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.

翻译：--- 使用Soft-Dice进行噪声图像分割的研究。本文研究了Soft-Dice loss在目标标签存在噪声的情况下的表现问题，特别是它们的最优解集被描述，并提供了这些最优解的体积偏差的严格界限。进一步表明，一系列趋近于最优Soft-Dice的Soft分割，当通过阈值处理转换为硬分割时，也趋近于最优Dice。这是一个重要的结果，因为Soft-Dice经常被用作最大化Dice度量的代理。最后，提供了能够证实理论结果的实验。