ORBSLAM2学习笔记9(Optimizer)

Optimizer.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 OPTIMIZER_H
#define OPTIMIZER_H

#include "Map.h"
#include "MapPoint.h"
#include "KeyFrame.h"
#include "LoopClosing.h"
#include "Frame.h"

#include "Thirdparty/g2o/g2o/types/types_seven_dof_expmap.h"

namespace ORB_SLAM2
{

class LoopClosing;

/**
 * 非线性优化类
 */
class Optimizer
{
public:
    void static BundleAdjustment(const std::vector<KeyFrame*> &vpKF, const std::vector<MapPoint*> &vpMP,
                                 int nIterations = 5, bool *pbStopFlag=NULL, const unsigned long nLoopKF=0,
                                 const bool bRobust = true);

    /**
     * @brief 全局BA
     * @param pMap:地图
     * @param nIterations:迭代次数
     * @param pbStopFlag:是否停止FLAG
     * @param nLoopKF:回环帧ID
     * @param bRobust:是否设置鲁棒核
     */
    void static GlobalBundleAdjustemnt(Map* pMap, int nIterations=5, bool *pbStopFlag=NULL,
                                       const unsigned long nLoopKF=0, const bool bRobust = true);

    /**
     * @brief 这里是进行局部的BA优化
     * @param pKF : 输入关键帧
     * @param pbStopFlag : 输入是否停止优化flag
     * @param pMap : 输入地图点
     */
    void static LocalBundleAdjustment(KeyFrame* pKF, bool *pbStopFlag, Map *pMap);

    /**
     * @brief 这里的顶点只有一个,那就是相机的Pose,因此这里只优化当前帧的pose,地图点固定. 
     * @param pFrame : 输入优化的关键帧
     */
    int static PoseOptimization(Frame* pFrame);

    // if bFixScale is true, 6DoF optimization (stereo,rgbd), 7DoF otherwise (mono)
    /**
     * @brief 优化EssentialGraph图,主要用在 LoopClosing::CorrectLoop()这个函数
     * @param pMap: 地图
     * @param pLoopKF: 回环帧
     * @param pCurKF: 当前帧
     * @param NonCorrectedSim3: 没有纠正的关键帧
     * @param CorrectedSim3: 纠正后的关键帧
     * @param LoopConnections: 回环的关系
     * @param bFixScale: 是否固定缩放比例,if bFixScale is true, optimize SE3 (stereo,rgbd), Sim3 otherwise (mono)
     */
    void static OptimizeEssentialGraph(Map* pMap, KeyFrame* pLoopKF, KeyFrame* pCurKF,
                                       const LoopClosing::KeyFrameAndPose &NonCorrectedSim3,
                                       const LoopClosing::KeyFrameAndPose &CorrectedSim3,
                                       const map<KeyFrame *, set<KeyFrame *> > &LoopConnections,
                                       const bool &bFixScale);

    /**
     * @brief 两针之间进行Sim3优化
     * @param pKF1:pKF1
     * @param pKF2:pKF2
     * @param vpMatches1:pKF2中匹配的特征点
     * @param g2oS12:两帧之间的Sim3位姿关系
     * @param th2:阈值
     * @param bFixScale: 是否固定缩放比例,if bFixScale is true, optimize SE3 (stereo,rgbd), Sim3 otherwise (mono)
     */
    static int OptimizeSim3(KeyFrame* pKF1, KeyFrame* pKF2, std::vector<MapPoint *> &vpMatches1,
                            g2o::Sim3 &g2oS12, const float th2, const bool bFixScale);
};

} //namespace ORB_SLAM

#endif // OPTIMIZER_H

Optimizer.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 "Optimizer.h"

#include "Thirdparty/g2o/g2o/core/block_solver.h"
#include "Thirdparty/g2o/g2o/core/optimization_algorithm_levenberg.h"
#include "Thirdparty/g2o/g2o/solvers/linear_solver_eigen.h"
#include "Thirdparty/g2o/g2o/types/types_six_dof_expmap.h"
#include "Thirdparty/g2o/g2o/core/robust_kernel_impl.h"
#include "Thirdparty/g2o/g2o/solvers/linear_solver_dense.h"
#include "Thirdparty/g2o/g2o/types/types_seven_dof_expmap.h"

