Intersection over Union(IoU) algorithms

　　IoU算法可用与评估两个多维度数据的相似度，举一个实际应用，做CV，目标检测，我们需要评估模型的识别准确率，不同于二元类问题，普通的评估算法不合适，于是用到了这个算法，这个算法简单易懂，评估效果也不错。

　　这里主要讨论如何计算并评估两个矩形相交程度。有空再训练一个目标检测器，来试试水。。

　　第一种对于数据形状是这样的 $ (x_{top-left}, y_{top-left}, w, h) $，意思是：给出了起始坐标，矩形沿着 $ w, h $ 扩展开。

　　算法实现：

double IoU(int*a, int*b)
{
    int overlap_w = min(a[0] + a[2], b[0] + b[2]) - max(a[0], b[0]);
    int overlap_h = min(a[1] + a[3], b[1] + b[3]) - max(a[1], b[1]);
    int overlap_s = overlap_w*overlap_h;
    return overlap_s / double(a[2]*a[3] + b[2]*b[3] - overlap_s);
}

　　第二种数据形状是这样的 $ (x_{top-left}, y_{top-left}, x_{right-down}, y_{right-down}) $，意思是：给出了起始坐标和终点坐标，如图：

　　

　　算法实现：

double IoU_2(int*a, int*b)
{
    int overlap_w = min(a[2], b[2]) - max(a[0], b[0]);
    int overlap_h = min(a[3], b[3]) - max(a[1], b[1]);
    int overlap_s = overlap_w*overlap_h;
    return overlap_s / double((a[2] - a[0])*(a[3] - a[1]) + (b[2] - b[0])*(b[3] - b[1]) - overlap_s);
}

　　用这几组数据测试一下：

1: [39, 63, 203, 112], [54, 66, 198, 114]
2: [49, 75, 203, 125], [42, 78, 186, 126]
3: [31, 69, 201, 125], [18, 63, 235, 135]
4: [50, 72, 197, 121], [54, 72, 198, 120]
5: [35, 51, 196, 110], [36, 60, 180, 108]

　　output:

0.825758
0.795771
=====================
0.809624
0.787838
=====================
0.791962
0.609319
=====================
0.947743
0.946628
=====================
0.79667
0.727656
=====================

　　参考：

　　　　1.https://www.pyimagesearch.com/2016/11/07/intersection-over-union-iou-for-object-detection/

　　　　2.https://en.wikipedia.org/wiki/Jaccard_index