  With recent advances in computing hardware and surges of deep-learning
architectures, learning-based deep image registration methods have surpassed
their traditional counterparts, in terms of metric performance and inference
time. However, these methods focus on improving performance measurements such
as Dice, resulting in less attention given to model behaviors that are equally
desirable for registrations, especially for medical imaging. This paper
investigates these behaviors for popular learning-based deep registrations
under a sanity-checking microscope. We find that most existing registrations
suffer from low inverse consistency and nondiscrimination of identical pairs
due to overly optimized image similarities. To rectify these behaviors, we
propose a novel regularization-based sanity-enforcer method that imposes two
sanity checks on the deep model to reduce its inverse consistency errors and
increase its discriminative power simultaneously. Moreover, we derive a set of
theoretical guarantees for our sanity-checked image registration method, with
experimental results supporting our theoretical findings and their
effectiveness in increasing the sanity of models without sacrificing any
performance. Our code and models are available at
https://github.com/tuffr5/Saner-deep-registration.
