  This work presents a study on label noise in medical image segmentation by
considering a noise model based on Gaussian field deformations. Such noise is
of interest because it yields realistic looking segmentations and because it is
unbiased in the sense that the expected deformation is the identity mapping.
Efficient methods for sampling and closed form solutions for the marginal
probabilities are provided. Moreover, theoretically optimal solutions to the
loss functions cross-entropy and soft-Dice are studied and it is shown how they
diverge as the level of noise increases. Based on recent work on loss function
characterization, it is shown that optimal solutions to soft-Dice can be
recovered by thresholding solutions to cross-entropy with a particular a priori
unknown threshold that efficiently can be computed. This raises the question
whether the decrease in performance seen when using cross-entropy as compared
to soft-Dice is caused by using the wrong threshold. The hypothesis is
validated in 5-fold studies on three organ segmentation problems from the
TotalSegmentor data set, using 4 different strengths of noise. The results show
that changing the threshold leads the performance of cross-entropy to go from
systematically worse than soft-Dice to similar or better results than
soft-Dice.
