认真的虎ORBSLAM2源码解读(七)：单目初始化器Initializer

1.前言

1.1.参考博客

ORB-SLAM2的源码阅读（九）：Initializer类
Rap_GodORBSLAM2源码学习（7） Initializer类
单目相机标定
通过奇异值分解（SVD）求解透视变换单应性矩阵
RANSAC算法详解

1.2.介绍

在orbslam2中，第一次新建Initializer对象实在Tracking的构造函数里。

2.头文件

class Initializer
{
    typedef pair<int,int> Match;

public:


    /**
    * Initializer构造函数
    * @param ReferenceFrame 输入Initializer的参考帧
    * @param sigma  //计算单应矩阵H和基础矩阵得分F时候一个参数
    * @param iterations  RANSAC迭代次数
    */
    // Fix the reference frame
    Initializer(const Frame &ReferenceFrame, float sigma = 1.0, int iterations = 200);


    /**
    * 开启初始化
    * @param CurrentFrame 当前帧
    * @param vMatches12 orbmatcher计算的初匹配
    * @param R21
    * @param t21
    * @param vP3D 其大小为vKeys1大小，表示三角化重投影成功的匹配点的3d点在相机1下的坐标
    * @param vbTriangulated  其大小为vKeys1大小，表示初始化成功后，特征点中三角化投影成功的情况
    */
    // Computes in parallel a fundamental matrix and a homography
    // Selects a model and tries to recover the motion and the structure from motion
    bool Initialize(const Frame &CurrentFrame, const vector<int> &vMatches12,
                    cv::Mat &R21, cv::Mat &t21, vector<cv::Point3f> &vP3D, vector<bool> &vbTriangulated);


private:


    /**
    * 计算单应矩阵及其得分
    * @param vbMatchesInliers 匹配点中哪些可以通过H21重投影成功
    * @param score 输出H21得分
    * @param H21 输出H21
    */
    void FindHomography(vector<bool> &vbMatchesInliers, float &score, cv::Mat &H21);
    /**
    * 计算基础矩阵及其得分
    * @param vbMatchesInliers 匹配点中哪些可以通过H21重投影成功
    * @param score 输出F21得分
    * @param H21 输出F21
    */
    void FindFundamental(vector<bool> &vbInliers, float &score, cv::Mat &F21);
    //视觉slam十四讲P147,7.3.3.单应矩阵
    //通过vP1，vP2求得单应矩阵并返回
    cv::Mat ComputeH21(const vector<cv::Point2f> &vP1, const vector<cv::Point2f> &vP2);
    //通过vP1，vP2求得基础矩阵并返回
    cv::Mat ComputeF21(const vector<cv::Point2f> &vP1, const vector<cv::Point2f> &vP2);


    /**
    * 计算单应矩阵得分，判断哪些点重投影成功
    * @param vbMatchesInliers 通过H21，H12，匹配点重投影成功情况
    * @param sigma 计算得分时需要的参数
    * @return 单应矩阵得分
    */
    float CheckHomography(const cv::Mat &H21, const cv::Mat &H12, vector<bool> &vbMatchesInliers, float sigma);

    /**
    * 计算基础得分，判断哪些匹配点重投影成功
    * @param
    * @param vbMatchesInliers 针对输入的单应矩阵F，匹配点重投影成功情况
    * @param
    * @return 基础矩阵得分
    */
    float CheckFundamental(const cv::Mat &F21, vector<bool> &vbMatchesInliers, float sigma);

    /**
    * 通过输入的F21计算Rt
    * @param vbMatchesInliers 匹配点中哪些可以通过F21重投影成功
    * @param F21 基础
    * @param K 内参
    * @param R21 输出
    * @param t21 输出
    * @param vP3D 其大小为vKeys1大小，表示三角化重投影成功的匹配点的3d点在相机1下的坐标
    * @param vbTriangulated 其大小为vKeys1大小，特征点中哪些可以通过F21重投影成功
    * @param minParallax 设置的最小视差角余弦值参数，输出Rt模型的视差角小于此值则返回失败
    * @param minTriangulated 匹配点中F21重投影成功的个数如果小于此值，返回失败
    * @return 通过输入的F21计算Rt是否成功
    */
    bool ReconstructF(vector<bool> &vbMatchesInliers, cv::Mat &F21, cv::Mat &K,
                      cv::Mat &R21, cv::Mat &t21, vector<cv::Point3f> &vP3D, vector<bool> &vbTriangulated, float minParallax, int minTriangulated);

    /**
    * 通过输入的H21计算Rt
    * @param vbMatchesInliers 匹配点中哪些可以通过H21重投影成功
    * @param H21 单应矩阵
    * @param K 内参
    * @param R21 输出
    * @param t21 输出
    * @param vP3D 其大小为vKeys1大小，表示三角化重投影成功的匹配点的3d点在相机1下的坐标
    * @param vbTriangulated 其大小为vKeys1大小，特征点中哪些可以通过H21重投影成功
    * @param minParallax 设置的最小视差角余弦值参数，输出Rt模型的视差角小于此值则返回失败
    * @param minTriangulated 匹配点中H21重投影成功的个数如果小于此值，返回失败
    * @return 通过输入的H21计算Rt是否成功
    */
    bool ReconstructH(vector<bool> &vbMatchesInliers, cv::Mat &H21, cv::Mat &K,
                      cv::Mat &R21, cv::Mat &t21, vector<cv::Point3f> &vP3D, vector<bool> &vbTriangulated, float minParallax, int minTriangulated);

    /**
    * 计算kp1,kp2是匹配的关键点，它对应着世界坐标系中的一个点。
    * P1,P2是F1，F2对应的投影矩阵。
    * 输出综合考虑了P1,P2,kp1,kp2的在世界坐标系中的齐次坐标3D点坐标
    * @param kp1 
    * @param kp2 
    * @param P1 
    * @param P2
    * @param x3D 输出综合考虑了P1,P2,kp1,kp2的在世界坐标系中的齐次坐标3D点坐标
    */
    void Triangulate(const cv::KeyPoint &kp1, const cv::KeyPoint &kp2, const cv::Mat &P1, const cv::Mat &P2, cv::Mat &x3D);

    /**
    * 将一个特征点集合归一化到另一个坐标系，使得归一化后的坐标点集合均值为0，一阶绝对矩为1
    * @param vKeys 输入待归一化特征点集合
    * @param vNormalizedPoints  输出归一化后特征点集合
    * @param T    vNormalizedPoints=T*vKeys
    */
    void Normalize(const vector<cv::KeyPoint> &vKeys, vector<cv::Point2f> &vNormalizedPoints, cv::Mat &T);

