  Deep learning methods for unsupervised registration often rely on objectives
that assume a uniform noise level across the spatial domain (e.g. mean-squared
error loss), but noise distributions are often heteroscedastic and
input-dependent in real-world medical images. Thus, this assumption often leads
to degradation in registration performance, mainly due to the undesired
influence of noise-induced outliers. To mitigate this, we propose a framework
for heteroscedastic image uncertainty estimation that can adaptively reduce the
influence of regions with high uncertainty during unsupervised registration.
The framework consists of a collaborative training strategy for the
displacement and variance estimators, and a novel image fidelity weighting
scheme utilizing signal-to-noise ratios. Our approach prevents the model from
being driven away by spurious gradients caused by the simplified homoscedastic
assumption, leading to more accurate displacement estimation. To illustrate its
versatility and effectiveness, we tested our framework on two representative
registration architectures across three medical image datasets. Our method
consistently outperforms baselines and produces sensible uncertainty estimates.
The code is publicly available at
\url{https://voldemort108x.github.io/hetero_uncertainty/}.
