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本任务，在广泛的临床应用中扮演着关键角色。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果。然而，现有的深度学习图像配准技术在理论上无法保证拓扑保持变换，而这一性质对于保留解剖结构、实现可用于真实临床场景的合理变换至关重要。本文提出了一种新型可变形图像配准框架。首先，我们基于非线性弹性理论中的共形不变性质引入了一种新型正则化器。该正则化器能够强制形变场保持平滑、可逆且保定向性。更重要的是，我们严格保证了拓扑保持性，从而实现了具有临床意义的配准。其次，我们通过坐标MLP（多层感知机）提升了正则化器的性能——该网络可将待配准图像视为连续可微实体。数值实验和可视化实验表明，我们的框架能够超越当前图像配准技术。