多类别语义分割中常见 Loss 函数总结

2024-07-06 20:01| 来源: 网络整理| 查看: 265

文章目录 1 综述1.1 Dice with weight1.2 Tversky loss1.3 Focal loss1.4 Generalized dice with weight1.5 Cross Entropy with weight1.6 Dice + crossEntropy1.7 Dice + Focal loss 参考文献

1 综述

学习并整理了一下语义分割的常见Loss，希望能为大家训练语义分割网络的时候提供一些关于Loss方面的知识，之后会不定期更新；【tensorflow实现】

看到一篇2020年论文《A survey of loss functions for semantic segmentation》，文章对目前常见语义分割中Loss functions进行了总结，大家有兴趣可以看看；

论文地址：A survey of loss functions for semantic segmentation code地址：Semantic-Segmentation-Loss-Functions

1.1 Dice with weight

（1）Dice Loss 对正负样本严重不平衡的场景有着不错的性能，训练过程中更侧重对前景区域的挖掘；（2）Dice Loss是一种区域相关的loss，像素点的loss以及梯度值不仅和该点的label以及预测值相关，和其他点的label以及预测值也相关；（3）但训练loss容易不稳定，尤其是小目标的情况下；

Dice with weight代码如下：

def Dice_weight_loss(Y_pred, Y_gt, weight_loss): """ multi label dice loss with weighted WDL=1-2*(sum(w*sum(r&p))/sum((w*sum(r+p)))),w=array of shape (C,) :param Y_pred: [None, self.image_depth, self.image_height, self.image_width, self.numclass],Y_pred is softmax result :param Y_gt:[None, self.image_depth, self.image_height, self.image_width, self.numclass],Y_gt is one hot result :param weight_loss: numpy array of shape (C,) where C is the number of classes :return: """ weight_loss = np.array(weight_loss) smooth = 1.e-5 smooth_tf = tf.constant(smooth, tf.float32) Y_pred = tf.cast(Y_pred, tf.float32) Y_gt = tf.cast(Y_gt, tf.float32) # Compute gen dice coef: numerator = Y_gt * Y_pred numerator = tf.reduce_sum(numerator, axis=(1, 2, 3)) denominator = Y_gt + Y_pred denominator = tf.reduce_sum(denominator, axis=(1, 2, 3)) gen_dice_coef = tf.reduce_mean(2. * (numerator + smooth_tf) / (denominator + smooth_tf), axis=0) loss = -tf.reduce_mean(weight_loss * gen_dice_coef) return loss 1.2 Tversky loss

论文地址为：Tversky loss function for image segmentation using 3D fully convolutional deep networks

实际上Dice Loss只是Tversky loss的一种特殊形式而已，我们先来看一下Tversky系数的定义，它是Dice系数和Jaccard系数的广义系数。当 alpha 和 beta 均为0.5的时候，这个公式就是Dice系数，当 alpha 和 beta 均为1的时候，这个公式就是Jaccard系数。

def tversky_loss(Y_pred, Y_gt, beta, weight_loss): """ multi label tversky with weighted Tversky loss (TL) is a generalization of Dice loss. TL adds a weight to FP and FN. define:TL(p,p')=(p&p')/(p&p'+b*((1-p)&p')+(1-b)*(p&(1-p'))) :param Y_pred: [None, self.image_depth, self.image_height, self.image_width, self.numclass],Y_pred is softmax result :param Y_gt:[None, self.image_depth, self.image_height, self.image_width, self.numclass],Y_gt is one hot result :param beta:beta=1/2,just Dice loss,beta must(0,1) :return: """ weight_loss = np.array(weight_loss) smooth = 1.e-5 smooth_tf = tf.constant(smooth, tf.float32) Y_pred = tf.cast(Y_pred, tf.float32) Y_gt = tf.cast(Y_gt, tf.float32) p0 = Y_pred p1 = 1 - Y_pred g0 = Y_gt g1 = 1 - Y_gt # Compute gen dice coef: numerator = p0 * g0 numerator = tf.reduce_sum(numerator, axis=(1, 2, 3)) denominator = tf.reduce_sum(beta * p0 * g1, axis=(1, 2, 3)) + tf.reduce_sum((1 - beta) * p1 * g0, axis=(1, 2, 3)) + numerator gen_dice_coef = tf.reduce_mean((numerator + smooth_tf) / (denominator + smooth_tf), axis=0) loss = -tf.reduce_mean(weight_loss * gen_dice_coef) return loss 1.3 Focal loss