    /**计算在输入Rt下，匹配点三角化重投影成功的数量
    * @param vMatches12 orbmatcher计算的初匹配
    * @param vbInliers 匹配点中哪些可以通过H或者F重投影成功
    * @param vP3D 其大小为vKeys1大小，表示三角化重投影成功的匹配点的3d点在相机1下的坐标
    * @param th2 根据三角化重投影误差判断匹配点是否重投影成功的阈值
    * @param vbGood 输出：特征点哪些三角化重投影成功
    * @param parallax 三角化重投影成功匹配点的视差角
    * @return 匹配点三角化重投影成功的数量
    */
    int CheckRT(const cv::Mat &R, const cv::Mat &t, const vector<cv::KeyPoint> &vKeys1, const vector<cv::KeyPoint> &vKeys2,
                       const vector<Match> &vMatches12, vector<bool> &vbInliers,
                       const cv::Mat &K, vector<cv::Point3f> &vP3D, float th2, vector<bool> &vbGood, float &parallax);
    
    /**将本质矩阵分解成Rt,有四种模型
    * @param E 
    * @param R1 输出其中一种R
    * @param R2 输出其中一种R
    * @param t 输出t
    */
    void DecomposeE(const cv::Mat &E, cv::Mat &R1, cv::Mat &R2, cv::Mat &t);


    // Keypoints from Reference Frame (Frame 1)
    vector<cv::KeyPoint> mvKeys1;

    // Keypoints from Current Frame (Frame 2)
    vector<cv::KeyPoint> mvKeys2;

    // Current Matches from Reference to Current
    //储存着匹配点对在参考帧F1和当前帧F2中的序号
    vector<Match> mvMatches12;
    //描述参考帧F1中特征点匹配情况
    vector<bool> mvbMatched1;

    // Calibration
    //内参
    cv::Mat mK;

    // Standard Deviation and Variance
    //mSigma在CheckFundamental和CheckHomography计算F和H得分的时候有用到的参数，以及判断匹配点通过H或者F重投影是否成功的参数
    //mSigma2在checkRt中判断匹配点三角重投影是否成功的一个参数
    float mSigma, mSigma2;

    // Ransac max iterations
    //Ransac算法的最大迭代次数
    int mMaxIterations;

    // Ransac sets
    //使用8点法计算F或者H时的RANSAC点对
    vector<vector<size_t> > mvSets;   

};

3.源码

3.1.类方法Initializer::FindHomography()

3.1.1.源码

void Initializer::FindHomography(vector<bool> &vbMatchesInliers, float &score, cv::Mat &H21)
{
    // Number of putative matches
    //假定匹配的数量
    const int N = mvMatches12.size();

    // Normalize coordinates
    vector<cv::Point2f> vPn1, vPn2;
    cv::Mat T1, T2;
    Normalize(mvKeys1,vPn1, T1);
    Normalize(mvKeys2,vPn2, T2);
    cv::Mat T2inv = T2.inv();

    // Best Results variables
    score = 0.0;
    vbMatchesInliers = vector<bool>(N,false);

    // Iteration variables
    vector<cv::Point2f> vPn1i(8);
    vector<cv::Point2f> vPn2i(8);
    cv::Mat H21i, H12i;
    vector<bool> vbCurrentInliers(N,false);
    float currentScore;

    // Perform all RANSAC iterations and save the solution with highest score
    for(int it=0; it<mMaxIterations; it++)
    {
        // Select a minimum set
        for(size_t j=0; j<8; j++)
        {
            int idx = mvSets[it][j];

            vPn1i[j] = vPn1[mvMatches12[idx].first];
            vPn2i[j] = vPn2[mvMatches12[idx].second];
        }

        //计算H
        cv::Mat Hn = ComputeH21(vPn1i,vPn2i);
        H21i = T2inv*Hn*T1;
        H12i = H21i.inv();

	//在参数 mSigma下，能够通过H21，H12重投影成功的点有哪些，并返回分数
        currentScore = CheckHomography(H21i, H12i, vbCurrentInliers, mSigma);

        if(currentScore>score)
        {
            H21 = H21i.clone();
            vbMatchesInliers = vbCurrentInliers;
            score = currentScore;
        }
    }
}

3.2.类方法Normalize()

3.2.1.源码

/**
* 将一个特征点集合归一化到另一个坐标系，使得归一化后的坐标点集合均值为0，一阶绝对矩为1
* @param vKeys 输入待归一化特征点集合
* @param vNormalizedPoints  输出归一化后特征点集合
* @param T    vNormalizedPoints=T*vKeys
*/

void Initializer::Normalize(const vector<cv::KeyPoint> &vKeys, vector<cv::Point2f> &vNormalizedPoints, cv::Mat &T)
{
    float meanX = 0;
    float meanY = 0;
    const int N = vKeys.size();

    vNormalizedPoints.resize(N);

    for(int i=0; i<N; i++)
    {
        meanX += vKeys[i].pt.x;
        meanY += vKeys[i].pt.y;
    }

    meanX = meanX/N;
    meanY = meanY/N;

    float meanDevX = 0;
    float meanDevY = 0;

    for(int i=0; i<N; i++)
    {
        vNormalizedPoints[i].x = vKeys[i].pt.x - meanX;
        vNormalizedPoints[i].y = vKeys[i].pt.y - meanY;

        meanDevX += fabs(vNormalizedPoints[i].x);
        meanDevY += fabs(vNormalizedPoints[i].y);
    }

    meanDevX = meanDevX/N;
    meanDevY = meanDevY/N;

    float sX = 1.0/meanDevX;
    float sY = 1.0/meanDevY;

    for(int i=0; i<N; i++)
    {
        vNormalizedPoints[i].x = vNormalizedPoints[i].x * sX;
        vNormalizedPoints[i].y = vNormalizedPoints[i].y * sY;
    }

    T = cv::Mat::eye(3,3,CV_32F);
    T.at<float>(0,0) = sX;
    T.at<float>(1,1) = sY;
    T.at<float>(0,2) = -meanX*sX;
    T.at<float>(1,2) = -meanY*sY;
}

