Hello,

I’m trying to understand the implementation of the dice coefficient which is defined by:

I would like to know: What does this ∩ sign means?

Also I have an implementation of the function in Pytorch:

```
def dice_coeff(pred, target):
smooth = 1.
num = pred.size(0)
m1 = pred.view(num, -1) # Flatten
m2 = target.view(num, -1) # Flatten
intersection = (m1 * m2).sum()
return (2. * intersection + smooth) / (m1.sum() + m2.sum() + smooth)
class SoftDiceLoss(nn.Module):
def __init__(self, weight=None, size_average=True):
super(SoftDiceLoss, self).__init__()
def forward(self, logits, targets):
probs = F.sigmoid(logits)
num = targets.size(0) # Number of batches
score = dice_coeff(probs, targets)
score = 1 - score.sum() / num
return score
```

If I try to map the math formula to the code the ∩ sign is actually a multiplication and |X| is actually taking the sum of the matrice right?

One last question: The author used a “smooth” factor. Why do we want to do that?

Thank you.