非极大值抑制（Non-Maximum-Suppression）

注意看哦，有两个版本的。

理论基础

         说实话，讲理论基础实在不是我的强项，但是还是得硬着头皮来讲，希望我的讲解不至于晦涩难懂。

         非极大值抑制，简称为NMS算法。是一种获取局部最大值的有效方法。在3领域中，假设一个行向量的长度为w，从左向右，由第一个到第w个和其3领域中的数值进行比对。

如果某个i大于i+1并且小于i-1，则其为一个绝不最大值，同时也就意味着i+1不是一个局部最大值，所以将i移动2个步长，从i+2开始继续向后进行比较判断。如果某个i不满足上述条件，则将i+1，继续对i+1进行比对。当比对到最后一个w时，直接将w设置为局部最大值。算法流程如下图所示。

应用范围

         非极大值抑制NMS在目标检测，定位等领域是一种被广泛使用的方法。对于目标具体位置定位过程，不管是使用sw(sliding Window)还是ss(selective search)方法，都会产生好多的候选区域。实际看到的情形就是好多区域的交叉重叠，难以满足实际的应用。如下图所示。

针对该问题有3种传统的解决思路。

         第一种，选取好多矩形框的交集，即公共区域作为最后的目标区域。

         第二种，选取好多矩形框的并集，即所有矩形框的最小外截矩作为目标区域。当然这里也不是只要相交就直接取并集，需要相交的框满足交集占最小框的面积达到一定比例(也就是阈值)才合并。

         第三种,也就是本文的NMS，简单的说，对于有相交的就选取其中置信度最高的一个作为最后结果，对于没相交的就直接保留下来，作为最后结果。

         总体来说，3种处理思路都各有千秋，不能一概评论哪种好坏。各种顶会论文也会选择不同的处理方法。

#include 
#include 
#include 
#include 
// 新版本写在下面文件中：
#include 
//#include "opencv2/features2d/features2d.hpp"
#include

using namespace std;
using namespace cv;


void nms(
         const std::vector& srcRects,
         std::vector& resRects,
         float thresh
         )
{
    resRects.clear();
    
    const size_t size = srcRects.size();
    if (!size)
    {
        return;
    }
    
    // Sort the bounding boxes by the bottom - right y - coordinate of the bounding box
    std::multimap idxs;
    for (size_t i = 0; i < size; ++i)
    {
        idxs.insert(std::pair(srcRects[i].br().y, i));
    }
    
    // keep looping while some indexes still remain in the indexes list
    while (idxs.size() > 0)
    {
        // grab the last rectangle
        auto lastElem = --std::end(idxs);
        const cv::Rect& rect1 = srcRects[lastElem->second];
        
        resRects.push_back(rect1);
        
        idxs.erase(lastElem);
        
        for (auto pos = std::begin(idxs); pos != std::end(idxs); )
        {
            // grab the current rectangle
            const cv::Rect& rect2 = srcRects[pos->second];
            
            float intArea = (rect1 & rect2).area();
            float unionArea = rect1.area() + rect2.area() - intArea;
            float overlap = intArea / unionArea;
            
            // if there is sufficient overlap, suppress the current bounding box
            if (overlap > thresh)
            {
                pos = idxs.erase(pos);
            }
            else
            {
                ++pos;
            }
        }
    }
}


/**
 *******************************************************************************
 *
 *   main
 *
 *******************************************************************************
 */
int main(int argc, char* argv[])
{
    std::vector srcRects;
    
    /*
     // Test 1
     srcRects.push_back(cv::Rect(cv::Point(114, 60), cv::Point(178, 124)));
     srcRects.push_back(cv::Rect(cv::Point(120, 60), cv::Point(184, 124)));
     srcRects.push_back(cv::Rect(cv::Point(114, 66), cv::Point(178, 130)));*/
    
    /*
     // Test 2
     srcRects.push_back(cv::Rect(cv::Point(12, 84), cv::Point(140, 212)));
     srcRects.push_back(cv::Rect(cv::Point(24, 84), cv::Point(152, 212)));
     srcRects.push_back(cv::Rect(cv::Point(12, 96), cv::Point(140, 224)));
     srcRects.push_back(cv::Rect(cv::Point(36, 84), cv::Point(164, 212)));
     srcRects.push_back(cv::Rect(cv::Point(24, 96), cv::Point(152, 224)));
     srcRects.push_back(cv::Rect(cv::Point(24, 108), cv::Point(152, 236)));*/
    
    // Test 3
    srcRects.push_back(cv::Rect(cv::Point(12, 30), cv::Point(76, 94)));
    srcRects.push_back(cv::Rect(cv::Point(12, 36), cv::Point(76, 100)));
    srcRects.push_back(cv::Rect(cv::Point(72, 36), cv::Point(200, 164)));
    srcRects.push_back(cv::Rect(cv::Point(84, 48), cv::Point(212, 176)));
    
    cv::Size size(0, 0);
    for (const auto& r : srcRects)
    {
        size.width = std::max(size.width, r.x + r.width);
        size.height = std::max(size.height, r.y + r.height);
    }
    
    cv::Mat img = cv::Mat(2 * size.height, 2 * size.width, CV_8UC3, cv::Scalar(0, 0, 0));
    
    cv::Mat imgCopy = img.clone();
    