3.2.2.讲解

假设我们有一待归一化的特征点集合$(u_i,v_i)$, $i\in [0,N-1]$，如果有另一个点集合$(m_i,n_i)$, $i\in [0,N-1]$满足下面条件
$$\{\begin{array}{l}{u}_i=(meandevx)\ast m_i+meanx\\ v_i=(meandevy)\ast n_i+meany\\ meanx=\frac{1}{N}{\sum }_{i=0}^N{u}_i\\ meany=\frac{1}{N}{\sum }_{i=0}^N{v}_i\\ meanx=\frac{1}{N}{\sum }_{i=0}^N|u_i-meanx|\\ meany=\frac{1}{N}{\sum }_{i=0}^N|v_i-meanv|\end{array}$$
那么此时点集合$(m_i,n_i)$的坐标均值为0，一阶绝对矩为1。
将上面前两个式子转化一下得
$$\{\begin{array}{l}{m}_i=\frac{1}{meandevx}\ast u_i-\frac{1}{meandevx}\ast meanx\\ n_i=\frac{1}{meandevy}\ast v_i-\frac{1}{meandevy}\ast meany\end{array}$$
然后再将上面两个式子向量化得
$$\left[\begin{array}{c}{m}_i\\ n_i\\ 1\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{meandevx}& 0& -\frac{1}{meandevx}\ast meanx\\ 0& \frac{1}{meandevy}& -\frac{1}{meandevy}\ast meany\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{u}_i\\ v_i\\ 1\end{array}\right]$$
令
$$vNormalizedPoints=\left[\begin{array}{c}{m}_i\\ n_i\\ 1\end{array}\right]T=\left[\begin{array}{ccc}\frac{1}{meandevx}& 0& -\frac{1}{meandevx}\ast meanx\\ 0& \frac{1}{meandevy}& -\frac{1}{meandevy}\ast meany\\ 0& 0& 1\end{array}\right]vKeys=\left[\begin{array}{c}{u}_i\\ v_i\\ 1\end{array}\right]$$
则有
$$vNormalizedPoints=T\ast vKeys$$
vKeys为归一化前的特征点
vNormalizedPoints为归一化后的特征点
计算单应矩阵将使用vNormalizedPoints，这样误差更小。

3.3.类方法Initialize()

/**
* 开启初始化
* @param CurrentFrame 当前帧
* @param vMatches12 orbmatcher计算的初匹配
* @param R21
* @param t21
* @param vP3D 其大小为vKeys1大小，表示三角化重投影成功的匹配点的3d点在相机1下的坐标
* @param vbTriangulated  其大小为vKeys1大小，表示初始化成功后，特征点中三角化投影成功的情况
*/

bool Initializer::Initialize(const Frame &CurrentFrame, const vector<int> &vMatches12, cv::Mat &R21, cv::Mat &t21,
                             vector<cv::Point3f> &vP3D, vector<bool> &vbTriangulated)
{
    // Fill structures with current keypoints and matches with reference frame
    // Reference Frame: 1, Current Frame: 2
    mvKeys2 = CurrentFrame.mvKeysUn;
    
    //mvMatches12储存着匹配点对在参考帧F1和当前帧F2中的序号
    mvMatches12.clear();
    mvMatches12.reserve(mvKeys2.size());
    //描述参考帧F1中特征点匹配情况
    mvbMatched1.resize(mvKeys1.size());
    for(size_t i=0, iend=vMatches12.size();i<iend; i++)
    {
        if(vMatches12[i]>=0)
        {
            mvMatches12.push_back(make_pair(i,vMatches12[i]));
            mvbMatched1[i]=true;
        }
        else
            mvbMatched1[i]=false;
    }
    
    //匹配点数
    const int N = mvMatches12.size();

    // Indices for minimum set selection
    vector<size_t> vAllIndices;
    vAllIndices.reserve(N);
    vector<size_t> vAvailableIndices;

    for(int i=0; i<N; i++)
    {
        vAllIndices.push_back(i);
    }

    // Generate sets of 8 points for each RANSAC iteration
    // 在所有匹配特征点对中随机选择8对匹配特征点为一组，共选择mMaxIterations组
    // 用于FindHomography和FindFundamental求解
    // mMaxIterations:200
    mvSets = vector< vector<size_t> >(mMaxIterations,vector<size_t>(8,0));

    DUtils::Random::SeedRandOnce(0);

    //RANSAC循环mMaxIterations次
    for(int it=0; it<mMaxIterations; it++)
    {
        vAvailableIndices = vAllIndices;

        // Select a minimum set
        for(size_t j=0; j<8; j++)
        {
            int randi = DUtils::Random::RandomInt(0,vAvailableIndices.size()-1);
            int idx = vAvailableIndices[randi];

            mvSets[it][j] = idx;

            vAvailableIndices[randi] = vAvailableIndices.back();
            vAvailableIndices.pop_back();
        }
    }

    // Launch threads to compute in parallel a fundamental matrix and a homography
    //vbMatchesInliersH，ORBmatcher计算出的匹配中，哪些能够通过H重投影成功
    vector<bool> vbMatchesInliersH, vbMatchesInliersF;
    //SH计算单应矩阵的得分，SF计算基础矩阵得分
    float SH, SF;
    cv::Mat H, F;

    //启动线程，第一个参数是启用函数的指针，后面是调用这个函数所需的参数
    //由于FindHomography第二三个参数是引用，所以需要用ref()包裹
    // 计算homograpy和得分
    thread threadH(&Initializer::FindHomography,this,ref(vbMatchesInliersH), ref(SH), ref(H));
    // 计算fundamental和得分
    thread threadF(&Initializer::FindFundamental,this,ref(vbMatchesInliersF), ref(SF), ref(F));

    // Wait until both threads have finished
    //在这里等待线程threadH，threadF结束才往下继续执行
    //也就是等待SH，SF的结果
    threadH.join();
    threadF.join();

    // Compute ratio of scores
    float RH = SH/(SH+SF);

    // Try to reconstruct from homography or fundamental depending on the ratio (0.40-0.45)
    // 从H矩阵或F矩阵中恢复R,t
    if(RH>0.40)
        return ReconstructH(vbMatchesInliersH,H,mK,R21,t21,vP3D,vbTriangulated,1.0,50);
    else //if(pF_HF>0.6)
        return ReconstructF(vbMatchesInliersF,F,mK,R21,t21,vP3D,vbTriangulated,1.0,50);

    return false;
}

3.4.类方法 FindFundamental()

/**
* 计算基础矩阵及其得分
* @param vbMatchesInliers 匹配点中哪些可以通过H21重投影成功
* @param score 输出F21得分
* @param H21 输出F21
*/

void Initializer::FindFundamental(vector<bool> &vbMatchesInliers, float &score, cv::Mat &F21)
{
    // Number of putative matches
    const int N = vbMatchesInliers.size();