#include

#include "Converter.h"

#include

namespace ORB_SLAM2
{


void Optimizer::GlobalBundleAdjustemnt(Map* pMap, int nIterations, bool* pbStopFlag, const unsigned long nLoopKF, const bool bRobust)
{
    vector<KeyFrame*> vpKFs = pMap->GetAllKeyFrames();
    vector<MapPoint*> vpMP = pMap->GetAllMapPoints();
    BundleAdjustment(vpKFs,vpMP,nIterations,pbStopFlag, nLoopKF, bRobust);
}


void Optimizer::BundleAdjustment(const vector<KeyFrame *> &vpKFs, const vector<MapPoint *> &vpMP,
                                 int nIterations, bool* pbStopFlag, const unsigned long nLoopKF, const bool bRobust)
{
    vector<bool> vbNotIncludedMP;
    vbNotIncludedMP.resize(vpMP.size());

    g2o::SparseOptimizer optimizer;
    g2o::BlockSolver_6_3::LinearSolverType * linearSolver;
    //指定块解析器的模板类型
    linearSolver = new g2o::LinearSolverEigen<g2o::BlockSolver_6_3::PoseMatrixType>();

    g2o::BlockSolver_6_3 * solver_ptr = new g2o::BlockSolver_6_3(linearSolver);

    g2o::OptimizationAlgorithmLevenberg* solver = new g2o::OptimizationAlgorithmLevenberg(solver_ptr);
    optimizer.setAlgorithm(solver);

    if(pbStopFlag)
        optimizer.setForceStopFlag(pbStopFlag);

    long unsigned int maxKFid = 0;

    // Set KeyFrame vertices
    for(size_t i=0; i<vpKFs.size(); i++)
    {
        KeyFrame* pKF = vpKFs[i];
        if(pKF->isBad())
            continue;
        g2o::VertexSE3Expmap * vSE3 = new g2o::VertexSE3Expmap();
        vSE3->setEstimate(Converter::toSE3Quat(pKF->GetPose()));
        vSE3->setId(pKF->mnId);
        vSE3->setFixed(pKF->mnId==0);
        optimizer.addVertex(vSE3);
        if(pKF->mnId>maxKFid)
            maxKFid=pKF->mnId;
    }

    const float thHuber2D = sqrt(5.99);
    const float thHuber3D = sqrt(7.815);

    // Set MapPoint vertices
    for(size_t i=0; i<vpMP.size(); i++)
    {
        MapPoint* pMP = vpMP[i];
        if(pMP->isBad())
            continue;
        g2o::VertexSBAPointXYZ* vPoint = new g2o::VertexSBAPointXYZ();
        vPoint->setEstimate(Converter::toVector3d(pMP->GetWorldPos()));
        const int id = pMP->mnId+maxKFid+1;
        vPoint->setId(id);
        vPoint->setMarginalized(true);//参与边缘化
        optimizer.addVertex(vPoint);

       const map<KeyFrame*,size_t> observations = pMP->GetObservations();

        int nEdges = 0;
        //SET EDGES
        //地图点和关键帧之间添加边
        for(map<KeyFrame*,size_t>::const_iterator mit=observations.begin(); mit!=observations.end(); mit++)
        {

            KeyFrame* pKF = mit->first;
            if(pKF->isBad() || pKF->mnId>maxKFid)
                continue;

            nEdges++;

            const cv::KeyPoint &kpUn = pKF->mvKeysUn[mit->second];

