PDE-LDDMM meets NODEs: Introducing neural ordinary differential equation solvers in PDE-constrained Large Deformation Diffeomorphic Metric Mapping

Hernandez, Monica (Universidad de Zaragoza)

Resumen: Non-rigid image registration is a crucial task in various medical applications, allowing the alignment of images with complex spatial or temporal variations. This paper introduces NODEO-LDDMM and NODEO-PDE-LDDMM, two innovative deep-learning-based approaches that bridge the gap between Large Deformation Diffeomorphic Metric Mapping (LDDMM) and neural ordinary differential equations (NODEs). LDDMM and PDE-LDDMM offer mathematically well-established formulations for diffeomorphic registration, while NODEs provide the flexibility of deep-learning in the solution of the ODEs involved in both methods. Both NODEO-LDDMM and NODEO-PDE-LDDMM include the strengths of deep-learning into LDDMM, enabling a robust optimization with a good balance between accuracy and transformation smoothness in their solutions. Our proposed methods reached or outperformed their traditional counterparts and the nearly diffeomorphic deep-learning-based approaches selected as benchmarks. This work contributes to advancing non-rigid image registration techniques, with a methodology suited to overcome some of the limitations of deep-learning in medical image registration.

Idioma: Inglés

DOI: 10.1016/j.jocs.2024.102507

Año: 2025

Publicado en: Journal of computational science 85 (2025), 102507 18 pp.]
ISSN: 1877-7503

Financiación: info:eu-repo/grantAgreement/ES/DGA/T64-23R
Financiación: info:eu-repo/grantAgreement/ES/ISCIII/RD24-0007-0022
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2019-104358RB-I00
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2022-138703OB-I00

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Lenguajes y Sistemas Inf. (Dpto. Informát.Ingenie.Sistms.)