Learning homeomorphic image registration via conformal-invariant hyperelastic regularisation.
Authors
Affiliations (5)
Affiliations (5)
- Center for Smart Health, School of Nursing, The Hong Kong Polytechnic University, HKSAR, China; Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK.
- Université Clermont Auvergne, France.
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK.
- Center for Smart Health, School of Nursing, The Hong Kong Polytechnic University, HKSAR, China. Electronic address: [email protected].
- Yau Mathematical Sciences Center, Tsinghua University, China.
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 mooth, 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.