            //单目
            if(pKF->mvuRight[mit->second]<0)
            {
                Eigen::Matrix<double,2,1> obs;
                obs << kpUn.pt.x, kpUn.pt.y;

                g2o::EdgeSE3ProjectXYZ* e = new g2o::EdgeSE3ProjectXYZ();

                e->setVertex(0, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(id)));
                e->setVertex(1, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(pKF->mnId)));
                e->setMeasurement(obs);
                const float &invSigma2 = pKF->mvInvLevelSigma2[kpUn.octave];
                e->setInformation(Eigen::Matrix2d::Identity()*invSigma2);

                if(bRobust)
                {
                    g2o::RobustKernelHuber* rk = new g2o::RobustKernelHuber;
                    e->setRobustKernel(rk);
                    rk->setDelta(thHuber2D);
                }

                e->fx = pKF->fx;
                e->fy = pKF->fy;
                e->cx = pKF->cx;
                e->cy = pKF->cy;

                optimizer.addEdge(e);
            }
            //双目
            else
            {
                Eigen::Matrix<double,3,1> obs;
                const float kp_ur = pKF->mvuRight[mit->second];
                obs << kpUn.pt.x, kpUn.pt.y, kp_ur;

                g2o::EdgeStereoSE3ProjectXYZ* e = new g2o::EdgeStereoSE3ProjectXYZ();

                e->setVertex(0, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(id)));
                e->setVertex(1, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(pKF->mnId)));
                e->setMeasurement(obs);
                const float &invSigma2 = pKF->mvInvLevelSigma2[kpUn.octave];
                Eigen::Matrix3d Info = Eigen::Matrix3d::Identity()*invSigma2;
                e->setInformation(Info);

                if(bRobust)
                {
                    g2o::RobustKernelHuber* rk = new g2o::RobustKernelHuber;
                    e->setRobustKernel(rk);
                    rk->setDelta(thHuber3D);
                }

                e->fx = pKF->fx;
                e->fy = pKF->fy;
                e->cx = pKF->cx;
                e->cy = pKF->cy;
                e->bf = pKF->mbf;

                optimizer.addEdge(e);
            }
        }

        if(nEdges==0)
        {
            optimizer.removeVertex(vPoint);
            vbNotIncludedMP[i]=true;
        }
        else
        {
            vbNotIncludedMP[i]=false;
        }
    }

    // Optimize!
    optimizer.initializeOptimization();
    optimizer.optimize(nIterations);

    // Recover optimized data

    //Keyframes
    for(size_t i=0; i<vpKFs.size(); i++)
    {
        KeyFrame* pKF = vpKFs[i];
        if(pKF->isBad())
            continue;
        g2o::VertexSE3Expmap* vSE3 = static_cast<g2o::VertexSE3Expmap*>(optimizer.vertex(pKF->mnId));
        g2o::SE3Quat SE3quat = vSE3->estimate();
        if(nLoopKF==0)
        {
            pKF->SetPose(Converter::toCvMat(SE3quat));
        }
        else
        {
            pKF->mTcwGBA.create(4,4,CV_32F);
            Converter::toCvMat(SE3quat).copyTo(pKF->mTcwGBA);
            pKF->mnBAGlobalForKF = nLoopKF;//标记为已经经过BA优化处理过的
        }
    }

    //Points
    for(size_t i=0; i<vpMP.size(); i++)
    {
        if(vbNotIncludedMP[i])
            continue;

        MapPoint* pMP = vpMP[i];

        if(pMP->isBad())
            continue;
        g2o::VertexSBAPointXYZ* vPoint = static_cast<g2o::VertexSBAPointXYZ*>(optimizer.vertex(pMP->mnId+maxKFid+1));

        if(nLoopKF==0)
        {
            pMP->SetWorldPos(Converter::toCvMat(vPoint->estimate()));
            pMP->UpdateNormalAndDepth();
        }
        else
        {
            pMP->mPosGBA.create(3,1,CV_32F);
            Converter::toCvMat(vPoint->estimate()).copyTo(pMP->mPosGBA);
            pMP->mnBAGlobalForKF = nLoopKF;
        }
    }

}

int Optimizer::PoseOptimization(Frame *pFrame)
{
    g2o::SparseOptimizer optimizer;

    ///6:6 freedom, 3: 3D point
    g2o::BlockSolver_6_3::LinearSolverType * linearSolver;
    linearSolver = new g2o::LinearSolverDense<g2o::BlockSolver_6_3::PoseMatrixType>();

    g2o::BlockSolver_6_3 * solver_ptr = new g2o::BlockSolver_6_3(linearSolver);

    g2o::OptimizationAlgorithmLevenberg* solver = new g2o::OptimizationAlgorithmLevenberg(solver_ptr);
    optimizer.setAlgorithm(solver);

    int nInitialCorrespondences=0;