论文地址：Focal Loss for Dense Object Detection

何凯明团队在RetinaNet论文中引入了Focal Loss来解决难易样本数量不平衡，gamma用来控制易分样本和难分样本的权重，alpha用来控制正负样本的权重。

Focal loss模块代码如下:

def Focal_loss(Y_pred, Y_gt, gamma, alpha): """ focal_loss between an output and a target :param Y_pred: A tensor resulting from a softmax(-1,z,h,w,numclass) :param Y_gt: A tensor of the same shape as `y_pred` :param alpha: Sample category weight,which is shape (C,) where C is the number of classes :param gamma: Difficult sample weight :return: """ weight_loss = np.array(alpha) epsilon = 1.e-5 # Scale predictions so that the class probas of each sample sum to 1 output = Y_pred / tf.reduce_sum(Y_pred, axis=- 1, keepdims=True) # Clip the prediction value to prevent NaN's and Inf's output = tf.clip_by_value(output, epsilon, 1. - epsilon) # Calculate Cross Entropy cross_entropy = -Y_gt * tf.log(output) # Calculate Focal Loss loss = tf.pow(1 - output, gamma) * cross_entropy loss = tf.reduce_sum(loss, axis=(1, 2, 3)) loss = tf.reduce_mean(loss, axis=0) loss = tf.reduce_mean(weight_loss * loss) return loss 1.4 Generalized dice with weight

论文地址：Generalized Overlap Measures for Evaluation and Validation in Medical Image Analysis

因 Dice Loss 对小目标的预测是十分不利的，因为一旦小目标有部分像素预测错误，就可能会引起Dice系数大幅度波动，导致梯度变化大训练不稳定。另外从上面的代码实现可以发现，Dice Loss针对的是某一个特定类别的分割的损失。当类似于病灶分割有多个场景的时候一般都会使用多个Dice Loss，所以Generalized Dice loss就是将多个类别的Dice Loss进行整合，使用一个指标作为分割结果的量化指标。

Generalized dice with weight代码如下：

def Generalized_dice_loss_w(Y_pred, Y_gt): """ Generalized Dice Loss with class weights GDL=1-2*(sum(w*sum(r*p))/sum((w*sum(r+p)))),w=1/sum(r)*sum(r) rln为类别l在第n个像素的标准值(GT)，而pln为相应的预测概率值。此处最关键的是wl,为每个类别的权重 :param Y_gt:[None, self.image_depth, self.image_height, self.image_width, self.numclass],Y_gt is one hot result :param Y_pred:[None, self.image_depth, self.image_height, self.image_width, self.numclass],Y_pred is softmax result :return: """ smooth = 1.e-5 smooth_tf = tf.constant(smooth, tf.float32) Y_pred = tf.cast(Y_pred, tf.float32) Y_gt = tf.cast(Y_gt, tf.float32) # Compute weights: "the contribution of each label is corrected by the inverse of its volume" weight_loss = tf.reduce_sum(Y_gt, axis=(0, 1, 2, 3)) weight_loss = 1 / (tf.pow(weight_loss, 2) + smooth_tf) # Compute gen dice coef: numerator = Y_gt * Y_pred numerator = weight_loss * tf.reduce_sum(numerator, axis=(0, 1, 2, 3)) numerator = tf.reduce_sum(numerator) denominator = Y_gt + Y_pred denominator = weight_loss * tf.reduce_sum(denominator, axis=(0, 1, 2, 3)) denominator = tf.reduce_sum(denominator) loss = -2 * (numerator + smooth_tf) / (denominator + smooth_tf) return loss 1.5 Cross Entropy with weight

Cross entropy with weight代码如下：

def weighted_categorical_crossentropy(Y_pred, Y_gt, weights): """ weighted_categorical_crossentropy between an output and a target loss=-weight*y*log(y') :param Y_pred:A tensor resulting from a softmax :param Y_gt:A tensor of the same shape as `output` :param weights:numpy array of shape (C,) where C is the number of classes :return:categorical_crossentropy loss Usage: weights = np.array([0.5,2,10]) # Class one at 0.5, class 2 twice the normal weights, class 3 10x. """ weights = np.array(weights) epsilon = 1.e-5 # scale preds so that the class probas of each sample sum to 1 output = Y_pred / tf.reduce_sum(Y_pred, axis=- 1, keep_dims=True) # manual computation of crossentropy output = tf.clip_by_value(output, epsilon, 1. - epsilon) loss = - Y_gt * tf.log(output) loss = tf.reduce_sum(loss, axis=(1, 2, 3)) loss = tf.reduce_mean(loss, axis=0) loss = tf.reduce_mean(weights * loss) return loss 1.6 Dice + crossEntropy