    // Normalize coordinates
    vector<cv::Point2f> vPn1, vPn2;
    cv::Mat T1, T2;
    Normalize(mvKeys1,vPn1, T1);
    Normalize(mvKeys2,vPn2, T2);
    cv::Mat T2t = T2.t();

    // Best Results variables
    score = 0.0;
    vbMatchesInliers = vector<bool>(N,false);

    // Iteration variables
    vector<cv::Point2f> vPn1i(8);
    vector<cv::Point2f> vPn2i(8);
    cv::Mat F21i;
    vector<bool> vbCurrentInliers(N,false);
    float currentScore;

    // Perform all RANSAC iterations and save the solution with highest score
    for(int it=0; it<mMaxIterations; it++)
    {
        // Select a minimum set
        for(int j=0; j<8; j++)
        {
            int idx = mvSets[it][j];

            vPn1i[j] = vPn1[mvMatches12[idx].first];
            vPn2i[j] = vPn2[mvMatches12[idx].second];
        }

        //计算出归一化特征点对应的基础矩阵
        cv::Mat Fn = ComputeF21(vPn1i,vPn2i);

	//转换成归一化前特征点对应的基础矩阵
        F21i = T2t*Fn*T1;
	//在参数 mSigma下，能够通过F21li，
	//重投影成功的点有哪些，并返回分数
        currentScore = CheckFundamental(F21i, vbCurrentInliers, mSigma);

        if(currentScore>score)
        {
            F21 = F21i.clone();
            vbMatchesInliers = vbCurrentInliers;
            score = currentScore;
        }
    }
}

3.5.类方法ComputeH21()

通过vP1，vP2求得单应矩阵并返回

cv::Mat Initializer::ComputeH21(const vector<cv::Point2f> &vP1, const vector<cv::Point2f> &vP2)
{
    const int N = vP1.size();

    cv::Mat A(2*N,9,CV_32F);

    //虽然书上说最少用4个点对就可以解出单应矩阵，但是这里依然用的是8个点对
    for(int i=0; i<N; i++)
    {
        const float u1 = vP1[i].x;
        const float v1 = vP1[i].y;
        const float u2 = vP2[i].x;
        const float v2 = vP2[i].y;

        A.at<float>(2*i,0) = 0.0;
        A.at<float>(2*i,1) = 0.0;
        A.at<float>(2*i,2) = 0.0;
        A.at<float>(2*i,3) = -u1;
        A.at<float>(2*i,4) = -v1;
        A.at<float>(2*i,5) = -1;
        A.at<float>(2*i,6) = v2*u1;
        A.at<float>(2*i,7) = v2*v1;
        A.at<float>(2*i,8) = v2;

        A.at<float>(2*i+1,0) = u1;
        A.at<float>(2*i+1,1) = v1;
        A.at<float>(2*i+1,2) = 1;
        A.at<float>(2*i+1,3) = 0.0;
        A.at<float>(2*i+1,4) = 0.0;
        A.at<float>(2*i+1,5) = 0.0;
        A.at<float>(2*i+1,6) = -u2*u1;
        A.at<float>(2*i+1,7) = -u2*v1;
        A.at<float>(2*i+1,8) = -u2;

    }

    cv::Mat u,w,vt;

    //SVD分解A=u*w*vt
    cv::SVDecomp(A,w,u,vt,cv::SVD::MODIFY_A | cv::SVD::FULL_UV);

    //返回了vt最后一个行向量
    return vt.row(8).reshape(0, 3);
}

3.6.类方法ComputeF21()

通过vP1，vP2求得基础矩阵并返回

cv::Mat Initializer::ComputeF21(const vector<cv::Point2f> &vP1,const vector<cv::Point2f> &vP2)
{
    const int N = vP1.size();

    cv::Mat A(N,9,CV_32F);

    //八点法计算F
    for(int i=0; i<N; i++)
    {
        const float u1 = vP1[i].x;
        const float v1 = vP1[i].y;
        const float u2 = vP2[i].x;
        const float v2 = vP2[i].y;

        A.at<float>(i,0) = u2*u1;
        A.at<float>(i,1) = u2*v1;
        A.at<float>(i,2) = u2;
        A.at<float>(i,3) = v2*u1;
        A.at<float>(i,4) = v2*v1;
        A.at<float>(i,5) = v2;
        A.at<float>(i,6) = u1;
        A.at<float>(i,7) = v1;
        A.at<float>(i,8) = 1;
    }

    cv::Mat u,w,vt;

    cv::SVDecomp(A,w,u,vt,cv::SVD::MODIFY_A | cv::SVD::FULL_UV);

    //用SVD算出基础矩阵
    cv::Mat Fpre = vt.row(8).reshape(0, 3);

    //将基础矩阵svd分解
    cv::SVDecomp(Fpre,w,u,vt,cv::SVD::MODIFY_A | cv::SVD::FULL_UV);

    //根据基础矩阵的性质分解出来的w第三个元素应该为0
    w.at<float>(2)=0;

    //返回复合要求的基础矩阵
    return  u*cv::Mat::diag(w)*vt;
}

3.7.类方法CheckHomography()

/**
* 计算单应矩阵得分，判断哪些点重投影成功
* @param vbMatchesInliers 通过H21，H12，匹配点重投影成功情况
* @param sigma 计算得分时需要的参数
* @return 单应矩阵得分
*/

float Initializer::CheckHomography(const cv::Mat &H21, const cv::Mat &H12, vector<bool> &vbMatchesInliers, float sigma)
{   
    const int N = mvMatches12.size();

    const float h11 = H21.at<float>(0,0);
    const float h12 = H21.at<float>(0,1);
    const float h13 = H21.at<float>(0,2);
    const float h21 = H21.at<float>(1,0);
    const float h22 = H21.at<float>(1,1);
    const float h23 = H21.at<float>(1,2);
    const float h31 = H21.at<float>(2,0);
    const float h32 = H21.at<float>(2,1);
    const float h33 = H21.at<float>(2,2);

    const float h11inv = H12.at<float>(0,0);
    const float h12inv = H12.at<float>(0,1);
    const float h13inv = H12.at<float>(0,2);
    const float h21inv = H12.at<float>(1,0);
    const float h22inv = H12.at<float>(1,1);
    const float h23inv = H12.at<float>(1,2);
    const float h31inv = H12.at<float>(2,0);
    const float h32inv = H12.at<float>(2,1);
    const float h33inv = H12.at<float>(2,2);

    vbMatchesInliers.resize(N);

    float score = 0;