    // Set Frame vertex
    g2o::VertexSE3Expmap * vSE3 = new g2o::VertexSE3Expmap();
    vSE3->setEstimate(Converter::toSE3Quat(pFrame->mTcw));
    vSE3->setId(0);
    vSE3->setFixed(false);
    optimizer.addVertex(vSE3);

    // Set MapPoint vertices
    const int N = pFrame->N;

    vector<g2o::EdgeSE3ProjectXYZOnlyPose*> vpEdgesMono;
    vector<size_t> vnIndexEdgeMono;
    vpEdgesMono.reserve(N);
    vnIndexEdgeMono.reserve(N);

    vector<g2o::EdgeStereoSE3ProjectXYZOnlyPose*> vpEdgesStereo;
    vector<size_t> vnIndexEdgeStereo;
    vpEdgesStereo.reserve(N);
    vnIndexEdgeStereo.reserve(N);

    const float deltaMono = sqrt(5.991);
    const float deltaStereo = sqrt(7.815);


    {
    unique_lock<mutex> lock(MapPoint::mGlobalMutex);

    ///遍历所有特征点,添加Edge
    for(int i=0; i<N; i++)
    {
        MapPoint* pMP = pFrame->mvpMapPoints[i];
        if(pMP)
        {
            // Monocular observation
            if(pFrame->mvuRight[i]<0)
            {
                nInitialCorrespondences++;
                pFrame->mvbOutlier[i] = false;

                Eigen::Matrix<double,2,1> obs;
                const cv::KeyPoint &kpUn = pFrame->mvKeysUn[i];
                obs << kpUn.pt.x, kpUn.pt.y;

                g2o::EdgeSE3ProjectXYZOnlyPose* e = new g2o::EdgeSE3ProjectXYZOnlyPose();

                e->setVertex(0, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(0)));
                e->setMeasurement(obs);
                const float invSigma2 = pFrame->mvInvLevelSigma2[kpUn.octave];
                e->setInformation(Eigen::Matrix2d::Identity()*invSigma2);

                g2o::RobustKernelHuber* rk = new g2o::RobustKernelHuber;
                e->setRobustKernel(rk);
                rk->setDelta(deltaMono);

                e->fx = pFrame->fx;
                e->fy = pFrame->fy;
                e->cx = pFrame->cx;
                e->cy = pFrame->cy;
                cv::Mat Xw = pMP->GetWorldPos();
                e->Xw[0] = Xw.at<float>(0);
                e->Xw[1] = Xw.at<float>(1);
                e->Xw[2] = Xw.at<float>(2);

                optimizer.addEdge(e);

                vpEdgesMono.push_back(e);
                vnIndexEdgeMono.push_back(i);
            }
            else  // Stereo observation
            {
                nInitialCorrespondences++;
                pFrame->mvbOutlier[i] = false;

                //SET EDGE
                Eigen::Matrix<double,3,1> obs;
                const cv::KeyPoint &kpUn = pFrame->mvKeysUn[i];
                const float &kp_ur = pFrame->mvuRight[i];
                obs << kpUn.pt.x, kpUn.pt.y, kp_ur;

                g2o::EdgeStereoSE3ProjectXYZOnlyPose* e = new g2o::EdgeStereoSE3ProjectXYZOnlyPose();

                e->setVertex(0, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(0)));
                e->setMeasurement(obs);
                const float invSigma2 = pFrame->mvInvLevelSigma2[kpUn.octave];
                Eigen::Matrix3d Info = Eigen::Matrix3d::Identity()*invSigma2;
                e->setInformation(Info);

                g2o::RobustKernelHuber* rk = new g2o::RobustKernelHuber;
                e->setRobustKernel(rk);
                rk->setDelta(deltaStereo);

                e->fx = pFrame->fx;
                e->fy = pFrame->fy;
                e->cx = pFrame->cx;
                e->cy = pFrame->cy;
                e->bf = pFrame->mbf;
                cv::Mat Xw = pMP->GetWorldPos();
                e->Xw[0] = Xw.at<float>(0);
                e->Xw[1] = Xw.at<float>(1);
                e->Xw[2] = Xw.at<float>(2);

                optimizer.addEdge(e);

                vpEdgesStereo.push_back(e);
                vnIndexEdgeStereo.push_back(i);
            }
        }

