Introduction

在目标检测中，我们需要定位出目标的位置，而我们的算法不可能百分百跟人工标注的数据完全匹配，因此需要一种衡量目标定位精度的标准。

IoU（Intersection over Union）是一种常见的用于衡量目标定位精度的标准，可以理解为重叠度，是一种简单的测量标准，只要是在输出中得出一个预测范围(bounding box)的任务都可以用IoU来进行测量。

IoU

如上图所示，ground-truth和predicted的存在误差，绿色框是人为标记的正确结果，红色框是算法预测出来的结果，IoU要做的就是在这两个结果中测量算法的准确度，它定义了两个bounding box的重叠度 ，如下图所示：

IoU

IoU=A⋂BA⋃B=A⋂BA+B−A⋂BIoU = \frac {A\bigcap B}{A\bigcup B}=\frac{A\bigcap B}{A+B-A\bigcap B}

就是矩形框A、B的重叠面积，占 A⋃BA\bigcup B 的面积比例。

一般来说，IoU>0.5IoU>0.5 就可以被认为一个不错的结果，IoU>0.7IoU>0.7 结果就非常不错了，可以参见下图

IoU examples

实现

因为IoU的思想很简单，Python实现可以参考[1]：

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def bb_intersection_over_union(boxA, boxB):
	# determine the (x, y)-coordinates of the intersection rectangle
	xA = max(boxA[0], boxB[0])
	yA = max(boxA[1], boxB[1])
	xB = min(boxA[2], boxB[2])
	yB = min(boxA[3], boxB[3])
 
	# compute the area of intersection rectangle
	interArea = (xB - xA + 1) * (yB - yA + 1)
 
	# compute the area of both the prediction and ground-truth
	# rectangles
	boxAArea = (boxA[2] - boxA[0] + 1) * (boxA[3] - boxA[1] + 1)
	boxBArea = (boxB[2] - boxB[0] + 1) * (boxB[3] - boxB[1] + 1)
 
	# compute the intersection over union by taking the intersection
	# area and dividing it by the sum of prediction + ground-truth
	# areas - the interesection area
	iou = interArea / float(boxAArea + boxBArea - interArea)
 
	# return the intersection over union value
	return iou

在Pytorch中，可以写成如下形式：

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import torch 
def bbox_iou(box1, box2):
    """
    Returns the IoU of two bounding boxes 
    """
    #Get the coordinates of bounding boxes
    b1_x1, b1_y1, b1_x2, b1_y2 = box1[:,0], box1[:,1], box1[:,2], box1[:,3]
    b2_x1, b2_y1, b2_x2, b2_y2 = box2[:,0], box2[:,1], box2[:,2], box2[:,3]
    
    #get the corrdinates of the intersection rectangle
    inter_rect_x1 =  torch.max(b1_x1, b2_x1)
    inter_rect_y1 =  torch.max(b1_y1, b2_y1)
    inter_rect_x2 =  torch.min(b1_x2, b2_x2)
    inter_rect_y2 =  torch.min(b1_y2, b2_y2)
    
    #Intersection area
    inter_area = torch.clamp(inter_rect_x2 - inter_rect_x1 + 1, min=0) * torch.clamp(inter_rect_y2 - inter_rect_y1 + 1, min=0)

    #Union Area
    b1_area = (b1_x2 - b1_x1 + 1)*(b1_y2 - b1_y1 + 1)
    b2_area = (b2_x2 - b2_x1 + 1)*(b2_y2 - b2_y1 + 1)
    
    iou = inter_area / (b1_area + b2_area - inter_area)
    
    return iou

Reference

[1]Intersection over Union (IoU) for object detection