This work proposes $\texttt{NePhi}$, a neural deformation model which results in approximately diffeomorphic transformations. In contrast to the predominant voxel-based approaches, $\texttt{NePhi}$ represents deformations functionally which allows for memory-efficient training and inference. This is of particular importance for large volumetric registrations. Further, while medical image registration approaches representing transformation maps via multi-layer perceptrons have been proposed, $\texttt{NePhi}$ facilitates both pairwise optimization-based registration $\textit{as well as}$ learning-based registration via predicted or optimized global and local latent codes. Lastly, as deformation regularity is a highly desirable property for most medical image registration tasks, $\texttt{NePhi}$ makes use of gradient inverse consistency regularization which empirically results in approximately diffeomorphic transformations. We show the performance of $\texttt{NePhi}$ on two 2D synthetic datasets as well as on real 3D lung registration. Our results show that $\texttt{NePhi}$ can achieve similar accuracies as voxel-based representations in a single-resolution registration setting while using less memory and allowing for faster instance-optimization.

翻译：本文提出$\texttt{NePhi}$，一种可生成近似微分同胚变换的神经形变模型。与主流的基于体素的方法不同，$\texttt{NePhi}$以函数形式表征形变，从而支持内存高效训练与推理，这对大规模体素配准任务尤为重要。此外，尽管已有研究提出通过多层感知器表示变换映射的医学图像配准方法，但$\texttt{NePhi}$既支持基于配对优化的配准，也支持通过预测或优化的全局与局部潜码实现的基于学习的配准。最后，针对形变正则化这一多数医学图像配准任务的关键需求，$\texttt{NePhi}$采用梯度逆一致性正则化，经验证可产生近似微分同胚变换。我们在两个二维合成数据集以及真实三维肺部配准数据上验证了$\texttt{NePhi}$的性能。结果表明，在单分辨率配准设置下，$\texttt{NePhi}$能达到与基于体素表征方法相当的精度，同时内存消耗更低且实例优化速度更快。