    }
    }


    if(nInitialCorrespondences<3)
        return 0;

    // We perform 4 optimizations, after each optimization we classify observation as inlier/outlier
    // At the next optimization, outliers are not included, but at the end they can be classified as inliers again.
    ///执行四次优化,每次最多迭代10次,每次优化之后,我们将观测的特征点分为inlier和outlier,在下一次优化的时候,outlier不参加,
    ///但是最后可以再次被分类为inlier
    ///一般取 [公式] 为95%，一个内点只有5%的可能被错误的认为是外点
    const float chi2Mono[4]={5.991,5.991,5.991,5.991};
    const float chi2Stereo[4]={7.815,7.815,7.815, 7.815};
    const int its[4]={10,10,10,10};    

    int nBad=0;
    for(size_t it=0; it<4; it++)
    {

        vSE3->setEstimate(Converter::toSE3Quat(pFrame->mTcw));
        optimizer.initializeOptimization(0);
        optimizer.optimize(its[it]);

        nBad=0;
        ///遍历优化后的Edge
        for(size_t i=0, iend=vpEdgesMono.size(); i<iend; i++)
        {
            g2o::EdgeSE3ProjectXYZOnlyPose* e = vpEdgesMono[i];

            const size_t idx = vnIndexEdgeMono[i];

            if(pFrame->mvbOutlier[idx])
            {
                e->computeError();
            }

            ///得到卡方分布的的值
            const float chi2 = e->chi2();

            ///误差比较大,设置为outlier
            if(chi2>chi2Mono[it])
            {                
                pFrame->mvbOutlier[idx]=true;
                e->setLevel(1);
                nBad++;
            }
            else
            {
                pFrame->mvbOutlier[idx]=false;
                e->setLevel(0);
            }

            if(it==2)
                e->setRobustKernel(0);
        }

        for(size_t i=0, iend=vpEdgesStereo.size(); i<iend; i++)
        {
            g2o::EdgeStereoSE3ProjectXYZOnlyPose* e = vpEdgesStereo[i];

            const size_t idx = vnIndexEdgeStereo[i];

            if(pFrame->mvbOutlier[idx])
            {
                e->computeError();
            }

            const float chi2 = e->chi2();

            if(chi2>chi2Stereo[it])
            {
                pFrame->mvbOutlier[idx]=true;
                e->setLevel(1);
                nBad++;
            }
            else
            {                
                e->setLevel(0);
                pFrame->mvbOutlier[idx]=false;
            }

            if(it==2)
                e->setRobustKernel(0);
        }

        if(optimizer.edges().size()<10)
            break;
    }    

    // Recover optimized pose and return number of inliers
    g2o::VertexSE3Expmap* vSE3_recov = static_cast<g2o::VertexSE3Expmap*>(optimizer.vertex(0));
    g2o::SE3Quat SE3quat_recov = vSE3_recov->estimate();
    cv::Mat pose = Converter::toCvMat(SE3quat_recov);
    pFrame->SetPose(pose);

    return nInitialCorrespondences-nBad;
}

void Optimizer::LocalBundleAdjustment(KeyFrame *pKF, bool* pbStopFlag, Map* pMap)
{    
    // Local KeyFrames: First Breath Search from Current Keyframe
    list<KeyFrame*> lLocalKeyFrames;

    lLocalKeyFrames.push_back(pKF);
    pKF->mnBALocalForKF = pKF->mnId;

