  The clinical interest is often to measure the volume of a structure, which is
typically derived from a segmentation. In order to evaluate and compare
segmentation methods, the similarity between a segmentation and a predefined
ground truth is measured using popular discrete metrics, such as the Dice
score. Recent segmentation methods use a differentiable surrogate metric, such
as soft Dice, as part of the loss function during the learning phase. In this
work, we first briefly describe how to derive volume estimates from a
segmentation that is, potentially, inherently uncertain or ambiguous. This is
followed by a theoretical analysis and an experimental validation linking the
inherent uncertainty to common loss functions for training CNNs, namely
cross-entropy and soft Dice. We find that, even though soft Dice optimization
leads to an improved performance with respect to the Dice score and other
measures, it may introduce a volume bias for tasks with high inherent
uncertainty. These findings indicate some of the method's clinical limitations
and suggest doing a closer ad-hoc volume analysis with an optional
re-calibration step.
