ORBSLAM2学习笔记4(Initializer)

单目初始化的类

Initializer.h

/**
* This file is part of ORB-SLAM2.
*
* Copyright (C) 2014-2016 Raúl Mur-Artal  (University of Zaragoza)
* For more information see 
*
* ORB-SLAM2 is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* ORB-SLAM2 is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with ORB-SLAM2. If not, see .
*/
#ifndef INITIALIZER_H
#define INITIALIZER_H

#include
#include "Frame.h"


namespace ORB_SLAM2
{

// THIS IS THE INITIALIZER FOR MONOCULAR SLAM. NOT USED IN THE STEREO OR RGBD CASE.
//单目初始化器
class Initializer
{
    typedef pair<int,int> Match;

public:

    // Fix the reference frame
    Initializer(const Frame &ReferenceFrame, float sigma = 1.0, int iterations = 200);

    // 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:

    void FindHomography(vector<bool> &vbMatchesInliers, float &score, cv::Mat &H21);
    void FindFundamental(vector<bool> &vbInliers, float &score, cv::Mat &F21);

    cv::Mat ComputeH21(const vector<cv::Point2f> &vP1, const vector<cv::Point2f> &vP2);
    cv::Mat ComputeF21(const vector<cv::Point2f> &vP1, const vector<cv::Point2f> &vP2);

    float CheckHomography(const cv::Mat &H21, const cv::Mat &H12, vector<bool> &vbMatchesInliers, float sigma);

    float CheckFundamental(const cv::Mat &F21, vector<bool> &vbMatchesInliers, float sigma);

    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);

    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);

    void Triangulate(const cv::KeyPoint &kp1, const cv::KeyPoint &kp2, const cv::Mat &P1, const cv::Mat &P2, cv::Mat &x3D);

    void Normalize(const vector<cv::KeyPoint> &vKeys, vector<cv::Point2f> &vNormalizedPoints, cv::Mat &T);

    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);

    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
    vector<Match> mvMatches12;
    vector<bool> mvbMatched1;

    // Calibration
    cv::Mat mK;

    // Standard Deviation and Variance
    float mSigma, mSigma2;

    // Ransac max iterations
    int mMaxIterations;

    // Ransac sets
    vector<vector<size_t> > mvSets;   

};

} //namespace ORB_SLAM

#endif // INITIALIZER_H

Initializer.cc

/**
* This file is part of ORB-SLAM2.
*
* Copyright (C) 2014-2016 Raúl Mur-Artal  (University of Zaragoza)
* For more information see 
*
* ORB-SLAM2 is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* ORB-SLAM2 is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with ORB-SLAM2. If not, see .
*/

#include "Initializer.h"

#include "Thirdparty/DBoW2/DUtils/Random.h"

#include "Optimizer.h"
#include "ORBmatcher.h"

#include

namespace ORB_SLAM2
{

Initializer::Initializer(const Frame &ReferenceFrame, float sigma, int iterations)
{
    mK = ReferenceFrame.mK.clone();

    mvKeys1 = ReferenceFrame.mvKeysUn;

    mSigma = sigma;
    mSigma2 = sigma*sigma;
    mMaxIterations = iterations;
}


/**
 * 初始化
 * 1.RANSAC随机选择200组数据,每组数据8个特征点
 * 2.分别计算H和F矩阵,选择效果最好的那个
 */
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.clear();
    mvMatches12.reserve(mvKeys2.size());
    mvbMatched1.resize(mvKeys1.size());
    //将vMatches12中的特征点匹配关系填充到mvMatches12中
    for(size_t i=0, iend=vMatches12.size();i<iend; i++)
    {
        if(vMatches12[i]>=0)
        {
            //pair [ref frame keypoint id, current frame keypoint id]
            mvMatches12.push_back(make_pair(i,vMatches12[i]));
            mvbMatched1[i]=true;
        }
        else /// -1 means not matched
            mvbMatched1[i]=false;
    }

    /// matched key points size
    ///匹配的特征点的数目
    const int N = mvMatches12.size();

    // Indices for minimum set selection
    vector<size_t> vAllIndices;
    vAllIndices.reserve(N);
    vector<size_t> vAvailableIndices;
    //索引值
    for(int i=0; i<N; i++)
    {
        vAllIndices.push_back(i);
    }

    // Generate sets of 8 points for each RANSAC iteration
     ///200 * vector
     //为每次的RANSAC迭代生成8个点
    mvSets = vector< vector<size_t> >(mMaxIterations,vector<size_t>(8,0));

    DUtils::Random::SeedRandOnce(0);

    /// 200 times iterations,生成200次迭代数据
    for(int it=0; it<mMaxIterations; it++)
    {
        vAvailableIndices = vAllIndices;

        // Select a minimum set
        for(size_t j=0; j<8; j++)
        {
            /// get a random int number between [0, avalible_index]
            int randi = DUtils::Random::RandomInt(0,vAvailableIndices.size()-1);
            /// get key point index according random int number
            int idx = vAvailableIndices[randi];

