Table of contents
2. The connection between dice and iou
3.4 The relationship curve between dice and iou
1 Introduction
Both dice and iou are measures of the similarity between two sets
dice calculation formula:
IOU calculation formula:
Set comprehension for iou:
Iou is actually the ratio of the overlap part and the union part of the two regions, that is, the intersection/union of the two sets
The denominator of dice is not a union, because the denominator of dice is the sum of two areas, A+B = A + B - A∩B, so the denominator of dice is actually minus one A∩B, so let the numerator A∩B (intersection) expands by 2 times
2. The connection between dice and iou
If the relationship between the two collections is divided a little more finely, this is the form:
Then A∩B = TP, A∪B = FN + TP + FP, A+B = FN + TP +TP + FP
dice ：
iou ：
Then according to the deformation, it can be concluded that:
3. Code implementation
|A ∩ B| = sum of A * B = sum of products of two areas
|A| + |B| = sum of A + B = sum of two regions added
|A∪B| = |A| + |B| - |A ∩ B| = sum of intersection of two regions - sum of multiplication of two regions
3.1 dice
implementation of dice
# Dice
def Dice(pred,true):
intersection = pred * true # 计算交集 pred ∩ true
temp = pred + true # pred + true
smooth = 1e-8 # 防止分母为 0
dice_score = 2*intersection.sum() / (temp.sum() + smooth)
return dice_score
intersection is the intersection of two areas, that is, the product of two areas
temp is the sum of the two areas, (Note: this is not a union, because the intersecting part is not subtracted)
3.2 iou
implementation of iou
# Iou
def Iou(pred,true):
intersection = pred * true # 计算交集 pred ∩ true
temp = pred + true # pred + true
union = temp - intersection # 计算并集：A ∪ B = A + B - A ∩ B
smooth = 1e-8 # 防止分母为 0
iou_score = intersection.sum() / (union.sum() + smooth)
return iou_score
intersection is the intersection of two areas, that is, the product of two areas
temp is the sum of the two areas, (Note: this is not a union, because the intersecting part is not subtracted)
union is the union of two regions
3.3 test
predict:
# prediction
predict = torch.tensor([0.01,0.03,0.02,0.02,0.05,0.12,0.09,0.07,0.89,0.85,0.88,0.91,0.99,0.97,0.95,0.97]).reshape(1,1,4,4)
'''
tensor([[[[0.0100, 0.0300, 0.0200, 0.0200],
[0.0500, 0.1200, 0.0900, 0.0700],
[0.8900, 0.8500, 0.8800, 0.9100],
[0.9900, 0.9700, 0.9500, 0.9700]]]])
'''label：
# label
label = torch.tensor([0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1]).reshape(1,1,4,4)
'''
tensor([[[[0, 0, 0, 0],
[0, 0, 0, 0],
[1, 1, 1, 1],
[1, 1, 1, 1]]]])
'''Calculation results:
The formula shows that the relationship between dice and iou is:
Verification shows that:
Note: Some slight differences are caused by smooth
3.4 The relationship curve between dice and iou
According to the formula, the relationship between dice and iou is as follows:
The relationship curve is shown in the figure:
4. Code
import os
os.environ['KMP_DUPLICATE_LIB_OK'] = 'True'
import torch
import numpy as np
import matplotlib.pyplot as plt
# prediction
predict = torch.tensor([0.01,0.03,0.02,0.02,0.05,0.12,0.09,0.07,0.89,0.85,0.88,0.91,0.99,0.97,0.95,0.97]).reshape(1,1,4,4)
'''
tensor([[[[0.0100, 0.0300, 0.0200, 0.0200],
[0.0500, 0.1200, 0.0900, 0.0700],
[0.8900, 0.8500, 0.8800, 0.9100],
[0.9900, 0.9700, 0.9500, 0.9700]]]])
'''
# label
label = torch.tensor([0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1]).reshape(1,1,4,4)
'''
tensor([[[[0, 0, 0, 0],
[0, 0, 0, 0],
[1, 1, 1, 1],
[1, 1, 1, 1]]]])
'''
# Dice
def Dice(pred,true):
intersection = pred * true # 计算交集 pred ∩ true
temp = pred + true # pred + true
smooth = 1e-8 # 防止分母为 0
dice_score = 2*intersection.sum() / (temp.sum() + smooth)
return dice_score
# Iou
def Iou(pred,true):
intersection = pred * true # 计算交集 pred ∩ true
temp = pred + true # pred + true
union = temp - intersection # 计算并集：A ∪ B = A + B - A ∩ B
smooth = 1e-8 # 防止分母为 0
iou_score = intersection.sum() / (union.sum() + smooth)
return iou_score
# dice 和 iou 的换算
def dice_and_iou(x):
y = x / (2 - x)
return y
dice = np.arange(0,1,0.001)
iou = dice_and_iou(dice)
plt.plot(dice,iou)
plt.xlabel('dice')
plt.ylabel('iou')
plt.show()