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This paper proposes a heteroscedastic uncertainty estimation framework forunsupervised 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 noisedistribution in real-world medical images. This further introduces noisygradients due to undesired penalization on outliers, causing unnaturaldeformation and performance degradation. To mitigate this, we propose anadaptive weighting scheme with a relative $\gamma$-exponentiatedsignal-to-noise ratio (SNR) for the displacement estimator after modeling theheteroscedastic noise using a separate variance estimator to prevent the modelfrom being driven away by spurious gradients from error residuals, leading tomore accurate displacement estimation. To illustrate the versatility andeffectiveness of the proposed method, we tested our framework on tworepresentative registration architectures across three medical image datasets.Our proposed framework consistently outperforms other baselines bothquantitatively and qualitatively while also providing accurate and sensibleuncertainty measures. Paired t-tests show that our improvements in registrationaccuracy are statistically significant. The code will be publicly available at\url{https://voldemort108x.github.io/hetero_uncertainty/}.

Heteroscedastic Uncertainty Estimation for Probabilistic Unsupervised Registration of Noisy Medical Images