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.

翻译：本文研究了医学图像分割中两种最流行的性能指标——准确率（Accuracy）和Dice系数——在目标标签带有噪声时的表现。针对这两种指标，我们证明了最优分割解集的特征化及体积属性的若干结论，并提供了相关实验验证。主要发现包括：（i）两种指标求解所得的分割体积可能显著偏离目标的预期体积；（ii）准确率最优解的体积始终小于或等于Dice最优解的体积；（iii）当可行分割集被约束为体积等于目标预期体积的分割集合时，这两种指标的最优解保持一致。