Recent works in medical image registration have proposed the use of Implicit Neural Representations, demonstrating performance that rivals state-of-the-art learning-based methods. However, these implicit representations need to be optimized for each new image pair, which is a stochastic process that may fail to converge to a global minimum. To improve robustness, we propose a deformable registration method using pairs of cycle-consistent Implicit Neural Representations: each implicit representation is linked to a second implicit representation that estimates the opposite transformation, causing each network to act as a regularizer for its paired opposite. During inference, we generate multiple deformation estimates by numerically inverting the paired backward transformation and evaluating the consensus of the optimized pair. This consensus improves registration accuracy over using a single representation and results in a robust uncertainty metric that can be used for automatic quality control. We evaluate our method with a 4D lung CT dataset. The proposed cycle-consistent optimization method reduces the optimization failure rate from 2.4% to 0.0% compared to the current state-of-the-art. The proposed inference method improves landmark accuracy by 4.5% and the proposed uncertainty metric detects all instances where the registration method fails to converge to a correct solution. We verify the generalizability of these results to other data using a centerline propagation task in abdominal 4D MRI, where our method achieves a 46% improvement in propagation consistency compared with single-INR registration and demonstrates a strong correlation between the proposed uncertainty metric and registration accuracy.

翻译：近期医学图像配准领域的研究提出了使用隐式神经表示的方法，其性能可与最先进的基于学习的方法相媲美。然而，这些隐式表示需要针对每对新图像进行优化，这是一个可能无法收敛到全局最小值的随机过程。为了提高鲁棒性，我们提出了一种使用成对循环一致隐式神经表示的可变形配准方法：每个隐式表示与另一个估计反向变换的隐式表示相连接，使每个网络充当其配对网络的正则化器。在推理过程中，我们通过数值求逆配对的反向变换并评估优化对的一致性，生成多个变形估计。这种一致性相比使用单一表示提高了配准精度，并产生可用于自动质量控制的鲁棒不确定性度量。我们使用4D肺部CT数据集评估了该方法。与当前最先进方法相比，所提出的循环一致优化方法将优化失败率从2.4%降至0.0%。所提出的推理方法将标志点精度提高了4.5%，且所提出的不确定性度量能够检测所有配准方法未能收敛到正确解的情况。我们通过腹部4D MRI中的中心线传播任务验证了这些结果对其他数据的泛化能力，在该任务中，我们的方法相比单隐式神经表示配准实现了传播一致性46%的改进，并证明了所提出的不确定性度量与配准精度之间存在强相关性。