    /// add covisibility key frame to lLocalKeyFrames
    ///1.将当前帧的共视帧加入lLocalKeyFrames队列
    const vector<KeyFrame*> vNeighKFs = pKF->GetVectorCovisibleKeyFrames();
    for(int i=0, iend=vNeighKFs.size(); i<iend; i++)
    {
        KeyFrame* pKFi = vNeighKFs[i];
        pKFi->mnBALocalForKF = pKF->mnId;
        if(!pKFi->isBad())
            lLocalKeyFrames.push_back(pKFi);
    }

    // Local MapPoints seen in Local KeyFrames
    ///2.将所有共视帧的地图点加入lLocalMapPoints
    list<MapPoint*> lLocalMapPoints;
    for(list<KeyFrame*>::iterator lit=lLocalKeyFrames.begin() , lend=lLocalKeyFrames.end(); lit!=lend; lit++)
    {
        vector<MapPoint*> vpMPs = (*lit)->GetMapPointMatches();
        for(vector<MapPoint*>::iterator vit=vpMPs.begin(), vend=vpMPs.end(); vit!=vend; vit++)
        {
            MapPoint* pMP = *vit;
            if(pMP)
                if(!pMP->isBad())
                    if(pMP->mnBALocalForKF!=pKF->mnId)
                    {
                        lLocalMapPoints.push_back(pMP);
                        pMP->mnBALocalForKF=pKF->mnId;
                    }
        }
    }

    // Fixed Keyframes. Keyframes that see Local MapPoints but that are not Local Keyframes
    ///3.选出看到这些MapPoint点但不是LocalKeyFrame的关键帧,加入lFixedCameras,这些帧是固定的
    list<KeyFrame*> lFixedCameras;
    for(list<MapPoint*>::iterator lit=lLocalMapPoints.begin(), lend=lLocalMapPoints.end(); lit!=lend; lit++)
    {
        map<KeyFrame*,size_t> observations = (*lit)->GetObservations();
        for(map<KeyFrame*,size_t>::iterator mit=observations.begin(), mend=observations.end(); mit!=mend; mit++)
        {
            KeyFrame* pKFi = mit->first;

            if(pKFi->mnBALocalForKF!=pKF->mnId && pKFi->mnBAFixedForKF!=pKF->mnId)
            {                
                pKFi->mnBAFixedForKF=pKF->mnId;
                if(!pKFi->isBad())
                    lFixedCameras.push_back(pKFi);
            }
        }
    }

    // Setup optimizer
    ///4.设置优化器
    g2o::SparseOptimizer optimizer;
    g2o::BlockSolver_6_3::LinearSolverType * linearSolver;

    linearSolver = new g2o::LinearSolverEigen<g2o::BlockSolver_6_3::PoseMatrixType>();

    g2o::BlockSolver_6_3 * solver_ptr = new g2o::BlockSolver_6_3(linearSolver);

    g2o::OptimizationAlgorithmLevenberg* solver = new g2o::OptimizationAlgorithmLevenberg(solver_ptr);
    optimizer.setAlgorithm(solver);

    if(pbStopFlag)
        optimizer.setForceStopFlag(pbStopFlag);

    unsigned long maxKFid = 0;

    // Set Local KeyFrame vertices
    ///5.设置Local KeyFrame的顶点
    for(list<KeyFrame*>::iterator lit=lLocalKeyFrames.begin(), lend=lLocalKeyFrames.end(); lit!=lend; lit++)
    {
        KeyFrame* pKFi = *lit;
        g2o::VertexSE3Expmap * vSE3 = new g2o::VertexSE3Expmap();
        vSE3->setEstimate(Converter::toSE3Quat(pKFi->GetPose()));
        vSE3->setId(pKFi->mnId);
        vSE3->setFixed(pKFi->mnId==0);///first frame is fixed, and other is not fixed
        optimizer.addVertex(vSE3);
        if(pKFi->mnId>maxKFid)
            maxKFid=pKFi->mnId;
    }

