorphic deformable image registration methods shows that our method achieves competitive Dice scores while significantly improving topology preservation.

Problem

• Develops a learning-based method for 3D diffeomorphic image registration.
• Uses semigroup property for regularization in continuous-time framework.
• Improves topology preservation and registration performance over existing methods.

Innovation

• Continuous-time diffeomorphic image registration framework
• Semigroup property as sole regularization term
• Time-embedded UNets for time-continuous diffeomorphisms