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We study two of the most popular performance metrics in medical imagesegmentation, Accuracy and Dice, when the target labels are noisy. For bothmetrics, several statements related to characterization and volume propertiesof the set of optimal segmentations are proved, and associated experiments areprovided. Our main insights are: (i) the volume of the solutions to bothmetrics 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 volumeof a solution to Dice and (iii) the optimal solutions to both of these metricscoincide when the set of feasible segmentations is constrained to the set ofsegmentations with the volume equal to the expected volume of the target.

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