    // Set Fixed KeyFrame vertices
    ///6.设置lFixedCameras的顶点
    for(list<KeyFrame*>::iterator lit=lFixedCameras.begin(), lend=lFixedCameras.end(); lit!=lend; lit++)
    {
        KeyFrame* pKFi = *lit;
        g2o::VertexSE3Expmap * vSE3 = new g2o::VertexSE3Expmap();
        vSE3->setEstimate(Converter::toSE3Quat(pKFi->GetPose()));
        vSE3->setId(pKFi->mnId);
        vSE3->setFixed(true);/// fixed variable
        optimizer.addVertex(vSE3);
        if(pKFi->mnId>maxKFid)
            maxKFid=pKFi->mnId;
    }

    // Set MapPoint vertices
    ///7.设置MapPoint顶点
    const int nExpectedSize = (lLocalKeyFrames.size()+lFixedCameras.size())*lLocalMapPoints.size();

    vector<g2o::EdgeSE3ProjectXYZ*> vpEdgesMono;
    vpEdgesMono.reserve(nExpectedSize);

    vector<KeyFrame*> vpEdgeKFMono;
    vpEdgeKFMono.reserve(nExpectedSize);

    vector<MapPoint*> vpMapPointEdgeMono;
    vpMapPointEdgeMono.reserve(nExpectedSize);

    vector<g2o::EdgeStereoSE3ProjectXYZ*> vpEdgesStereo;
    vpEdgesStereo.reserve(nExpectedSize);

    vector<KeyFrame*> vpEdgeKFStereo;
    vpEdgeKFStereo.reserve(nExpectedSize);

    vector<MapPoint*> vpMapPointEdgeStereo;
    vpMapPointEdgeStereo.reserve(nExpectedSize);

    const float thHuberMono = sqrt(5.991);
    const float thHuberStereo = sqrt(7.815);

    /// loop all map points
    ///8.遍历所有的点,设置MapPoint边
    for(list<MapPoint*>::iterator lit=lLocalMapPoints.begin(), lend=lLocalMapPoints.end(); lit!=lend; lit++)
    {
        MapPoint* pMP = *lit;
        g2o::VertexSBAPointXYZ* vPoint = new g2o::VertexSBAPointXYZ();
        vPoint->setEstimate(Converter::toVector3d(pMP->GetWorldPos()));
        int id = pMP->mnId+maxKFid+1;
        vPoint->setId(id);
        vPoint->setMarginalized(true);
        optimizer.addVertex(vPoint);

        const map<KeyFrame*,size_t> observations = pMP->GetObservations();

        //Set edges
        /// loop one MapPoint all observations
        ///遍历该MapPoint的所有观测帧,添加边
        for(map<KeyFrame*,size_t>::const_iterator mit=observations.begin(), mend=observations.end(); mit!=mend; mit++)
        {
            KeyFrame* pKFi = mit->first;

            if(!pKFi->isBad())
            {                
                const cv::KeyPoint &kpUn = pKFi->mvKeysUn[mit->second];

                // Monocular observation
                if(pKFi->mvuRight[mit->second]<0)
                {
                    Eigen::Matrix<double,2,1> obs;
                    obs << kpUn.pt.x, kpUn.pt.y;

                    /// new edge g2o::EdgeSE3ProjectXYZ
                    g2o::EdgeSE3ProjectXYZ* e = new g2o::EdgeSE3ProjectXYZ();
                    /// add one corresondence vertex
                    e->setVertex(0, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(id)));
                    /// add another one corresondence vertex, set pKFi' id
                    e->setVertex(1, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(pKFi->mnId)));
                    e->setMeasurement(obs);
                    const float &invSigma2 = pKFi->mvInvLevelSigma2[kpUn.octave];
                    /// set information matrix
                    e->setInformation(Eigen::Matrix2d::Identity()*invSigma2);

                    g2o::RobustKernelHuber* rk = new g2o::RobustKernelHuber;
                    e->setRobustKernel(rk);
                    rk->setDelta(thHuberMono);

                    e->fx = pKFi->fx;
                    e->fy = pKFi->fy;
                    e->cx = pKFi->cx;
                    e->cy = pKFi->cy;