    //判断通过单应矩阵重投影是否成功的阈值
    const float th = 5.991;

    const float invSigmaSquare = 1.0/(sigma*sigma);

    //遍历所有的匹配点
    for(int i=0; i<N; i++)
    {
        bool bIn = true;

        const cv::KeyPoint &kp1 = mvKeys1[mvMatches12[i].first];
        const cv::KeyPoint &kp2 = mvKeys2[mvMatches12[i].second];

        const float u1 = kp1.pt.x;
        const float v1 = kp1.pt.y;
        const float u2 = kp2.pt.x;
        const float v2 = kp2.pt.y;

        // Reprojection error in first image
        // x2in1 = H12*x2
        const float w2in1inv = 1.0/(h31inv*u2+h32inv*v2+h33inv);
        const float u2in1 = (h11inv*u2+h12inv*v2+h13inv)*w2in1inv;
        const float v2in1 = (h21inv*u2+h22inv*v2+h23inv)*w2in1inv;

	//计算u2，v2投影到F1后与u1,v1的距离的平方，也就是重投影误差
        const float squareDist1 = (u1-u2in1)*(u1-u2in1)+(v1-v2in1)*(v1-v2in1);

        const float chiSquare1 = squareDist1*invSigmaSquare;

	//chiSquare1>th说明匹配的点对F1投影到F2，重投影失败
        if(chiSquare1>th)
            bIn = false;
        else
            score += th - chiSquare1;

        // Reprojection error in second image
        // x1in2 = H21*x1

        const float w1in2inv = 1.0/(h31*u1+h32*v1+h33);
        const float u1in2 = (h11*u1+h12*v1+h13)*w1in2inv;
        const float v1in2 = (h21*u1+h22*v1+h23)*w1in2inv;
	
        const float squareDist2 = (u2-u1in2)*(u2-u1in2)+(v2-v1in2)*(v2-v1in2);

        const float chiSquare2 = squareDist2*invSigmaSquare;

        if(chiSquare2>th)
            bIn = false;
        else
            score += th - chiSquare2;

	//bIn标志着此对匹配点是否重投影成功
        if(bIn)
            vbMatchesInliers[i]=true;
        else
            vbMatchesInliers[i]=false;
    }

    return score;
}

3.8.类方法CheckFundamental()

/**
* 计算基础得分，判断哪些匹配点重投影成功
* @param
* @param vbMatchesInliers 针对输入的单应矩阵F，匹配点重投影成功情况
* @param
* @return 基础矩阵得分
*/

float Initializer::CheckFundamental(const cv::Mat &F21, vector<bool> &vbMatchesInliers, float sigma)
{
    const int N = mvMatches12.size();

    const float f11 = F21.at<float>(0,0);
    const float f12 = F21.at<float>(0,1);
    const float f13 = F21.at<float>(0,2);
    const float f21 = F21.at<float>(1,0);
    const float f22 = F21.at<float>(1,1);
    const float f23 = F21.at<float>(1,2);
    const float f31 = F21.at<float>(2,0);
    const float f32 = F21.at<float>(2,1);
    const float f33 = F21.at<float>(2,2);

    vbMatchesInliers.resize(N);

    float score = 0;

    const float th = 3.841;
    const float thScore = 5.991;

    const float invSigmaSquare = 1.0/(sigma*sigma);

    for(int i=0; i<N; i++)
    {
        bool bIn = true;

        const cv::KeyPoint &kp1 = mvKeys1[mvMatches12[i].first];
        const cv::KeyPoint &kp2 = mvKeys2[mvMatches12[i].second];

        const float u1 = kp1.pt.x;
        const float v1 = kp1.pt.y;
        const float u2 = kp2.pt.x;
        const float v2 = kp2.pt.y;

        // Reprojection error in second image
        // l2=F21x1=(a2,b2,c2)

        const float a2 = f11*u1+f12*v1+f13;
        const float b2 = f21*u1+f22*v1+f23;
        const float c2 = f31*u1+f32*v1+f33;
	
	// num2=x2*F21*x1
        const float num2 = a2*u2+b2*v2+c2;

        const float squareDist1 = num2*num2/(a2*a2+b2*b2);

        const float chiSquare1 = squareDist1*invSigmaSquare;

        if(chiSquare1>th)
            bIn = false;
        else
            score += thScore - chiSquare1;

        // Reprojection error in second image
        // l1 =x2tF21=(a1,b1,c1)

        const float a1 = f11*u2+f21*v2+f31;
        const float b1 = f12*u2+f22*v2+f32;
        const float c1 = f13*u2+f23*v2+f33;

        const float num1 = a1*u1+b1*v1+c1;

        const float squareDist2 = num1*num1/(a1*a1+b1*b1);

        const float chiSquare2 = squareDist2*invSigmaSquare;

        if(chiSquare2>th)
            bIn = false;
        else
            score += thScore - chiSquare2;

        if(bIn)
            vbMatchesInliers[i]=true;
        else
            vbMatchesInliers[i]=false;
    }

    return score;
}

3.9.类方法ReconstructF()

/**
* 通过输入的F21计算Rt
* @param vbMatchesInliers 匹配点中哪些可以通过F21重投影成功
* @param F21 基础
* @param K 内参
* @param R21 输出
* @param t21 输出
* @param vP3D 其大小为vKeys1大小，表示三角化重投影成功的匹配点的3d点在相机1下的坐标
* @param vbTriangulated 其大小为vKeys1大小，特征点中哪些可以通过F21重投影成功
* @param minParallax 设置的最小视差角余弦值参数，输出Rt模型的视差角小于此值则返回失败
* @param minTriangulated 匹配点中F21重投影成功的个数如果小于此值，返回失败
* @return 通过输入的F21计算Rt是否成功
*/

bool Initializer::ReconstructF(vector<bool> &vbMatchesInliers, cv::Mat &F21, cv::Mat &K,
                            cv::Mat &R21, cv::Mat &t21, vector<cv::Point3f> &vP3D, vector<bool> &vbTriangulated, float minParallax, int minTriangulated)
{
    int N=0;
    //匹配点中
    for(size_t i=0, iend = vbMatchesInliers.size() ; i<iend; i++)
        if(vbMatchesInliers[i])
            N++;

    // Compute Essential Matrix from Fundamental Matrix
    cv::Mat E21 = K.t()*F21*K;

    cv::Mat R1, R2, t;

    // Recover the 4 motion hypotheses
    DecomposeE(E21,R1,R2,t);  

    cv::Mat t1=t;
    cv::Mat t2=-t;

