Learning Homeomorphic Image Registration via Conformal-Invariant Hyperelastic Regularisation

• URL: http://arxiv.org/abs/2303.08113v2
• Date: Fri, 30 Jun 2023 13:15:17 GMT
• Title: Learning Homeomorphic Image Registration via Conformal-Invariant Hyperelastic Regularisation
• Authors: Jing Zou, No\'emie Debroux, Lihao Liu, Jing Qin, Carola-Bibiane Sch\"onlieb, and Angelica I Aviles-Rivero
• Abstract summary: We propose a novel framework for deformable image registration based on conformal-invariant properties. Our regulariser enforces the deformation field yielding to be smooth, invertible and orientation-preserving. We demonstrate, through numerical and visual experiments, that our framework is able to outperform current techniques for image registration.
• Score: 9.53064372566798
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Deformable image registration is a fundamental task in medical image analysis and plays a crucial role in a wide range of clinical applications. Recently, deep learning-based approaches have been widely studied for deformable medical image registration and achieved promising results. However, existing deep learning image registration techniques do not theoretically guarantee topology-preserving transformations. This is a key property to preserve anatomical structures and achieve plausible transformations that can be used in real clinical settings. We propose a novel framework for deformable image registration. Firstly, we introduce a novel regulariser based on conformal-invariant properties in a nonlinear elasticity setting. Our regulariser enforces the deformation field to be smooth, invertible and orientation-preserving. More importantly, we strictly guarantee topology preservation yielding to a clinical meaningful registration. Secondly, we boost the performance of our regulariser through coordinate MLPs, where one can view the to-be-registered images as continuously differentiable entities. We demonstrate, through numerical and visual experiments, that our framework is able to outperform current techniques for image registration.

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