About NSD metric

[Yedahang]

Thank you for your impactful work in "Towards Generalizable Tumor Synthesis" and related studies. While attempting to reproduce your experiments, I have encountered an inconsistency in the definition of the "NSD" metric across your paper series and would greatly appreciate your clarification:

1. In "Towards Generalizable Tumor Synthesis" and "Text-Driven Tumor Synthesis", “NSD” is explicitly referred to as "Normalized Surface Distance."
2. However, in "Label-Free Liver Tumor Segmentation," the same acronym, NSD, is redefined as "Normalized Surface Dice (NSD) with a 2mm tolerance."
3. Upon reviewing the code implementations across all three papers (e.g., the cal_dice_nsd() function in STEP3.SegmentationModel/validation.py), it appears that the implementation aligns more closely with Surface Dice, where the overlap between predicted and ground truth surfaces is computed within a specified tolerance region (e.g., 2mm), similar to the Dice coefficient.

Could you kindly provide the precise definition of the NSD metric? It would be greatly appreciated if you could clarify whether "Normalized Surface Distance" and "Normalized Surface Dice" refer to the same or different metrics.

Thank you for your time and assistance.