Brain vessel segmentation of MR scans is a critical step in the diagnosis of cerebrovascular diseases. Due to the fine vessel structure, manual vessel segmentation is time consuming. Therefore, automatic deep learning (DL) based segmentation techniques are intensively investigated. As conventional DL models yield a high complexity and lack an indication of decision reliability, they are often considered as not trustworthy. This work aims to increase trust in DL based models by incorporating epistemic uncertainty quantification into cerebrovascular segmentation models for the first time. By implementing an efficient ensemble model combining the advantages of Bayesian Approximation and Deep Ensembles, we aim to overcome the high computational costs of conventional probabilistic networks. Areas of high model uncertainty and erroneous predictions are aligned which demonstrates the effectiveness and reliability of the approach. We perform extensive experiments applying the ensemble model on out-of-distribution (OOD) data. We demonstrate that for OOD-images, the estimated uncertainty increases. Additionally, omitting highly uncertain areas improves the segmentation quality, both for in- and out-of-distribution data. The ensemble model explains its limitations in a reliable manner and can maintain trustworthiness also for OOD data and could be considered in clinical applications

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