Uncertainty estimation and probabilistic skull shape reconstruction using bayesian neural networks

3D shape reconstruction is an active area of research and a fundamental problem in computer vision, with growing applications in the medical domain, where it enables the recovery of missing or fine anatomical structures. Numerous approaches have been proposed for medical shape reconstruction, emphasizing accurate and anatomically plausible reconstructions. However, 3D shape reconstruction remains an inherently ill-posed problem, meaning (1) both neural network-based methods and conventional shape modeling approaches naturally introduce uncertainty in their predictions, and (2) multiple anatomically plausible reconstructions exist for a given partial or low-resolution input. While the uncertainty aspects have been widely explored in general computer vision, they remain relatively under-explored in the context of medical shape reconstruction. In this paper, we developed a 3D Bayesian U-Net and investigated its use for uncertainty estimation and probabilistic reconstructions across three key tasks: cranial reconstruction, facial reconstruction, and skull shape super-resolution. Our findings show that the Bayesian model is able to produce a range of anatomically plausible skull reconstructions while capturing natural skull variations arising from the learned weight uncertainty. Notably, these variations are primarily expressed through differences in bone thickness, which aligns with anatomical expectations, particularly relevant in real-world applications like cranial implant design. Additionally, we propose a principled framework to study the relationship between weight uncertainty and reconstruction uncertainty by analyzing the learned posterior distribution of the weights, demonstrating that our Bayesian U-Net achieves comparable reconstruction performance to a deterministic U-Net baseline while providing reliable uncertainty estimates. Our study also reveals a clear cross-task uncertainty pattern, where tasks with stronger structural constraints, like super-resolution, yield lower predictive uncertainty, while less constrained tasks, like facial reconstruction, result in higher uncertainty. Refer to the project page for more visual results https://git.zib.de/jli/uncertainty-aware-skull-reconstruction/ .