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This paper presents a study on the soft-Dice loss, one of the most popularloss functions in medical image segmentation, for situations where noise ispresent in target labels. In particular, the set of optimal solutions arecharacterized and sharp bounds on the volume bias of these solutions areprovided. It is further shown that a sequence of soft segmentations convergingto optimal soft-Dice also converges to optimal Dice when converted to hardsegmentations using thresholding. This is an important result because soft-Diceis often used as a proxy for maximizing the Dice metric. Finally, experimentsconfirming the theoretical results are provided.

Noisy Image Segmentation With Soft-Dice