    // Reconstruct with the 4 hyphoteses and check
    vector<cv::Point3f> vP3D1, vP3D2, vP3D3, vP3D4;
    vector<bool> vbTriangulated1,vbTriangulated2,vbTriangulated3, vbTriangulated4;
    float parallax1,parallax2, parallax3, parallax4;

    int nGood1 = CheckRT(R1,t1,mvKeys1,mvKeys2,mvMatches12,vbMatchesInliers,K, vP3D1, 4.0*mSigma2, vbTriangulated1, parallax1);
    int nGood2 = CheckRT(R2,t1,mvKeys1,mvKeys2,mvMatches12,vbMatchesInliers,K, vP3D2, 4.0*mSigma2, vbTriangulated2, parallax2);
    int nGood3 = CheckRT(R1,t2,mvKeys1,mvKeys2,mvMatches12,vbMatchesInliers,K, vP3D3, 4.0*mSigma2, vbTriangulated3, parallax3);
    int nGood4 = CheckRT(R2,t2,mvKeys1,mvKeys2,mvMatches12,vbMatchesInliers,K, vP3D4, 4.0*mSigma2, vbTriangulated4, parallax4);

    int maxGood = max(nGood1,max(nGood2,max(nGood3,nGood4)));

    R21 = cv::Mat();
    t21 = cv::Mat();

    int nMinGood = max(static_cast<int>(0.9*N),minTriangulated);

    int nsimilar = 0;
    if(nGood1>0.7*maxGood)
        nsimilar++;
    if(nGood2>0.7*maxGood)
        nsimilar++;
    if(nGood3>0.7*maxGood)
        nsimilar++;
    if(nGood4>0.7*maxGood)
        nsimilar++;

    // If there is not a clear winner or not enough triangulated points reject initialization
    //nsimilar>1表明没有哪个模型明显胜出
    //匹配点三角化重投影成功数过少
    if(maxGood<nMinGood || nsimilar>1)
    {
        return false;
    }

    // If best reconstruction has enough parallax initialize
    if(maxGood==nGood1)
    {
	//如果模型一对应的视差角大于最小值
        if(parallax1>minParallax)
        {
            vP3D = vP3D1;
            vbTriangulated = vbTriangulated1;

            R1.copyTo(R21);
            t1.copyTo(t21);
            return true;
        }
    }else if(maxGood==nGood2)
    {
        if(parallax2>minParallax)
        {
            vP3D = vP3D2;
            vbTriangulated = vbTriangulated2;

            R2.copyTo(R21);
            t1.copyTo(t21);
            return true;
        }
    }else if(maxGood==nGood3)
    {
        if(parallax3>minParallax)
        {
            vP3D = vP3D3;
            vbTriangulated = vbTriangulated3;

            R1.copyTo(R21);
            t2.copyTo(t21);
            return true;
        }
    }else if(maxGood==nGood4)
    {
        if(parallax4>minParallax)
        {
            vP3D = vP3D4;
            vbTriangulated = vbTriangulated4;

            R2.copyTo(R21);
            t2.copyTo(t21);
            return true;
        }
    }

    return false;
}

3.10.类方法ReconstructH()

/**
* 通过输入的H21计算Rt
* @param vbMatchesInliers 匹配点中哪些可以通过H21重投影成功
* @param H21 单应矩阵
* @param K 内参
* @param R21 输出
* @param t21 输出
* @param vP3D 其大小为vKeys1大小，表示三角化重投影成功的匹配点的3d点在相机1下的坐标
* @param vbTriangulated 其大小为vKeys1大小，特征点中哪些可以通过H21重投影成功
* @param minParallax 设置的最小视差角余弦值参数，输出Rt模型的视差角小于此值则返回失败
* @param minTriangulated 匹配点中H21重投影成功的个数如果小于此值，返回失败
* @return 通过输入的H21计算Rt是否成功
*/

bool Initializer::ReconstructH(vector<bool> &vbMatchesInliers, cv::Mat &H21, cv::Mat &K,
                      cv::Mat &R21, cv::Mat &t21, vector<cv::Point3f> &vP3D, vector<bool> &vbTriangulated, float minParallax, int minTriangulated)
{
    //N，通过H重投影成功的数量
    int N=0;
    for(size_t i=0, iend = vbMatchesInliers.size() ; i<iend; i++)
        if(vbMatchesInliers[i])
            N++;

    // We recover 8 motion hypotheses using the method of Faugeras et al.
    // Motion and structure from motion in a piecewise planar environment.
    // International Journal of Pattern Recognition and Artificial Intelligence, 1988

    
    // 将H矩阵由图像坐标系变换到相机坐标系
    cv::Mat invK = K.inv();
    cv::Mat A = invK*H21*K;

    cv::Mat U,w,Vt,V;
    cv::SVD::compute(A,w,U,Vt,cv::SVD::FULL_UV);
    //vt转置
    V=Vt.t();
    //cv::determinant(U)为U的行列式
    float s = cv::determinant(U)*cv::determinant(Vt);

    float d1 = w.at<float>(0);
    float d2 = w.at<float>(1);
    float d3 = w.at<float>(2);

    //注意d1>d2>d3
    //看吴博讲解的ppt19页，只考虑d1!=d2!=d3的情况，其他情况返回失败
    if(d1/d2<1.00001 || d2/d3<1.00001)
    {
        return false;
    }

    vector<cv::Mat> vR, vt, vn;
    vR.reserve(8);
    vt.reserve(8);
    vn.reserve(8);

    //n'=[x1 0 x3] 4 posibilities e1=e3=1, e1=1 e3=-1, e1=-1 e3=1, e1=e3=-1
    float aux1 = sqrt((d1*d1-d2*d2)/(d1*d1-d3*d3));
    float aux3 = sqrt((d2*d2-d3*d3)/(d1*d1-d3*d3));
    float x1[] = {aux1,aux1,-aux1,-aux1};
    float x3[] = {aux3,-aux3,aux3,-aux3};

