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.

翻译：可变形图像配准是医学图像分析中的基础任务，在广泛的临床应用场景中起着关键作用。近年来，基于深度学习的可变形医学图像配准方法得到广泛研究并取得了显著成效。然而，现有深度学习图像配准技术无法从理论上保证拓扑保持变换——这一保持解剖结构完整性、实现可用于真实临床环境的合理变换的关键特性。我们提出了一种新型的可变形图像配准框架。首先，在非线性弹性力学框架下引入基于共形不变特性的新型正则化项。该正则化项强制形变场保持光滑性、可逆性与方向保持性。更重要的是，我们严格保证了拓扑保持性，从而获得具有临床意义的配准结果。其次，通过坐标MLP（多层感知机）提升正则化器性能，实现将待配准图像视为连续可微实体。数值实验与可视化实验均表明，本框架在图像配准任务中能够超越现有技术水平。