Clarification required for `SurfaceDiceMetric`

[tvercaut]

Describe the bug
The documentation of the SurfaceDiceMetric is confusing and would benefit from being clarified:
https://github.com/Project-MONAI/MONAI/blob/dev/monai/metrics/surface_dice.py

It indeed says it computes the "Normalized Surface Distance (NSD)" intially and later it says it computes the "(Normalized) Surface Dice (NSD)". It then refers to https://github.com/deepmind/surface-distance which does not provide a metric called "Normalized Surface Distance" or "Normalized Surface Dice".

The DeepMind repo however provides a Surface Dice (with compute_surface_dice_at_tolerance) which may be what SurfaceDiceMetric implements but compute_surface_dice_at_tolerance requires a tolerance as input whereas SurfaceDiceMetric does not. It's thus unclear how these can be the same.

The referenced paper in MONAI's documentation, https://arxiv.org/abs/1809.04430, also does not mention a metric which accronym would be NSD. The reference for the 2D extension does though: https://arxiv.org/abs/2111.05408

Additional context
Similar confusions can be found in biomedical challenges:
https://doi.org/10.1038/s41467-022-30695-9
https://doi.org/10.1016/j.media.2020.101920

It's thus not only MONAI being confusing but it would be helpful to clarify nonetheless.

[Nic-Ma]

Hi @yiheng-wang-nv ,

Could you please help take a look at this ticket?

Thanks in advance.

[tvercaut]

I had a quick discussion with @mjorgecardoso and Michela about NSD in the medical segmentation decathlon (https://doi.org/10.1038/s41467-022-30695-9). They confirmed that what they refer to as NSD in the challenge is the same as the Surface Dice in the Deepmind repo (compute_surface_dice_at_tolerance) and the Surface Dice Similarity Coefficient in section 2.2 of https://arxiv.org/abs/1809.04430

I further assume that what MONAI refers to as class_thresholds is actually similar to what the other source call "tolerance". However class_thresholds is given in pixels/voxels rather than milimetres. This makes is harder to relate. Also, it's unclear to me how anisotropix voxels would be handled. If this is a limitation of MONAI's implementation, it would be worth highlighting.

Given that the NSD acronym has been used in a few existing challenges, it may be worth keeping it in MONAI as well but maybe expand it to "Normalized Surface Dice" to improve clarity.