    //case d'=d2
    float aux_stheta = sqrt((d1*d1-d2*d2)*(d2*d2-d3*d3))/((d1+d3)*d2);

    float ctheta = (d2*d2+d1*d3)/((d1+d3)*d2);
    float stheta[] = {aux_stheta, -aux_stheta, -aux_stheta, aux_stheta};

    for(int i=0; i<4; i++)
    {
        cv::Mat Rp=cv::Mat::eye(3,3,CV_32F);
        Rp.at<float>(0,0)=ctheta;
        Rp.at<float>(0,2)=-stheta[i];
        Rp.at<float>(2,0)=stheta[i];
        Rp.at<float>(2,2)=ctheta;

        cv::Mat R = s*U*Rp*Vt;
        vR.push_back(R);

        cv::Mat tp(3,1,CV_32F);
        tp.at<float>(0)=x1[i];
        tp.at<float>(1)=0;
        tp.at<float>(2)=-x3[i];
        tp*=d1-d3;

        cv::Mat t = U*tp;
        vt.push_back(t/cv::norm(t));

        cv::Mat np(3,1,CV_32F);
        np.at<float>(0)=x1[i];
        np.at<float>(1)=0;
        np.at<float>(2)=x3[i];

        cv::Mat n = V*np;
        if(n.at<float>(2)<0)
            n=-n;
        vn.push_back(n);
    }

    //case d'=-d2
    float aux_sphi = sqrt((d1*d1-d2*d2)*(d2*d2-d3*d3))/((d1-d3)*d2);

    float cphi = (d1*d3-d2*d2)/((d1-d3)*d2);
    float sphi[] = {aux_sphi, -aux_sphi, -aux_sphi, aux_sphi};

    for(int i=0; i<4; i++)
    {
        cv::Mat Rp=cv::Mat::eye(3,3,CV_32F);
        Rp.at<float>(0,0)=cphi;
        Rp.at<float>(0,2)=sphi[i];
        Rp.at<float>(1,1)=-1;
        Rp.at<float>(2,0)=sphi[i];
        Rp.at<float>(2,2)=-cphi;

        cv::Mat R = s*U*Rp*Vt;
        vR.push_back(R);

        cv::Mat tp(3,1,CV_32F);
        tp.at<float>(0)=x1[i];
        tp.at<float>(1)=0;
        tp.at<float>(2)=x3[i];
        tp*=d1+d3;

        cv::Mat t = U*tp;
        vt.push_back(t/cv::norm(t));

        cv::Mat np(3,1,CV_32F);
        np.at<float>(0)=x1[i];
        np.at<float>(1)=0;
        np.at<float>(2)=x3[i];

        cv::Mat n = V*np;
        if(n.at<float>(2)<0)
            n=-n;
        vn.push_back(n);
    }


    int bestGood = 0;
    int secondBestGood = 0;    
    int bestSolutionIdx = -1;
    float bestParallax = -1;
    vector<cv::Point3f> bestP3D;
    vector<bool> bestTriangulated;

    // Instead of applying the visibility constraints proposed in the Faugeras' paper (which could fail for points seen with low parallax)
    // We reconstruct all hypotheses and check in terms of triangulated points and parallax
    //经过上面的计算，公共有8种R，t计算结果，遍历这8种可能模型
    //通过计算出匹配点的三角化重投影成功的数量，来找出最好模型和次好模型
    for(size_t i=0; i<8; i++)
    {
        float parallaxi;
        vector<cv::Point3f> vP3Di;
        vector<bool> vbTriangulatedi;
	
	//计算在输入Rt下，匹配点三角化重投影成功的数量
        int nGood = CheckRT(vR[i],vt[i],mvKeys1,mvKeys2,mvMatches12,vbMatchesInliers,K,vP3Di, 4.0*mSigma2, vbTriangulatedi, parallaxi);

        if(nGood>bestGood)
        {
            secondBestGood = bestGood;
            bestGood = nGood;
            bestSolutionIdx = i;
            bestParallax = parallaxi;
            bestP3D = vP3Di;
            bestTriangulated = vbTriangulatedi;
        }
        else if(nGood>secondBestGood)
        {
            secondBestGood = nGood;
        }
    }

    //secondBestGood<0.75*bestGood 如果最好模型与次好模型差距足够大
    //bestParallax>=minParallax 最好模型对应的视差角大于此值
    //bestGood>minTriangulated 最好模型对应的匹配点三角化重投影成功数量大于此阈值
    //bestGood>0.9*N 匹配点三角化重投影成功数量占通过H重投影成功数量的比例需要大于0.9
    if(secondBestGood<0.75*bestGood && bestParallax>=minParallax && bestGood>minTriangulated && bestGood>0.9*N)
    {
        vR[bestSolutionIdx].copyTo(R21);
        vt[bestSolutionIdx].copyTo(t21);
        vP3D = bestP3D;
        vbTriangulated = bestTriangulated;

        return true;
    }

    return false;
}

3.11.类方法Triangulate()

/**
* 计算kp1,kp2是匹配的关键点，它对应着世界坐标系中的一个点。
* P1,P2是F1，F2对应的投影矩阵。
* 输出综合考虑了P1,P2,kp1,kp2的在世界坐标系中的齐次坐标3D点坐标
* @param kp1 
* @param kp2 
* @param P1 
* @param P2
* @param x3D 输出综合考虑了P1,P2,kp1,kp2的在世界坐标系中的齐次坐标3D点坐标
*/

void Initializer::Triangulate(const cv::KeyPoint &kp1, const cv::KeyPoint &kp2, const cv::Mat &P1, const cv::Mat &P2, cv::Mat &x3D)
{
    cv::Mat A(4,4,CV_32F);

    A.row(0) = kp1.pt.x*P1.row(2)-P1.row(0);
    A.row(1) = kp1.pt.y*P1.row(2)-P1.row(1);
    A.row(2) = kp2.pt.x*P2.row(2)-P2.row(0);
    A.row(3) = kp2.pt.y*P2.row(2)-P2.row(1);

    cv::Mat u,w,vt;
    cv::SVD::compute(A,w,u,vt,cv::SVD::MODIFY_A| cv::SVD::FULL_UV);
    //取最后一个行向量
    x3D = vt.row(3).t();
    //转换为齐次坐标
    x3D = x3D.rowRange(0,3)/x3D.at<float>(3);
}

3.12.类方法CheckRT()

/**计算在输入Rt下，匹配点三角化重投影成功的数量
* @param vMatches12 orbmatcher计算的初匹配
* @param vbInliers 匹配点中哪些可以通过H或者F重投影成功
* @param vP3D 其大小为vKeys1大小，表示三角化重投影成功的匹配点的3d点在相机1下的坐标
* @param th2 根据三角化重投影误差判断匹配点是否重投影成功的阈值
* @param vbGood 输出：特征点哪些三角化重投影成功
* @param parallax 三角化重投影成功匹配点的视差角
* @return 匹配点三角化重投影成功的数量
*/

int Initializer::CheckRT(const cv::Mat &R, const cv::Mat &t, const vector<cv::KeyPoint> &vKeys1, const vector<cv::KeyPoint> &vKeys2,
                       const vector<Match> &vMatches12, vector<bool> &vbMatchesInliers,
                       const cv::Mat &K, vector<cv::Point3f> &vP3D, float th2, vector<bool> &vbGood, float &parallax)
{
    // Calibration parameters
    const float fx = K.at<float>(0,0);
    const float fy = K.at<float>(1,1);
    const float cx = K.at<float>(0,2);
    const float cy = K.at<float>(1,2);

    vbGood = vector<bool>(vKeys1.size(),false);
    vP3D.resize(vKeys1.size());

    vector<float> vCosParallax;
    vCosParallax.reserve(vKeys1.size());