Dice + crossEntropy代码如下：

def dice_and_crossentroy(Y_pred, Y_gt, weightdice, weightfocal, lamda1=100, lamda2=1): """ hybrid loss function from dice loss and crossentroy loss=Ldice+lamda*Lfocalloss :param Y_pred:A tensor resulting from a softmax(-1,z,h,w,numclass) :param Y_gt: A tensor of the same shape as `y_pred` :param gamma:Difficult sample weight :param alpha:Sample category weight,which is shape (C,) where C is the number of classes :param lamda:trade-off between dice loss and focal loss,can set 0.1,0.5,1 :return:diceplusfocalloss """ weight_loss1 = np.array(weightdice) weight_loss2 = np.array(weightfocal) smooth = 1.e-5 smooth_tf = tf.constant(smooth, tf.float32) Y_pred = tf.cast(Y_pred, tf.float32) Y_gt = tf.cast(Y_gt, tf.float32) # Compute gen dice coef: numerator = Y_gt * Y_pred numerator = tf.reduce_sum(numerator, axis=(1, 2, 3)) denominator = Y_gt + Y_pred denominator = tf.reduce_sum(denominator, axis=(1, 2, 3)) gen_dice_coef = tf.reduce_sum(2. * (numerator + smooth_tf) / (denominator + smooth_tf), axis=0) loss1 = tf.reduce_mean(weight_loss1 * gen_dice_coef) epsilon = 1.e-5 # scale preds so that the class probas of each sample sum to 1 output = Y_pred / tf.reduce_sum(Y_pred, axis=- 1, keep_dims=True) # manual computation of crossentropy output = tf.clip_by_value(output, epsilon, 1. - epsilon) loss = -Y_gt * tf.log(output) loss = tf.reduce_mean(loss, axis=(1, 2, 3)) loss = tf.reduce_mean(loss, axis=0) loss2 = tf.reduce_mean(weight_loss2 * loss) total_loss = lamda1 * (1 - loss1) + lamda2 * loss2 return total_loss 1.7 Dice + Focal loss

Dice + Focal loss代码如下：

def dice_and_Focalloss(Y_pred, Y_gt, weightdice, weightfocal, lamda1=100, lamda2=1, gamma=4.): """ hybrid loss function from dice loss and focalloss loss=Ldice+lamda*Lfocalloss :param Y_pred:A tensor resulting from a softmax(-1,z,h,w,numclass) :param Y_gt: A tensor of the same shape as `y_pred` :param gamma:Difficult sample weight :param alpha:Sample category weight,which is shape (C,) where C is the number of classes :param lamda:trade-off between dice loss and focal loss,can set 0.1,0.5,1 :return:dicePfocalloss """ weight_loss1 = np.array(weightdice) weight_loss2 = np.array(weightfocal) smooth = 1.e-5 smooth_tf = tf.constant(smooth, tf.float32) Y_pred = tf.cast(Y_pred, tf.float32) Y_gt = tf.cast(Y_gt, tf.float32) # Compute gen dice coef: numerator = Y_gt * Y_pred numerator = tf.reduce_sum(numerator, axis=(1, 2, 3)) denominator = Y_gt + Y_pred denominator = tf.reduce_sum(denominator, axis=(1, 2, 3)) gen_dice_coef = tf.reduce_sum(2. * (numerator + smooth_tf) / (denominator + smooth_tf), axis=0) loss1 = tf.reduce_mean(weight_loss1 * gen_dice_coef) epsilon = 1.e-5 # Scale predictions so that the class probas of each sample sum to 1 output = Y_pred / tf.reduce_sum(Y_pred, axis=- 1, keepdims=True) # Clip the prediction value to prevent NaN's and Inf's output = tf.clip_by_value(output, epsilon, 1. - epsilon) # Calculate Cross Entropy cross_entropy = -Y_gt * tf.log(output) # Calculate Focal Loss loss = tf.pow(1 - output, gamma) * cross_entropy loss = tf.reduce_mean(loss, axis=(1, 2, 3)) loss = tf.reduce_mean(loss, axis=0) loss2 = tf.reduce_mean(weight_loss2 * loss) total_loss = lamda1 * (1 - loss1) + lamda2 * loss2 return total_loss 参考文献

1、【损失函数合集】超详细的语义分割中的Loss大盘点 2、Tensorflow入门教程（四十七）——语义分割损失函数总结

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