由于 Dice系数是图像分割中常用的指标，而在Pytoch中没有官方的实现，下面结合网上的教程进行详细实现。

先来看一个我在网上经常看到的一个版本。

def diceCoeff(pred, gt, smooth=1, activation='sigmoid'):

r""" computational formula：

dice = (2 * (pred ∩ gt)) / (pred ∪ gt)

"""

if activation is None or activation == "none":

activation_fn = lambda x: x

elif activation == "sigmoid":

activation_fn = nn.Sigmoid()

elif activation == "softmax2d":

activation_fn = nn.Softmax2d()

else:

raise NotImplementedError("Activation implemented for sigmoid and softmax2d 激活函数的操作")

pred = activation_fn(pred)

N = gt.size(0)

pred_flat = pred.view(N, -1)

gt_flat = gt.view(N, -1)

intersection = (pred_flat * gt_flat).sum(1)

unionset = pred_flat.sum(1) + gt_flat.sum(1)

loss = 2 * (intersection + smooth) / (unionset + smooth)

return loss.sum() / N

整体思路就是运用dice的计算公式  2(A∩B / A∪B)。下面来分析一下可能存在的问题：

1)smooth参数是用来防止分母除0的，但是如果smooth=1的话，会使得dice的计算结果略微偏高，看下面的测试代码。

# shape = torch.Size([1, 2, 4, 4])

'''

1 0 0= bladder

0 1 0 = tumor

0 0 0= background

'''

pred = torch.Tensor([[

[[0, 1, 1, 0],

[1, 0, 0, 1],

[1, 0, 0, 1],

[0, 1, 1, 0]],

[[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0]],

[[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0]]]])

gt = torch.Tensor([[

[[0, 1, 1, 0],

[1, 0, 0, 1],

[1, 0, 0, 1],

[0, 1, 1, 0]],

[[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0]],

[[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0]]]])

dice_baldder1 = diceCoeff(pred[:, 0:1, :], gt[:, 0:1, :], smooth=1, activation=None)

dice_baldder2 = diceCoeff(pred[:, 0:1, :], gt[:, 0:1, :], smooth=1e-5, activation=None)

print('smooth=1 : dice={:.4}'.format(dice_baldder1.item()))

print('smooth=1e-5 : dice={:.4}'.format(dice_baldder2.item()))

# 输出结果

# smooth=1 : dice=1.059

# smooth=1e-5 : dice=1.0

我们最后预测的是一个3分类的分割图，第一类是baldder， 第二类是tumor， 第三类是背景。我们先假设bladder的预测pred和gt一样，计算bladder的dice值，发现当smooth=1的时候，dice偏高， 而smooth=1e-5时dice比较合理。

2) 当预测和gt都是背景时，即图中没有要分割的部分(没有tumor或者bladder)时，会导致dice=2。如下测试

# shape = torch.Size([1, 2, 4, 4])

'''

1 0 0= bladder

0 1 0 = tumor

0 0 0= background

'''

pred = torch.Tensor([[

[[0, 1, 1, 0],

[1, 0, 0, 1],

[1, 0, 0, 1],

[0, 1, 1, 0]],

[[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0]],

[[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0]]]])

gt = torch.Tensor([[

[[0, 1, 1, 0],

[1, 0, 0, 1],

[1, 0, 0, 1],

[0, 1, 1, 0]],

[[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0]],

[[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0],

[0, 0, 0, 0]]]])

dice_tumor1 = diceCoeff(pred[:, 1:2, :], gt[:, 1:2, :], smooth=1, activation=None)

dice_tumor2 = diceCoeff(pred[:, 1:2, :], gt[:, 1:2, :], smooth=1e-5, activation=None)

print('smooth=1 : dice={:.4}'.format(dice_tumor1.item()))

print('smooth=1e-5 : dice={:.4}'.format(dice_tumor2.item()))

# 输出结果

# smooth=1 : dice=2.0

# smooth=1e-5 : dice=2.0

这里我们还是用1)中的数据，只是这里进行tumor的dice计算，可以看到tumor的预测图和gt中的值全是0，即没有tumor，都是背景，但dice=2，这是因为根据公式此时A∩B和A∪B都为0，结果就是 2*smooth / smooth = 2。

解决办法：我想这里应该更改代码的实现方式，用下面的计算公式替换之前的，因为之前加smooth的位置有问题。

# loss = 2 * (intersection + smooth) / (unionset + smooth) # 之前的

loss = (2 * intersection + smooth) / (unionset + smooth)