    // Camera 1 Projection Matrix K[I|0]
    //相机1的投影矩阵K[I|0]，世界坐标系和相机1坐标系相同
    cv::Mat P1(3,4,CV_32F,cv::Scalar(0));
    K.copyTo(P1.rowRange(0,3).colRange(0,3));

    // 相机1的光心在世界坐标系坐标
    cv::Mat O1 = cv::Mat::zeros(3,1,CV_32F);

    // Camera 2 Projection Matrix K[R|t]
    //相机2的投影矩阵
    cv::Mat P2(3,4,CV_32F);
    R.copyTo(P2.rowRange(0,3).colRange(0,3));
    t.copyTo(P2.rowRange(0,3).col(3));
    P2 = K*P2;

    // 相机2的光心在世界坐标系坐标
    cv::Mat O2 = -R.t()*t;

    int nGood=0;

    //遍历所有的匹配点
    for(size_t i=0, iend=vMatches12.size();i<iend;i++)
    {
	//如果在
        if(!vbMatchesInliers[i])
            continue;

        const cv::KeyPoint &kp1 = vKeys1[vMatches12[i].first];
        const cv::KeyPoint &kp2 = vKeys2[vMatches12[i].second];
	
	//3d点在相机1和世界坐标系下的坐标
        cv::Mat p3dC1;
	
	//输出的p3dC1是综合考虑了P1,P2的kp1,kp2匹配点在世界坐标系中的齐次坐标
	//由于世界坐标系和相机1坐标系重合，所以p3dC1同时也是匹配点对应的空间点在相机1坐标系中的坐标
        Triangulate(kp1,kp2,P1,P2,p3dC1);
	//isfinite()判断一个浮点数是否是一个有限值
	//相当于是确定p3dC1前三位数值正常
        if(!isfinite(p3dC1.at<float>(0)) || !isfinite(p3dC1.at<float>(1)) || !isfinite(p3dC1.at<float>(2)))
        {
            vbGood[vMatches12[i].first]=false;
            continue;
        }

        // Check parallax
        //normal1是相机1到3d点的向量
        cv::Mat normal1 = p3dC1 - O1;
        float dist1 = cv::norm(normal1);
	
	//normal2是相机2到3d点的向量
        cv::Mat normal2 = p3dC1 - O2;
        float dist2 = cv::norm(normal2);

	//cosParallax为视差角的余弦，也就是normal1与normal2的余弦
        float cosParallax = normal1.dot(normal2)/(dist1*dist2);

        // Check depth in front of first camera (only if enough parallax, as "infinite" points can easily go to negative depth)
	//p3dC1.at(2)<=0说明3d点在光心后面，深度为负
	//p3dC1视差角较大，且深度为负则淘汰
        if(p3dC1.at<float>(2)<=0 && cosParallax<0.99998)
            continue;

        // Check depth in front of second camera (only if enough parallax, as "infinite" points can easily go to negative depth)
        cv::Mat p3dC2 = R*p3dC1+t;
	
	//p3dC2视差角较大，且深度为负则淘汰
        if(p3dC2.at<float>(2)<=0 && cosParallax<0.99998)
            continue;

        // Check reprojection error in first image
	// 计算3D点在第一个图像上的投影误差
        float im1x, im1y;
        float invZ1 = 1.0/p3dC1.at<float>(2);
        im1x = fx*p3dC1.at<float>(0)*invZ1+cx;
        im1y = fy*p3dC1.at<float>(1)*invZ1+cy;

	
        float squareError1 = (im1x-kp1.pt.x)*(im1x-kp1.pt.x)+(im1y-kp1.pt.y)*(im1y-kp1.pt.y);

        if(squareError1>th2)
            continue;

        // Check reprojection error in second image
        float im2x, im2y;
        float invZ2 = 1.0/p3dC2.at<float>(2);
        im2x = fx*p3dC2.at<float>(0)*invZ2+cx;
        im2y = fy*p3dC2.at<float>(1)*invZ2+cy;

        float squareError2 = (im2x-kp2.pt.x)*(im2x-kp2.pt.x)+(im2y-kp2.pt.y)*(im2y-kp2.pt.y);

	
        // 重投影误差太大，淘汰
        if(squareError2>th2)
            continue;

	//到这里说明这对匹配点三角化重投影成功了
        vCosParallax.push_back(cosParallax);
        vP3D[vMatches12[i].first] = cv::Point3f(p3dC1.at<float>(0),p3dC1.at<float>(1),p3dC1.at<float>(2));
        nGood++;

	//确认视差角最够大
        if(cosParallax<0.99998)
            vbGood[vMatches12[i].first]=true;
    }

    if(nGood>0)
    {
	//将视差角余弦有小到大排序
        sort(vCosParallax.begin(),vCosParallax.end());

	//取出第50个，或者最后那个也就是最大那个
        size_t idx = min(50,int(vCosParallax.size()-1));
	//计算出视差角
        parallax = acos(vCosParallax[idx])*180/CV_PI;
    }
    else
        parallax=0;

    return nGood;
}

3.13.类方法DecomposeE()

/**将本质矩阵分解成Rt,有四种模型
* @param E 
* @param R1 输出其中一种R
* @param R2 输出其中一种R
* @param t 输出t
*/

void Initializer::DecomposeE(const cv::Mat &E, cv::Mat &R1, cv::Mat &R2, cv::Mat &t)
{
    cv::Mat u,w,vt;
    cv::SVD::compute(E,w,u,vt);

    u.col(2).copyTo(t);
    t=t/cv::norm(t);

    cv::Mat W(3,3,CV_32F,cv::Scalar(0));
    W.at<float>(0,1)=-1;
    W.at<float>(1,0)=1;
    W.at<float>(2,2)=1;

    R1 = u*W*vt;
    if(cv::determinant(R1)<0)
        R1=-R1;

    R2 = u*W.t()*vt;
    if(cv::determinant(R2)<0)
        R2=-R2;
}