            //填充第it次迭代的第j个数据
            mvSets[it][j] = idx;

            /// move the last element to replace randi index, and delete the last element
            vAvailableIndices[randi] = vAvailableIndices.back();
            vAvailableIndices.pop_back();
        }
    }

    // Launch threads to compute in parallel a fundamental matrix and a homography
    //启动两个线程同步分别计算H和F矩阵
    vector<bool> vbMatchesInliersH, vbMatchesInliersF;
    float SH, SF;
    cv::Mat H, F;

    thread threadH(&Initializer::FindHomography,this,ref(vbMatchesInliersH), ref(SH), ref(H));
    thread threadF(&Initializer::FindFundamental,this,ref(vbMatchesInliersF), ref(SF), ref(F));

    // Wait until both threads have finished
    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)
    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;
}

/**
 * 找到最佳的Homography矩阵
 */
void Initializer::FindHomography(vector<bool> &vbMatchesInliers, float &score, cv::Mat &H21)
{
    // Number of putative matches
    const int N = mvMatches12.size();

    // Normalize coordinates
    //归一化坐标
    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
    //执行迭代,保存得分最高的解决方案
    for(int it=0; it<mMaxIterations; it++)
    {
        // Select a minimum set
        for(size_t j=0; j<8; j++)
        {
            int idx = mvSets[it][j];

            /// key point in frame 1
            vPn1i[j] = vPn1[mvMatches12[idx].first];
            /// key point in frame 2
            vPn2i[j] = vPn2[mvMatches12[idx].second];
        }
        /**
         *  这里计算出来的H矩阵是相对于归一化之后的特征点的,我们需要的是归一化之前的H21矩阵
         * 设P1,P2分别为F1和F2两帧上的匹配的特征点(未归一化),其通过Hn矩阵的映射关系为
         * 有1.T2*P2 = Hn*T1*P1
         *     2. H21*P1=P2 ,
         * 因此T2*H21*P1=Hn* T1*P1
         * ==>H21 = T2^-1*Hn*T1
         * */
        cv::Mat Hn = ComputeH21(vPn1i,vPn2i);
        H21i = T2inv*Hn*T1;
        H12i = H21i.inv();

        //在参数mSigma下给这个H矩阵评分
        currentScore = CheckHomography(H21i, H12i, vbCurrentInliers, mSigma);

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


/**计算F矩阵 */
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];
        }

        cv::Mat Fn = ComputeF21(vPn1i,vPn2i);

        F21i = T2t*Fn*T1;

        currentScore = CheckFundamental(F21i, vbCurrentInliers, mSigma);

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


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);

    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;

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

    return vt.row(8).reshape(0, 3);
}

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);

    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);

    cv::Mat Fpre = vt.row(8).reshape(0, 3);

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

    w.at<float>(2)=0;

    return  u*cv::Mat::diag(w)*vt;
}

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;

    //来源于卡方分布,有95%的可信度
    const float th = 5.991;
    //卡方分布的方差
    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 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v2,u2投影到F1之后,与v1,u1的差值的平方和
        const float squareDist1 = (u1-u2in1)*(u1-u2in1)+(v1-v2in1)*(v1-v2in1);
        //计算卡方值
        //ref https://en.wikipedia.org/wiki/Chi-square_distribution [Occurrence and applications] table(chi-square distribution)
        const float chiSquare1 = squareDist1*invSigmaSquare;

        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;

        //统计inlier和分数
        if(chiSquare2>th)
            bIn = false;
        else
            score += th - chiSquare2;

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

    return score;
}

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;
    
    //卡方分布1自由度,95%可信度
    const float th = 3.841;
    //卡方分布2自由度,95%可信度
    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;

        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)
        //F矩阵将点映射成一条直线
        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;

        //点到直线的距离的平方
        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;
}

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;
    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
    //用三角化的点的方式检测4种模型
    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
    //maxGood
    //nsimilar>1,没有一个模型明显好于其它模型
    if(maxGood<nMinGood || nsimilar>1)
    {
        return false;
    }

    // If best reconstruction has enough parallax initialize
    if(maxGood==nGood1)
    {
        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;
}

/**
 * 将H矩阵分解为R,t,并三角化点
 */
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)
{
    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

    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);
    V=Vt.t();

    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);

    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
    //遍历计算出来的8种,R,t,然后根据R,t计算三角化出来的匹配点的数目,找出最好和次好的模型
    for(size_t i=0; i<8; i++)
    {
        float parallaxi;
        vector<cv::Point3f> vP3Di;
        vector<bool> vbTriangulatedi;
        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;
        }
    }

    /**
     * 1.最好的模型比次好的模型有足够的差距;
     * 2.最好的模型视差>=最小视差
     * 3.最好模型的三角化陈宫的点的数目大于一定的阈值;
     * 4.最好的模型的三角化成功数量和通过H矩阵重投影的特征点数目的比例大于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;
}

/// 12.2 Linear triangulation methods
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);
    x3D = vt.row(3).t();
    x3D = x3D.rowRange(0,3)/x3D.at<float>(3);
}

