平滑骰子损失如何区分? [英] How is the smooth dice loss differentiable?

问题描述

我正在通过最小化普遍用于此问题的dice_loss函数来在keras中训练U-Net:此处修改和此处

I am training a U-Net in keras by minimizing the dice_loss function that is popularly used for this problem: adapted from here and here

def dsc(y_true, y_pred):
     smooth = 1.
     y_true_f = K.flatten(y_true)
     y_pred_f = K.flatten(y_pred)
     intersection = K.sum(y_true_f * y_pred_f)
     score = (2. * intersection + smooth) / (K.sum(y_true_f) + K.sum(y_pred_f) + smooth)
     return score

def dice_loss(y_true, y_pred):
    return (1 - dsc(y_true, y_pred))

此实现不同于传统骰子损失，因为它具有使可微"的平滑术语.我只是不明白如何在分母中添加smooth项而不是诸如1e-7之类的词会更好，因为它实际上会改变损耗值.我已经在具有常规dice实现的测试集上使用经过训练的unet模型进行了检查，如下所示:

This implementation is different from the traditional dice loss because it has a smoothing term to make it "differentiable". I just don't understand how adding the smooth term instead of something like 1e-7 in the denominator makes it better because it actually changes the loss values. I have checked this by using a trained unet model on a test set with a regular dice implementation as follows:

def dice(im1,im2):
     im1 = np.asarray(im1).astype(np.bool)
     im2 = np.asarray(im2).astype(np.bool)
     intersection = np.logical_and(im1, im2)
     return np.float(2. * intersection.sum()) / (im1.sum() + im2.sum() + 1e-7))

有人可以解释为什么通常使用平滑骰子损失吗?

Can someone explain why the smooth dice loss is conventionally used?

推荐答案

在损失中添加smooth并不能使其可区分.使其与众不同的是
1.放宽预测的阈值:您不将y_pred强制转换为np.bool，而是将其保留为介于0到1之间的连续值
2.请勿将set运算用作np.logical_and，而应使用逐元素乘积来近似不可微交运算.

Adding smooth to the loss does not make it differentiable. What makes it differentiable is
1. Relaxing the threshold on the prediction: You do not cast y_pred to np.bool, but leave it as a continuous value between 0 and 1
2. You do not use set operations as np.logical_and, but rather use element-wise product to approximate the non-differenetiable intersection operation.

只有当y_pred和y_true不包含任何前景像素时，才添加smooth以避免被零除.

You only add smooth to avoid devision by zero when both y_pred and y_true do not contain any foreground pixels.

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