more dice score definition

Subject of the feature

For the dice, the current definition is https://github.com/DeepRegNet/DeepReg/blob/main/deepreg/model/loss/label.py#L149. It corresponds to the definition in https://arxiv.org/abs/1707.03237. But in https://arxiv.org/abs/1606.04797, the terms in the denominator are squared.

Two forms are identical in the binary case as the square of 1 is 1. But when y_true and y_pred are probabilities. As far as I know, there’s no closed-form. Both formulations are an approximation.

In https://en.wikipedia.org/wiki/Sørensen–Dice_coefficient, dice score is defined as 2TP/(2TP+FP+FN). If we consider N i.i.d. voxel with y_true=p, which means with 100*p%, the voxel is foreground. Similarly, let y_pred=q. Then we expect TP=pq*N, FP=(1-p)q*N, FN=p(1-q)*N. This gives the non-squared version.

Therefore it could be nice to provide the square option in case anyone wants it. No need to change the default definition.

[tvercaut]

There is no bullet-proof answer to the question of how to implement the soft Dice for deep learning purposes. Different justification lead to different choices (square, non-square, what epsilons and where, foreground only or average between foreground and background dice, how to handle multi-classes, batch version, etc.). Many of the issues arise when you have ground truth with 0 foreground voxels. At least in our experience, the batch version of the soft Dice really helps the training.

If you are interested in that rabbit hole, here are some pointers: https://github.com/Project-MONAI/MONAI/issues/807 https://arxiv.org/abs/1707.00478 Section 3.6.1 in https://mediatum.ub.tum.de/doc/1395260/1395260.pdf

[YipengHu]

EDIT: a new ticket may be better - sorry