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.
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