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：本文研究了软Dice损失（soft-Dice loss）这一医学图像分割中最常用的损失函数之一，针对目标标签存在噪声的情况。具体而言，我们刻画了最优解集合并给出了这些解体积偏差的严格边界。进一步证明，当通过阈值化将收敛到最优软Dice的软分割序列转化为硬分割时，该序列也收敛到最优Dice度量。这一结果具有重要意义，因为软Dice常被用作最大化Dice度量的代理指标。最后，我们提供了验证理论结果的实验。