    
    
    for (auto r : srcRects)
    {
        cv::rectangle(img, r, cv::Scalar(0, 0, 255), 2);
    }
    
    cv::namedWindow("before", cv::WINDOW_NORMAL);
    cv::imshow("before", img);
    cv::waitKey(1);
    
    std::vector resRects;
    nms(srcRects, resRects, 0.3f);
    
    for (auto r : resRects)
    {
        cv::rectangle(imgCopy, r, cv::Scalar(0, 255, 0), 2);
    }
    
    cv::namedWindow("after", cv::WINDOW_NORMAL);
    cv::imshow("after", imgCopy);
    
    cv::waitKey(0);
    
    return 0;
}

实验结果：

#include 
#include 
#include 
#include 
// 新版本写在下面文件中：
#include 
//#include "opencv2/features2d/features2d.hpp"
#include

using namespace std;
using namespace cv;



static void sort(int n, const vector x, vector indices)
{
    // 排序函数，排序后进行交换的是indices中的数据
    // n：排序总数// x：带排序数// indices：初始为0~n-1数目
    
    int i, j;
    for (i = 0; i < n; i++)
        for (j = i + 1; j < n; j++)
        {
            if (x[indices[j]] > x[indices[i]])
            {
                //float x_tmp = x[i];
                int index_tmp = indices[i];
                //x[i] = x[j];
                indices[i] = indices[j];
                //x[j] = x_tmp;
                indices[j] = index_tmp;
            }
        }
}



int nonMaximumSuppression(int numBoxes, const vector points,const vector oppositePoints,
                          const vector score,	float overlapThreshold,int& numBoxesOut, vector& pointsOut,
                          vector& oppositePointsOut, vector scoreOut)
{
    // 实现检测出的矩形窗口的非极大值抑制nms
    // numBoxes：窗口数目// points：窗口左上角坐标点// oppositePoints：窗口右下角坐标点// score：窗口得分
    // overlapThreshold：重叠阈值控制// numBoxesOut：输出窗口数目// pointsOut：输出窗口左上角坐标点
    // oppositePoints：输出窗口右下角坐标点// scoreOut：输出窗口得分
    int i, j, index;
    vector box_area(numBoxes);				// 定义窗口面积变量并分配空间
    vector indices(numBoxes);					// 定义窗口索引并分配空间
    vector is_suppressed(numBoxes);			// 定义是否抑制表标志并分配空间
    // 初始化indices、is_supperssed、box_area信息
    for (i = 0; i < numBoxes; i++)
    {
        indices[i] = i;
        is_suppressed[i] = 0;
        box_area[i] = (float)( (oppositePoints[i].x - points[i].x + 1) *(oppositePoints[i].y - points[i].y + 1));
    }
    // 对输入窗口按照分数比值进行排序，排序后的编号放在indices中
    sort(numBoxes, score, indices);
    for (i = 0; i < numBoxes; i++)                // 循环所有窗口
    {
        if (!is_suppressed[indices[i]])           // 判断窗口是否被抑制
        {
            for (j = i + 1; j < numBoxes; j++)    // 循环当前窗口之后的窗口
            {
                if (!is_suppressed[indices[j]])   // 判断窗口是否被抑制
                {
                    int x1max = max(points[indices[i]].x, points[indices[j]].x);                     // 求两个窗口左上角x坐标最大值
                    int x2min = min(oppositePoints[indices[i]].x, oppositePoints[indices[j]].x);     // 求两个窗口右下角x坐标最小值
                    int y1max = max(points[indices[i]].y, points[indices[j]].y);                     // 求两个窗口左上角y坐标最大值
                    int y2min = min(oppositePoints[indices[i]].y, oppositePoints[indices[j]].y);     // 求两个窗口右下角y坐标最小值
                    int overlapWidth = x2min - x1max + 1;            // 计算两矩形重叠的宽度
                    int overlapHeight = y2min - y1max + 1;           // 计算两矩形重叠的高度
                    if (overlapWidth > 0 && overlapHeight > 0)
                    {
                        float overlapPart = (overlapWidth * overlapHeight) / box_area[indices[j]];    // 计算重叠的比率
                        if (overlapPart > overlapThreshold)          // 判断重叠比率是否超过重叠阈值
                        {
                            is_suppressed[indices[j]] = 1;           // 将窗口j标记为抑制
                        }
                    }
                }
            }
        }
    }
    
    numBoxesOut = 0;    // 初始化输出窗口数目0
    for (i = 0; i < numBoxes; i++)
    {
        if (!is_suppressed[i]) numBoxesOut++;    // 统计输出窗口数目
    }
    index = 0;
    for (i = 0; i < numBoxes; i++)                  // 遍历所有输入窗口
    {
        if (!is_suppressed[indices[i]])             // 将未发生抑制的窗口信息保存到输出信息中
        {
            pointsOut.push_back(Point(points[indices[i]].x,points[indices[i]].y));
            oppositePointsOut.push_back(Point(oppositePoints[indices[i]].x,oppositePoints[indices[i]].y));
            scoreOut.push_back(score[indices[i]]);
            index++;
        }
        
    }
    
    return true;
}

int main()
{
    Mat image=Mat::zeros(600,600,CV_8UC3);
    int numBoxes=4;
    vector points(numBoxes);
    vector oppositePoints(numBoxes);
    vector score(numBoxes);
    
    points[0]=Point(200,200);oppositePoints[0]=Point(400,400);score[0]=0.99;
    points[1]=Point(220,220);oppositePoints[1]=Point(420,420);score[1]=0.9;
    points[2]=Point(100,100);oppositePoints[2]=Point(150,150);score[2]=0.82;
    points[3]=Point(200,240);oppositePoints[3]=Point(400,440);score[3]=0.5;
    
    
    float overlapThreshold=0.8;
    int numBoxesOut;
    vector pointsOut;
    vector oppositePointsOut;
    vector scoreOut;
    
    nonMaximumSuppression( numBoxes,points,oppositePoints,score,overlapThreshold,numBoxesOut,pointsOut,oppositePointsOut,scoreOut);
    for (int i=0;i

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