IoU概念
交并比(Intersection-over-Union，IoU)，就是交集与并集的比值，是在目标检测中常用的算法。
分子部分就是Box1与Box2交集的面积，先设为A1。分母部分是Box1与Box2并集集的面积，设为A2，其实也是Box1面积S1加上Box2面积S2再减去一个A1，即：
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IoU = \frac{A1}{A2}\\[5pt] A2 = S1 + S2 - A1\\[5pt] IoU = \frac{A1}{S1+S2-A1}
IoU=A2A1A2=S1+S2−A1IoU=S1+S2−A1A1
问题就转化为对Box与A1的求解。
如上图，为了求交集面积，只要知道上图中两个蓝色点的坐标(或另外两个角坐标)即可。
Box的表示与计算
Box有常用的两种表达方式：
COCO与VOC数据集： b o x a = ( x m i n , y m i n , x m a x , y m a x ) box_a = (x_{min},y_{min},x_{max},y_{max}) boxa=(xmin,ymin,xmax,ymax)
YOLO格式： b o x b = ( x c e n t e r , y c e n t e r , w , h ) box_b = (x_{center},y_{center},w,h) boxb=(xcenter,ycenter,w,h)
两种格式的转换关系如下：
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x_{min},y_{min},x_{max},y_{max} = round(x_{center}-(w/2.0)),round(y_{center}-(h/2.0)),round(x_{center}+(w/2.0)),round(y_{center}+(h/2.0))\\[5pt] x_{center},y_{center},w,h = round((x_{min}+x_{max})/2.0),round((y_{min}+y_{max})/2.0),round(x_{max}-x_{min}),round(y_{max}-y_{min})\\[5pt] box_a = (round(box_b[0]-(box_b[2]/2.0)) ,round(box_b[1]-(box_b[3]/2.0),round(box_b[0]+(box_b[2]/2.0),round(box_b[1]+(box_b[3]/2.0))
xmin,ymin,xmax,ymax=round(xcenter−(w/2.0)),round(ycenter−(h/2.0)),round(xcenter+(w/2.0)),round(ycenter+(h/2.0))xcenter,ycenter,w,h=round((xmin+xmax)/2.0),round((ymin+ymax)/2.0),round(xmax−xmin),round(ymax−ymin)boxa=(round(boxb[0]−(boxb[2]/2.0)),round(boxb[1]−(boxb[3]/2.0),round(boxb[0]+(boxb[2]/2.0),round(boxb[1]+(boxb[3]/2.0))
box的面积计算：
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S_a = (x_{max}-x_{min})*(y_{max}-y_{min}) = (box_a[2]-box_a[0])*(box_a[3]-box_a[1])\\[5pt] S_b = w*h = box_b[2]*box_b[3]
Sa=(xmax−xmin)∗(ymax−ymin)=(boxa[2]−boxa[0])∗(boxa[3]−boxa[1])Sb=w∗h=boxb[2]∗boxb[3]
A1交集情况
计算相交的面积只需计算出相交框的w与h。相交时有：
left = max(left1, left2)#相交框left是两个框的左上角x坐标的最大值
top = max(top1, top2)#相交框top是两个框的左上角y坐标的最大值
right =min(right1, right2)#相交框right是两个框的右下角x坐标的最大值
bottom =min(bottom1, bottom2)#相交框bottom是两个框的右下角y坐标的最大值
不相交时如情况5和6，w、h中至少有一个值等于0，使得计算面积A1也为0。即可表示为：
w = max(0, right - left)
h = max(0, bottom - top)
所以，计算IoU的代码可以如下：
def cal_iou(box1, box2):
"""
:param box1: = [left1, top1, right1, bottom1]
:param box2: = [left2, top2, right2, bottom2]
:return:
"""
left1, top1, right1, bottom1 = box1
left2, top2, right2, bottom2 = box2
# 计算每个矩形的面积
s1 = (right1 - left1) * (bottom1 - top1) # b1的面积
s2 = (right2 - left2) * (bottom2 - top2) # b2的面积
# 计算相交矩形
left = max(left1, left2)
top = max(top1, top2)
right = min(right1, right2)
bottom = min(bottom1, bottom2)
# 相交框的w,h
w = max(0, right - left)
h = max(0, bottom - top)
a1 = w * h # C∩G的面积
a2 = s1 + s2 - a1
iou = a1 / a2 #iou = a1/ (s1 + s2 - a1)
return iou
参考：
Python极简实现IoU
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