文章目錄

• 知識鋪墊
• 1. Dice系數(shù)和IOU
• 2.敏感性（=Recall）、特異性和精確度（=precision=PPV)
• • 2.1 敏感性（召回率）和特異性
  • 2.2 敏感性和特異性之間的關(guān)系
  • 2.3 Recall和Precision之間的關(guān)系
• 3. F1

知識鋪墊

首先，對于像素點(diǎn)，我們要知道，當(dāng)預(yù)測的像素點(diǎn)類別和其真實(shí)類別不同或者相同時，我們可以用混淆矩陣來表示，如下圖：

1. Dice系數(shù)和IOU

解釋鏈接
由于網(wǎng)上給的Dice系數(shù)的求解代碼基本上都是batch_size=1的，當(dāng)batch_size>1的時候，就沒法用了，因此在這里對網(wǎng)上流行的代碼和自己改的代碼分別進(jìn)行總結(jié)。

Dice系數(shù)的計算公式如下：
$$Dice=\frac{2\times TP}{(TP+FN)+(TP+FP)}$$

def dice_coef(output, target): # batch_size=1smooth = 1e-5#output = torch.sigmoid(output).view(-1).data.cpu().numpy()output=torch.sigmoid(output)output[output > 0.5] = 1 #將概率輸出變?yōu)橛跇?biāo)簽相匹配的矩陣output[output <= 0.5] = 0#target = target.view(-1).data.cpu().numpy()intersection = (output * target).sum() = TP# \符號有換行的作用return (2. * intersection + smooth) / \(output.sum() + target.sum() + smooth) # dice=2*TP/(TP+FN)+(TP+FP) def dice_coef(output, target): # Batch_size>1時smooth = 1e-5#output = torch.sigmoid(output).view(-1).data.cpu().numpy()output=torch.sigmoid(output).data.cpu().numpy()output[output > 0.5] = 1 #將概率輸出變?yōu)橛跇?biāo)簽相匹配的矩陣output[output <= 0.5] = 0# target = target.view(-1).data.cpu().numpy()target = target.data.cpu().numpy()dice=0.# ipdb.set_trace() # 用于斷掉調(diào)試if len(output)>1:# 如果樣本量>1，則逐樣本累加for i in range(len(output)):intersection = (output[i] * target[i]).sum()dice += (2. * intersection + smooth)/(output[i].sum() + target[i].sum() + smooth)else:intersection = (output * target).sum() # 一個數(shù)字,=TPdice = (2. * intersection + smooth) /(output.sum() + target.sum() + smooth)return dice

IOU的計算公式如下：
$$Dice=\frac{TP}{TP+FN+FP}$$

# batch_size = 1 def iou_score(output, target):smooth = 1e-5if torch.is_tensor(output):output = torch.sigmoid(output).data.cpu().numpy()if torch.is_tensor(target):target = target.data.cpu().numpy()output_ = output > 0.5target_ = target > 0.5intersection = (output_ & target_).sum()union = (output_ | target_).sum()return (intersection + smooth) / (union + smooth) #batch_size > 1 def iou_score(output, target):smooth = 1e-5if torch.is_tensor(output):output = torch.sigmoid(output).data.cpu().numpy()if torch.is_tensor(target):target = target.data.cpu().numpy()output_ = output > 0.5target_ = target > 0.5# intersection = (output_ & target_).sum()# union = (output_ | target_).sum()iou = 0.if len(output)>1:for i in range(len(output)):union = (output_[i] | target_[i]).sum()intersection = (output_[i] & target_[i]).sum()iou += (intersection + smooth) / (union + smooth)else:intersection = (output_ & target_).sum()union = (output_ | target_).sum()iou = (intersection + smooth) / (union + smooth)return iou

2.敏感性（=Recall）、特異性和精確度（=precision=PPV)

2.1 敏感性（召回率）和特異性

Recall公式

def get_sensitivity(output, gt): # 求敏感度 se=TP/(TP+FN)SE = 0.output = output > 0.5gt = gt > 0.5TP = ((output==1).byte() + (gt==1).byte()) == 2FN = ((output==0).byte() + (gt==1).byte()) == 2#wfy:batch_num>1時，改進(jìn)if len(output)>1:for i in range(len(output)):SE += float(torch.sum(TP[i])) / (float(torch.sum(TP[i]+FN[i])) + 1e-6)else:SE = float(torch.sum(TP)) / (float(torch.sum(TP+FN)) + 1e-6) #原本只用這一句#SE = float(torch.sum(TP)) / (float(torch.sum(TP + FN)) + 1e-6) # 原本只用這一句return SE #返回batch中所有樣本的SE和

特異性：

def get_specificity(SR, GT, threshold=0.5):#求特異性 sp=TN/(FP+TN)SR = SR > threshold #得到true和falseGT = GT > thresholdSP=0.# wfy# TN : True Negative# FP : False PositiveTN = ((SR == 0).byte() + (GT == 0).byte()) == 2FP = ((SR == 1).byte() + (GT == 0).byte()) == 2#wfy:batch_num>1時，改進(jìn)if len(SR)>1:for i in range(len(SR)):SP += float(torch.sum(TN[i])) / (float(torch.sum(TN[i] + FP[i])) + 1e-6)else:SP = float(torch.sum(TN)) / (float(torch.sum(TN + FP)) + 1e-6) # 原本只用這一句## SP = float(torch.sum(TN)) / (float(torch.sum(TN + FP)) + 1e-6)return SP

這兩個指標(biāo)在醫(yī)療領(lǐng)域很常用，而在機(jī)器學(xué)習(xí)領(lǐng)域常用的是Recall和Precision。

2.2 敏感性和特異性之間的關(guān)系

暫略

2.3 Recall和Precision之間的關(guān)系

ppv=precision

def ppv(output, target): #陽性預(yù)測值，準(zhǔn)確率（precision）pr = TP/(TP+FP)smooth = 1e-5if torch.is_tensor(output):output = torch.sigmoid(output).data.cpu().numpy()if torch.is_tensor(target):target = target.data.cpu().numpy()ppv=0.if len(output)>1:for i in range(len(output)):intersection = (output[i] * target[i]).sum()ppv += (intersection + smooth)/(output[i].sum() + smooth)else:intersection = (output * target).sum() # 一個數(shù)字,=TPppv = (intersection + smooth)/(output.sum() + smooth)# intersection = (output * target).sum() # TPreturn ppv

3. F1

def get_F1(output, gt):se = get_sensitivity(output, gt)pc = get_precision(output, gt)f1 = 2*se*pc / (se+pc+1e-6)return f1

總結(jié)

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