Noisy Image Segmentation With Soft-Dice

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.