Heteroscedastic Uncertainty Estimation for Probabilistic Unsupervised
  Registration of Noisy Medical Images
Xiaoran Zhang Daniel H. Pak Shawn S. Ahn Xiaoxiao Li Chenyu You Lawrence Staib Albert J. Sinusas Alex Wong James S. Duncan
This paper proposes a heteroscedastic uncertainty estimation framework for
unsupervised medical image registration. Existing methods rely on objectives
(e.g. mean-squared error) that assume a uniform noise level across the image,
disregarding the heteroscedastic and input-dependent characteristics of noise
distribution in real-world medical images. This further introduces noisy
gradients due to undesired penalization on outliers, causing unnatural
deformation and performance degradation. To mitigate this, we propose an
adaptive weighting scheme with a relative $\gamma$-exponentiated
signal-to-noise ratio (SNR) for the displacement estimator after modeling the
heteroscedastic noise using a separate variance estimator to prevent the model
from being driven away by spurious gradients from error residuals, leading to
more accurate displacement estimation. To illustrate the versatility and
effectiveness of the proposed method, we tested our framework on two
representative registration architectures across three medical image datasets.
Our proposed framework consistently outperforms other baselines both
quantitatively and qualitatively while also providing accurate and sensible
uncertainty measures. Paired t-tests show that our improvements in registration
accuracy are statistically significant. The code will be publicly available at
\url{https://voldemort108x.github.io/hetero_uncertainty/}.