Heteroscedastic Uncertainty Estimation for Probabilistic Unsupervised Registration of Noisy Medical Images

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/}.