  In the domain of medical imaging, many supervised learning based methods for
segmentation face several challenges such as high variability in annotations
from multiple experts, paucity of labelled data and class imbalanced datasets.
These issues may result in segmentations that lack the requisite precision for
clinical analysis and can be misleadingly overconfident without associated
uncertainty quantification. We propose the PULASki for biomedical image
segmentation that accurately captures variability in expert annotations, even
in small datasets. Our approach makes use of an improved loss function based on
statistical distances in a conditional variational autoencoder structure
(Probabilistic UNet), which improves learning of the conditional decoder
compared to the standard cross-entropy particularly in class imbalanced
problems. We analyse our method for two structurally different segmentation
tasks (intracranial vessel and multiple sclerosis (MS) lesion) and compare our
results to four well-established baselines in terms of quantitative metrics and
qualitative output. Empirical results demonstrate the PULASKi method
outperforms all baselines at the 5\% significance level. The generated
segmentations are shown to be much more anatomically plausible than in the 2D
case, particularly for the vessel task. Our method can also be applied to a
wide range of multi-label segmentation tasks and and is useful for downstream
tasks such as hemodynamic modelling (computational fluid dynamics and data
assimilation), clinical decision making, and treatment planning.