替换后的dice如下：

def diceCoeff(pred, gt, smooth=1e-5, activation='sigmoid'):

r""" computational formula：

dice = (2 * (pred ∩ gt)) / (pred ∪ gt)

"""

if activation is None or activation == "none":

activation_fn = lambda x: x

elif activation == "sigmoid":

activation_fn = nn.Sigmoid()

elif activation == "softmax2d":

activation_fn = nn.Softmax2d()

else:

raise NotImplementedError("Activation implemented for sigmoid and softmax2d 激活函数的操作")

pred = activation_fn(pred)

N = gt.size(0)

pred_flat = pred.view(N, -1)

gt_flat = gt.view(N, -1)

intersection = (pred_flat * gt_flat).sum(1)

unionset = pred_flat.sum(1) + gt_flat.sum(1)

loss = (2 * intersection + smooth) / (unionset + smooth)

return loss.sum() / N

用2)中的数据做测试结果如下：dice计算正确

# smooth=1 : dice=1.0

# smooth=1e-5 : dice=1.0

dice的另一种计算方式：这里参考肾脏肿瘤挑战赛提供的dice计算方法。

def diceCoeffv2(pred, gt, eps=1e-5, activation='sigmoid'):

r""" computational formula：

dice = (2 * tp) / (2 * tp + fp + fn)

"""

if activation is None or activation == "none":

activation_fn = lambda x: x

elif activation == "sigmoid":

activation_fn = nn.Sigmoid()

elif activation == "softmax2d":

activation_fn = nn.Softmax2d()

else:

raise NotImplementedError("Activation implemented for sigmoid and softmax2d 激活函数的操作")

pred = activation_fn(pred)

N = gt.size(0)

pred_flat = pred.view(N, -1)

gt_flat = gt.view(N, -1)

tp = torch.sum(gt_flat * pred_flat, dim=1)

fp = torch.sum(pred_flat, dim=1) - tp

fn = torch.sum(gt_flat, dim=1) - tp

loss = (2 * tp + eps) / (2 * tp + fp + fn + eps)

return loss.sum() / N

经过测试，也是没问题的。

整理代码

def diceCoeff(pred, gt, smooth=1e-5, activation='sigmoid'):

r""" computational formula：

dice = (2 * (pred ∩ gt)) / (pred ∪ gt)

"""

if activation is None or activation == "none":

activation_fn = lambda x: x

elif activation == "sigmoid":

activation_fn = nn.Sigmoid()

elif activation == "softmax2d":

activation_fn = nn.Softmax2d()

else:

raise NotImplementedError("Activation implemented for sigmoid and softmax2d 激活函数的操作")

pred = activation_fn(pred)

N = gt.size(0)

pred_flat = pred.view(N, -1)

gt_flat = gt.view(N, -1)

intersection = (pred_flat * gt_flat).sum(1)

unionset = pred_flat.sum(1) + gt_flat.sum(1)

loss = (2 * intersection + smooth) / (unionset + smooth)

return loss.sum() / N

def diceCoeffv2(pred, gt, eps=1e-5, activation='sigmoid'):

r""" computational formula：

dice = (2 * tp) / (2 * tp + fp + fn)

"""

if activation is None or activation == "none":

activation_fn = lambda x: x

elif activation == "sigmoid":

activation_fn = nn.Sigmoid()

elif activation == "softmax2d":

activation_fn = nn.Softmax2d()

else:

raise NotImplementedError("Activation implemented for sigmoid and softmax2d 激活函数的操作")

pred = activation_fn(pred)

N = gt.size(0)

pred_flat = pred.view(N, -1)

gt_flat = gt.view(N, -1)

tp = torch.sum(gt_flat * pred_flat, dim=1)

fp = torch.sum(pred_flat, dim=1) - tp

fn = torch.sum(gt_flat, dim=1) - tp

loss = (2 * tp + eps) / (2 * tp + fp + fn + eps)

return loss.sum() / N

class DiceLoss(nn.Module):

__name__ = 'dice_loss'

def __init__(self, activation='sigmoid'):

super(DiceLoss, self).__init__()

self.activation = activation

def forward(self, y_pr, y_gt):

return 1 - diceCoeffv2(y_pr, y_gt, activation=self.activation)

总结：上面是这几天对dice以及dice loss的一些实思考和实现，如有问题和错误，还望指出。