  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.
