IoU(交并比)的理解及python实现
1. 概述
交并比(Intersection over Union, IoU)是目标检测、语义分割、追踪等任务最常用的评估指标。交并比，顾名思义是两区域交集与并集的比值，当两区域完全重叠时交并比最大，为1；当两区域完全不重叠时交并比最小，为0。
2. IoU计算公式
要计算候选框(candidate bound) A与真实框(ground truth bound) B的交并比。
B1框与B2框的IoU计算公式为：
I o U = ∣ A ∩ B ∣ ∣ A ∪ B ∣ IoU = \frac{\mid A\cap B\mid}{\mid A\cup B\mid} IoU=∣A∪B∣∣A∩B∣
A、B的坐标如下图：
交集的左上角坐标为：
x 1 = m a x ( x a 1 , x b 1 ) x_{1} = max\big(x_{a1}, x_{b1}) x1=max(xa1,xb1)
y 1 = m a x ( y a 1 , y b 1 ) y_{1} = max\big(y_{a1}, y_{b1}) y1=max(ya1,yb1)
交集的右下角坐标为：
x 2 = m i n ( x a 2 , x b 2 ) x_{2} = min\big(x_{a2}, x_{b2}) x2=min(xa2,xb2)
y 2 = m i n ( y a 2 , y b 2 ) y_{2} = min\big(y_{a2}, y_{b2}) y2=min(ya2,yb2)
交集部分的宽、高、面积：
w i d t h = m a x ( x 2 − x 1 , 0 ) width = max\big(x_{2}-x_{1}, 0) width=max(x2−x1,0)
h e i g h t = m a x ( y 2 − y 1 , 0 ) height = max\big(y_{2}-y_{1}, 0) height=max(y2−y1,0)
S A ∩ B = w i d t h ∗ h e i g h t S_{A \cap B} = width * height SA∩B=width∗height
A框的面积：
S A = ( x a 2 − x a 1 ) ⋅ ( y a 2 − y a 1 ) S_{A} = \big(x_{a2}-x_{a1})\cdot\big(y_{a2}-y_{a1}) SA=(xa2−xa1)⋅(ya2−ya1)
B框的面积：
S B = ( x b 2 − x b 1 ) ⋅ ( y b 2 − y b 1 ) S_{B} = \big(x_{b2}-x_{b1})\cdot\big(y_{b2}-y_{b1}) SB=(xb2−xb1)⋅(yb2−yb1)
并集部分：
S A ∪ B = S A + S B − S A ∩ B S_{A \cup B} = S_{A} + S_{B} - S_{A \cap B} SA∪B=SA+SB−SA∩B
交并比为：
I o U = S A ∩ B S A ∪ B IoU = \frac{S_{A \cap B}}{S_{A \cup B}} IoU=SA∪BSA∩B
3. IoU公式的python实现
def IoU(box1, box2) -> float:
"""
IOU, Intersection over Union
:param box1: list, 第一个框的两个坐标点位置 box1[x1, y1, x2, y2]
:param box2: list, 第二个框的两个坐标点位置 box2[x1, y1, x2, y2]
:return: float, 交并比
"""
weight = max(min(box1[2], box2[2]) - max(box1[0], box2[0]), 0)
height = max(min(box1[3], box2[3]) - max(box1[1], box2[1]), 0)
s_inter = weight * height
s_box1 = (box1[2] - box1[0]) * (box1[3] - box1[1])
s_box2 = (box2[2] - box2[0]) * (box2[3] - box2[1])
s_union = s_box1 + s_box2 - s_inter
return s_inter / s_union
if __name__ == '__main__':
box1 = [0, 0, 50, 50]
box2 = [0, 0, 100, 100]
print('IoU is %f' % IoU(box1, box2))