Tensorflow introductory tutorial (34) -- two types of image segmentation loss functions commonly used

Two commonly used loss functions of image segmentation are binary cross entropy ,dice coefficient ,tversky,FocalLoss etc. . Today I will be in TensorFlow The above loss function is reproduced under , And compare the results .

1、Cross Entropy

  The cross entropy loss function compares the class prediction value with the target value on a pixel by pixel basis , Then average all pixels . The formula is as follows , among p Is the true category value ,p’ Yes, the forecast belongs to the category 1 The probability of .

This function has the same weight for each category , Therefore, it is very vulnerable to category imbalance .

The reproduction code is as follows ：

      
      

       
       def binary_crossentropy(Y_pred, Y_gt):1.e-51.1    loss = tf.nn.sigmoid_cross_entropy_with_logits(labels=Y_gt, logits=logits)    loss = tf.reduce_mean(loss)return
      
      
      
      

       
       
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2、Dice loss

Dice loss Is in Ｖ-net Used in the model , Generally, the anatomical structure area of interest occupies a relatively small area , Therefore, increase the weight of the foreground area , It can reduce the impact of category imbalance . The formula is as follows , among TP,FP,FN They are true positive 、 False positive 、 The number of false negatives .

In some papers Dice loss The calculation formula can also be like this , As shown below , among p Is the true category value （0 or 1）,p’ Is the probability value of the prediction category （0~1）.

The reproduction code is as follows ：

      
      

       
       def binary_dice(Y_pred, Y_gt):1.e-5    smooth_tf = tf.constant(smooth, tf.float32)    pred_flat = tf.cast(Y_pred, tf.float32)    true_flat = tf.cast(Y_gt, tf.float32)1:]-1, H * W * C * Z])-1, H * W * C * Z])2 * tf.reduce_sum(pred_flat * true_flat, axis=-1) + smooth_tf-1) + tf.reduce_sum(true_flat, axis=-1) + smooth_tf    loss = -tf.reduce_mean(intersection / denominator)return
      
      
      
      

       
       
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3、Tversky loss

Tversky loss yes Dice loss The general expression of ,Tversky loss In false positive 、 The false negative area increases the weight factor . The formula is as follows , among p Is the true category value （0 or 1）,p’ Is the probability value of the prediction category （0~1）. You can find , When beta The value is 0.5 when ,Tversky loss Namely Dice loss 了 .

The reproduction code is as follows ：

      
      

       
       def binary_tversky(Y_pred, Y_gt, beta):1.e-5    smooth_tf = tf.constant(smooth, tf.float32)    pred_flat = tf.cast(Y_pred, tf.float32)    true_flat = tf.cast(Y_gt, tf.float32)1:]-1, H * W * C * Z])-1, H * W * C * Z])-1)1 - true_flat), axis=-1) + tf.reduce_sum(1 - beta) * true_flat * (1 - pred_flat), axis=-1)    loss = -tf.reduce_mean((intersection + smooth_tf) / (denominator + smooth_tf))return
      
      
      
      

       
       
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4、Focal loss

Focal loss It's right Cross Entropy Function improvements , This function reduces the simple sample loss weight , Thus, the network is more focused on the loss of difficult samples . The formula is as follows , among p Is the true category value ,p’ Yes, the forecast belongs to the category 1 The probability of .

The reproduction code is as follows ：

      
      

       
       def binary_focalloss(Y_pred, Y_gt, alpha=0.25, gamma=2.):1.e-51), Y_pred, tf.ones_like(Y_pred))0), Y_pred, tf.zeros_like(Y_pred))# clip to prevent NaN's and Inf's1.1.1.1 - alpha) * tf.pow(pt_0, gamma) * tf.log(1.    loss = -tf.reduce_sum(loss_1 + loss_0)    loss = tf.reduce_mean(loss)return
      
      
      
      

       
       
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5、Cross Entropy+Dice loss

Some articles combine different loss functions to train networks , Tencent medical AI Papers published in the laboratory 《AnatomyNet: Deep Learning for Fast and Fully Automated Whole-volume Segmentation of Head and Neck Anatomy》 In the proposed Dice loss + Focal loss To deal with the segmentation of small organs . It reappears here Cross Entropy+Dice loss Function implementation of , The reproduction code is as follows ：

      
      

       
       def binary_dicePcrossentroy(Y_pred, Y_gt):# step 1,calculate binary crossentroy1.e-51.1    loss1 = tf.nn.sigmoid_cross_entropy_with_logits(labels=Y_gt, logits=logits)    loss1 = tf.reduce_mean(loss1)# step 2,calculate binary dice    smooth_tf = tf.constant(epsilon, tf.float32)    pred_flat = tf.cast(Y_pred, tf.float32)    true_flat = tf.cast(Y_gt, tf.float32)1:]-1, H * W * C * Z])-1, H * W * C * Z])2 * tf.reduce_sum(pred_flat * true_flat, axis=-1) + smooth_tf-1) + tf.reduce_sum(true_flat, axis=-1) + smooth_tf1# step 3,calculate all loss    loss = loss1 + tf.log1p(loss2)return
      
      
      
      

       
       
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Train the above five loss functions , And in 10 Predict and calculate on the test data dice value , give the result as follows .

For everyone to learn better , I share the entire project code to github On ：

​ ​https://github.com/junqiangchen/Image-Segmentation-Loss-Functions​​

If you think this project is good , I hope you can give me Star and Fork, Can let more people learn . If you run into any problems , Leave a message at any time , I'll try to answer .