Basis of target detection (IOU)

Fundamentals of target detection （IoU）

What is? IOU?

IOU（ Occurring simultaneously than Intersection over Union） It's a term , Used to describe the degree of overlap between two boxes . The larger the overlap area ,IOU The bigger it is .

IOU It is mainly used in applications related to object detection , In this application , Our training model outputs an external rectangle that completely surrounds the target . for example , In the diagram above , We have a green box and a blue box . The green box represents the real box , The blue box represents the prediction box of our model . The purpose of the training model is to continuously improve the output of its prediction frame , Until the blue and green boxes completely overlap , Between two boxes IOU be equal to 1.

IOU It is often used in non maximum suppression , Multiple prediction frames of the same object are eliminated based on the confidence of the detection frame , To ensure the prediction box with the highest retention reliability .

IOU Calculation formula

In target detection , Let's assume that the box 1 from [x1,y1,x2,y2] Express , Same box 2 from [x3,y3,x4,y4] Express , Here's the picture 1 Shown .

Figure 1

here IOU The calculation formula of is as follows :
$$IoU=\frac{AreaofIntersectionoftwoboxes}{AreaofUnionoftwoboxes}$$
Use pictures 2 Shown by the following :

Figure 2

Next, we calculate the area corresponding to the intersection and union of the corresponding rectangular box step by step .

Calculate the intersection area

Intuitive to see , The intersection of two rectangular boxes has many situations , Let's intuitively observe the following figure 3, Obviously, the lower right two rectangular boxes completely coincide, and the intersection area is the largest .

First, we express the coordinates of the intersecting rectangles as [x_inter1,y_inter1,x_inter2,y_inter2], Represent the coordinates of the upper left corner and the lower right corner of the intersecting rectangle respectively .

Then start by defining the reference coordinate system . We use +X The axis is moving to the right ,+Y Computer graphics Convention for axial downward movement .

In order to calculate the coordinates of the upper left corner of the intersecting rectangle , We compare the upper left corner of each box . We can see from the example above ,x_inter1 You can find which box is closer to the right in the upper left corner . Similarly , You can find... By looking at which box's upper left corner is lower than the other box y_inter1. Mathematically speaking , They can be summarized as ：$x\_inter1=max(x1,x3)$,$y$_$inter1=max(y1,y3)$

To calculate the coordinates of the lower right corner of the intersecting rectangle , We compare the lower right corner of each box .

x_inter2 You can find by looking at which box's lower right corner is more left .

Similarly , You can find... By looking at which box's lower right corner is higher than the other box y_inter2.

Similarly , They can be summarized as ：$x\_inter2=max(x2,x4)$,$y$_$inter2=max(y2,y4)$

Now we have the coordinates of the intersecting rectangles , Then the area of the intersection is the area of the rectangle .（ in application , We will use the absolute values of width and height , To ensure that even if the order of boxes changes , The width and height are still positive ; namely , If x_inter1>x_inter2, We will still get a positive value for the width ）
$$\begin{gathered} width\_inter=(x\_inter2-x\_inter1) \\ height\_inter=(y\_inter2-y\_inter1) \\ area\_inter=width\_inter\ast height\_inter \end{gathered}$$

Calculate Union area

The union of boxes is the total area covered by two boxes , Pictured 2 Shown .

To find the total area , We first calculate the area of each rectangular box
$$\begin{gathered} width\_box1=(x\_2-x\_1) \\ height\_box1=(y\_2-y\_1) \\ width\_box2=(x\_4-x\_3) \\ height\_box2=(y\_4-y\_3) \\ area\_box1=width\_box1\ast height\_box1 \\ area\_box2=width\_box2\ast height\_box2 \end{gathered}$$

If we look at the total area covered by the two boxes , We will see that both boxes cover the part of the intersecting rectangle , That is, the area of the intersecting rectangle is included in box1 Areas and box2 In the region .

Because we only want to calculate the common intersection area once , We can subtract the intersection area we calculated from the total area of the two boxes . namely :
$$area\_union=area\_box1+area\_box2-area\_intersection$$

Calculate the ratio of intersection and union

Through the above calculation formula , We calculate the area of the corresponding intersection and union of two rectangular boxes , At this time, the rectangle is IOU The calculation formula is as follows :
$$IoU=\frac{area\_inter}{area\_union}$$

Observe the above formula , It can be concluded as follows :

• Two box IOU Can take 0 To 1 Any value between .
• If the two boxes do not intersect , Then their intersection area will be 0, therefore IOU Will also be 0.
• If two completely overlapping rectangular boxes , Then the area of the intersection will be equal to the area of its Union , therefore IOU Will be for 1

Code implementation

def IOU(box1, box2):
    x1, y1, x2, y2 = box1
    x3, y3, x4, y4 = box2
    x_inter1 = max(x1, x3)
    y_inter1 = max(y1, y3)
    x_inter2 = min(x2, x4)
    y_inter2 = min(y2, y4)
    width_inter = abs(x_inter2 - x_inter1)
    height_inter = abs(y_inter2 - y_inter1)
    area_inter = width_inter * height_inter
    width_box1 = abs(x2 - x1)
    height_box1 = abs(y2 - y1)
    width_box2 = abs(x4 - x3)
    height_box2 = abs(y4 - y3)
    area_box1 = width_box1 * height_box1
    area_box2 = width_box2 * height_box2
    area_union = area_box1 + area_box2 - area_inter
    iou = area_inter / area_union
    return iou

• function IOU Accept two boxes , namely box1 and box2 As input . The data in each box is a containing [x1,y1,x2,y2] A list of , It represents the coordinates of the upper left corner and the lower right corner .
• As mentioned earlier , Let's first calculate the area of intersecting rectangles , Then the area of the Union .
• abs The function is python The built-in function used to calculate the absolute value in . This ensures that we will never calculate the result with negative width or negative height .
• Back to IOU yes float Type value , Be situated between 0 and 1 Between .

The operation results are as follows :

Reference article