  Quantifying uncertainty in medical image segmentation applications is
essential, as it is often connected to vital decision-making. Compelling
attempts have been made in quantifying the uncertainty in image segmentation
architectures, e.g. to learn a density segmentation model conditioned on the
input image. Typical work in this field restricts these learnt densities to be
strictly Gaussian. In this paper, we propose to use a more flexible approach by
introducing Normalizing Flows (NFs), which enables the learnt densities to be
more complex and facilitate more accurate modeling for uncertainty. We prove
this hypothesis by adopting the Probabilistic U-Net and augmenting the
posterior density with an NF, allowing it to be more expressive. Our
qualitative as well as quantitative (GED and IoU) evaluations on the
multi-annotated and single-annotated LIDC-IDRI and Kvasir-SEG segmentation
datasets, respectively, show a clear improvement. This is mostly apparent in
the quantification of aleatoric uncertainty and the increased predictive
performance of up to 14 percent. This result strongly indicates that a more
flexible density model should be seriously considered in architectures that
attempt to capture segmentation ambiguity through density modeling. The benefit
of this improved modeling will increase human confidence in annotation and
segmentation, and enable eager adoption of the technology in practice.
