Dice Loss

Dice 出现在论文 V-Net 中，用于医疗图像检测，针对正负样本不均衡的场景，用于评估预测和GT相似度。就是IOU

Dice as Loss In V-Net

Dice

以下内容来自VNet

$D = \frac{2\displaystyle\sum_{i}^{N} p_i g_i}{\displaystyle\sum_{i}^{N} p_{i}^{2}+\displaystyle\sum_{i}^{N} g_{i}^{2}}$

$p$ 是概率，取值 $[0,1]$ ， $g$ 是ground truth，取值 $0,1$ ，所以 $p_i\times g_i$ 就算交集 $X\cap Y$ 了,分子乘2因为分母的总数算了两遍。

这个式子也很好求导

$\frac{\partial D}{\partial p_j} = 2\bigg[\frac{g_i(\sum_i^N p_i^2 +g_i^2) - 2p_j(\sum_i^N p_i g_i) }{(\sum_i^N p_i^2+g_i^2)^2}\bigg]$

Dice Loss

$1-D$ 即可，可以加个Smooth，即 D中分子分母各加 $1$ (有的地方写 $\gamma$ )

Generalised Dice Loss

Dice Loss 论文中。Dice function的分母可以不是平方和

$L_{DL} = 1 - \frac{2|X\cap Y| + 1}{|X| + |Y| + 1}$

具体计算就是分子 X 与 Y 按元素乘得到 $|X\cap Y|$ ，X.sum() + Y.sum()得到 $|X|+|Y|$

class DiceLoss(nn.Module):

    def __init__(self, eps=1e-6):
        super(DiceLoss, self).__init__()
        self.eps = eps

    def forward(self, pred: torch.Tensor, gt, mask=None):
        """
        :param pred: [N, NUM_CLASSES, H, W]
        :param gt: [N, NUM_CLASSES, H, W]
        :param mask: [N, H, W]
        :return: loss
        """
        assert pred.dim() == 4, pred.dim()
        assert pred.shape == gt.shape

        if mask is not None:
            assert (
                pred.shape == mask.shape
            ), f"pred.shape {pred.shape} mask.shape {mask.shape}"

            intersection = (pred * gt * mask).sum()
            union = (pred * mask).sum() + (gt * mask).sum()
        else:
            intersection = (pred * gt).sum()
            union = pred.sum() + gt.sum()

        loss = 1 - (2.0 * intersection + self.eps) / (union + self.eps)
        return loss