Marginal Thresholding in Noisy Image Segmentation

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.

Noisy Image Segmentation With Soft-Dice

This paper presents a study on the soft-Dice loss, one of the most popular loss functions in medical image segmentation, for situations where noise is present in target labels. In particular, the set of optimal solutions are characterized and sharp bounds on the volume bias of these solutions are provided. It is further shown that a sequence of soft segmentations converging to optimal soft-Dice also converges to optimal Dice when converted to hard segmentations using thresholding. This is an important result because soft-Dice is often used as a proxy for maximizing the Dice metric. Finally, experiments confirming the theoretical results are provided.

On Image Segmentation With Noisy Labels: Characterization and Volume Properties of the Optimal Solutions to Accuracy and Dice

We study two of the most popular performance metrics in medical image segmentation, Accuracy and Dice, when the target labels are noisy. For both metrics, several statements related to characterization and volume properties of the set of optimal segmentations are proved, and associated experiments are provided. Our main insights are: (i) the volume of the solutions to both metrics may deviate significantly from the expected volume of the target, (ii) the volume of a solution to Accuracy is always less than or equal to the volume of a solution to Dice and (iii) the optimal solutions to both of these metrics coincide when the set of feasible segmentations is constrained to the set of segmentations with the volume equal to the expected volume of the target.