IoU 计算

假设：预测框坐标为$(x_1,y_1,w_1,h_1)$，真实目标框坐标为$(x_2,y_2,w_2,h_1)$

计算过程：

判断预测框与真实框时候重合

$\begin{cases} x_{\min}=\min(x_1,x_2) \\ x_{\max}=\max(x_1+w_1,x_2+w_2) \\ y_{\min}=\min(y_1,y_2) \\ y_{\max}=\max(y_1+h_1,y_2+h_2) \end{cases} \\ \Rightarrow \begin{cases} width = w_1 + w_2 - (x_{\max}-x_{\min}) \quad \text{if$\quad width\leq0 \Rightarrow \quad$预测框与真实框不重合} \\ heigh = h_1 + h_2 - (y_{\max}-y_{\min}) \quad \text{if$\quad heigh\leq0 \Rightarrow \quad$预测框与真实框不重合} \end{cases}$

计算重合的面积以及IoU

$Area = width \times heigh \\ Area1 = w_1 \times h_1 \\ Area2 = w_2 \times w_2 \\ IoU = \cfrac{Area}{Area1 + Area2 -Area}$

Python程序实现：

def IOU(Prediction, GroundTruth):

    x1 = Prediction[0]
    y1 = Prediction[1]
    width1 = Prediction[2]
    height1 = Prediction[3]

    x2 = GroundTruth[0]
    y2 = GroundTruth[1]
    width2 = GroundTruth[2]
    height2 = GroundTruth[3]

    endx = max(x1+width1, x2+width2)
    startx = min(x1, x2)
    width = width1 + width2 - (endx - startx)

    endy = max(y1+height1, y2+height2)
    starty = min(y1, y2)
    height = height1 + height2 - (endy - starty)

    if width <=0 or height<=0:
        ratio = 0
    else:
        Area = width * height
        Area1 = width1 * height1
        Area2 = width2 * height2
        ratio = (Area * 1. / (Area1 + Area2 - Area)).item()

    return ratio

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