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：本文针对目标标签存在噪声的情况，研究了医学图像分割中最常用的损失函数之一——soft-Dice损失。具体而言，我们刻画了最优解集的特征，并给出了这些解体积偏差的严格界。进一步证明，当采用阈值化方法将软分割转换为硬分割时，收敛于最优soft-Dice的软分割序列也会收敛于最优Dice。这一结果具有重要意义，因为soft-Dice常被用作最大化Dice指标的代理函数。最后，本文提供了验证理论结果的实验数据。