Dice Loss

V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation

What is the formula for the dice loss used in segmentation tasks?

\[\mathcal{L}_{dice} = 1 - \frac{2 \cdot |A \cap B|}{|A| + |B|}\]Where \(A\) and \(B\) are the ground truth and predicted mask.
In PyTorch this can be implemented as:

def dice_loss(input, target):
    smooth = 1.

    iflat = input.view(-1)
    tflat = target.view(-1)
    intersection = (iflat * tflat).sum()
    return 1 - ((2. * intersection + smooth) /
              (iflat.sum() + tflat.sum() + smooth))

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