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：
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IoU = frac{mid Acap Bmid}{mid Acup Bmid}
IoU=∣A∪B∣∣A∩B∣
A、B的坐标如下图：
交集的左上角坐标为：
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x_{1} = maxbig(x_{a1}, x_{b1})
x1=max(xa1,xb1)
y 1 = m a x ( y a 1 , y b 1 ) y_{1} = maxbig(y_{a1}, y_{b1}) y1=max(ya1,yb1)
交集的右下角坐标为：
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x_{2} = minbig(x_{a2}, x_{b2})
x2=min(xa2,xb2)
y 2 = m i n ( y a 2 , y b 2 ) y_{2} = minbig(y_{a2}, y_{b2}) y2=min(ya2,yb2)
交集部分的宽、高、面积：
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width = maxbig(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 = maxbig(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：
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S_{A} = big(x_{a2}-x_{a1})cdotbig(y_{a2}-y_{a1})
SA=(xa2−xa1)⋅(ya2−ya1)
B框的面积：
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S_{B} = big(x_{b2}-x_{b1})cdotbig(y_{b2}-y_{b1})
SB=(xb2−xb1)⋅(yb2−yb1)
并集部分：
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S_{A cup B} = S_{A} + S_{B} - S_{A cap B}
SA∪B=SA+SB−SA∩B
交并比为：
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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], box1[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))