/// vNormalizedPoints=T*vKeys
///
/// T = [ sx 0  -meanX*sX; 
///           0  sy -meanY*sY; 
///           0  0          1 ]
/// 对特征点的像素坐标进行归一化
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);

    /// 1. get meanX and meanY
    for(int i=0; i<N; i++)
    {
        meanX += vKeys[i].pt.x;
        meanY += vKeys[i].pt.y;
    }

    //1.求出质心
    meanX = meanX/N;
    meanY = meanY/N;

    float meanDevX = 0;
    float meanDevY = 0;

    //2.减去质心
    for(int i=0; i<N; i++)
    {
        /// remove the center of mass
        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);
    }

    /// mean abs dis to center of mass
    //3.计算特征点到质心的平均距离
    meanDevX = meanDevX/N;
    meanDevY = meanDevY/N;

    ///4. 计算缩放因子 sX, sY
    float sX = 1.0/meanDevX;
    float sY = 1.0/meanDevY;

    ///5. 使用缩放因此缩放特征点
    for(int i=0; i<N; i++)
    {
        vNormalizedPoints[i].x = vNormalizedPoints[i].x * sX;
        vNormalizedPoints[i].y = vNormalizedPoints[i].y * sY;
    }

    //6.保存转换矩阵T,用来恢复归一化之前的尺度信息
    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;
}

/**
 * @brief:检测R,t
 * R:输入的旋转矩阵R;
 * t:输入的平移矩阵t;
 * vKeys1:输入的第一组特征点
 * vKeys2:输入的第二组特征点;
 * vMatches12:输入的匹配的数目;
 * vbMatchesInliers:输出inlier的vector
 * K:输入内参
 * vP3D:输出3D点的坐标;
 * th2:输入阈值
 * vbGood:输出好的点的flag;
 * parallax:输出视差
 */
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的坐标系和世界坐标系相同
    cv::Mat P1(3,4,CV_32F,cv::Scalar(0));
    K.copyTo(P1.rowRange(0,3).colRange(0,3));

    //假设相机光心的在世界坐标系的坐标为(0,0,0)
    cv::Mat O1 = cv::Mat::zeros(3,1,CV_32F);

    // Camera 2 Projection Matrix K[R|t]
    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;
    //将相机光心2转换到世界坐标系
    //O1=R12*O2+t12 ==> O2=R12'*(O1-t12) ==> O2=-R12'*t12
    cv::Mat O2 = -R.t()*t;
 
    int nGood=0;
    //遍历所有匹配的特征点
    for(size_t i=0, iend=vMatches12.size();i<iend;i++)
    {
        //如果不是inlier,则跳过
        if(!vbMatchesInliers[i])
            continue;

        const cv::KeyPoint &kp1 = vKeys1[vMatches12[i].first];
        const cv::KeyPoint &kp2 = vKeys2[vMatches12[i].second];
        cv::Mat p3dC1;

        //三角化匹配特征点
        Triangulate(kp1,kp2,P1,P2,p3dC1);

        //判断三角化点的大小是否无穷大
        if(!isfinite(p3dC1.at<float>(0)) || !isfinite(p3dC1.at<float>(1)) || !isfinite(p3dC1.at<float>(2)))
        {
            vbGood[vMatches12[i].first]=false;
            continue;
        }

        // Check parallax
        //检测视差
        cv::Mat normal1 = p3dC1 - O1;
        float dist1 = cv::norm(normal1);

        cv::Mat normal2 = p3dC1 - O2;
        float dist2 = cv::norm(normal2);

        //3D点和两个光心构成的夹角的cos值
        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)
        //视差角度太大,并且深度为负,就淘汰
        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)
        //视差角度太大,并且深度为负,就淘汰
        cv::Mat p3dC2 = R*p3dC1+t;

        if(p3dC2.at<float>(2)<=0 && cosParallax<0.99998)
            continue;

        // Check reprojection error in first image
        //将三角化出来的3D点重新投影到第一帧图像,然后计算方差
        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
         //将三角化出来的3D点重新投影到第二帧图像,然后计算方差
        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;

        //保存视差角
        vCosParallax.push_back(cosParallax);
        vP3D[vMatches12[i].first] = cv::Point3f(p3dC1.at<float>(0),p3dC1.at<float>(1),p3dC1.at<float>(2));
        nGood++;

        //视差角度足够大,三角化成功
        if(cosParallax<0.99998)
            vbGood[vMatches12[i].first]=true;
    }//for

    if(nGood>0)
    {
        //视差角度从大到小排列
        sort(vCosParallax.begin(),vCosParallax.end());

        //取出第50个,或者最后(就是最小的视差角度最大的那个)
        size_t idx = min(50,int(vCosParallax.size()-1));
        //计算视差角
        parallax = acos(vCosParallax[idx])*180/CV_PI;
    }
    else
        parallax=0;

    return nGood;
}

/**
 * 分解本质矩阵,得到两种不同R,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;
}

} //namespace ORB_SLAM