                    optimizer.addEdge(e);
                    vpEdgesMono.push_back(e);
                    vpEdgeKFMono.push_back(pKFi);
                    vpMapPointEdgeMono.push_back(pMP);
                }
                else // Stereo observation
                {
                    Eigen::Matrix<double,3,1> obs;
                    const float kp_ur = pKFi->mvuRight[mit->second];
                    obs << kpUn.pt.x, kpUn.pt.y, kp_ur;

                    g2o::EdgeStereoSE3ProjectXYZ* e = new g2o::EdgeStereoSE3ProjectXYZ();

                    e->setVertex(0, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(id)));
                    e->setVertex(1, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(pKFi->mnId)));
                    e->setMeasurement(obs);
                    const float &invSigma2 = pKFi->mvInvLevelSigma2[kpUn.octave];
                    Eigen::Matrix3d Info = Eigen::Matrix3d::Identity()*invSigma2;
                    e->setInformation(Info);

                    g2o::RobustKernelHuber* rk = new g2o::RobustKernelHuber;
                    e->setRobustKernel(rk);
                    rk->setDelta(thHuberStereo);

                    e->fx = pKFi->fx;
                    e->fy = pKFi->fy;
                    e->cx = pKFi->cx;
                    e->cy = pKFi->cy;
                    e->bf = pKFi->mbf;

                    optimizer.addEdge(e);
                    vpEdgesStereo.push_back(e);
                    vpEdgeKFStereo.push_back(pKFi);
                    vpMapPointEdgeStereo.push_back(pMP);
                }
            }
        }
    }

    if(pbStopFlag)
        if(*pbStopFlag)
            return;

    ///9.优化迭代5次
    optimizer.initializeOptimization();
    optimizer.optimize(5);

    bool bDoMore= true;

    if(pbStopFlag)
        if(*pbStopFlag)
            bDoMore = false;

    if(bDoMore)
    {

    // Check inlier observations
    ///10.检测inlier的观测
    for(size_t i=0, iend=vpEdgesMono.size(); i<iend;i++)
    {
        g2o::EdgeSE3ProjectXYZ* e = vpEdgesMono[i];
        MapPoint* pMP = vpMapPointEdgeMono[i];

        if(pMP->isBad())
            continue;

        /// 卡方值大于阈值或者深度为负,那么该边不参与优化
        if(e->chi2()>5.991 || !e->isDepthPositive())
        {
            //设置该边为level=1
            e->setLevel(1);
        }

        e->setRobustKernel(0);
    }

    for(size_t i=0, iend=vpEdgesStereo.size(); i<iend;i++)
    {
        g2o::EdgeStereoSE3ProjectXYZ* e = vpEdgesStereo[i];
        MapPoint* pMP = vpMapPointEdgeStereo[i];

        if(pMP->isBad())
            continue;

        if(e->chi2()>7.815 || !e->isDepthPositive())
        {
            e->setLevel(1);
        }

        e->setRobustKernel(0);
    }

    // Optimize again without the outliers
    ///11.删除outlier再次优化,迭代10次,指定只优化level=0的边
    optimizer.initializeOptimization(0);
    optimizer.optimize(10);

    }

    vector<pair<KeyFrame*,MapPoint*> > vToErase;
    vToErase.reserve(vpEdgesMono.size()+vpEdgesStereo.size());

    // Check inlier observations 
    ///12.挑出outlier
    for(size_t i=0, iend=vpEdgesMono.size(); i<iend;i++)
    {
        g2o::EdgeSE3ProjectXYZ* e = vpEdgesMono[i];
        MapPoint* pMP = vpMapPointEdgeMono[i];

        if(pMP->isBad())
            continue;

        /// 卡方值大于阈值或者深度为负,那么删除该MapPoint
        if(e->chi2()>5.991 || !e->isDepthPositive())
        {
            KeyFrame* pKFi = vpEdgeKFMono[i];
            vToErase.push_back(make_pair(pKFi,pMP));
        }
    }

    for(size_t i=0, iend=vpEdgesStereo.size(); i<iend;i++)
    {
        g2o::EdgeStereoSE3ProjectXYZ* e = vpEdgesStereo[i];
        MapPoint* pMP = vpMapPointEdgeStereo[i];

        if(pMP->isBad())
            continue;

        if(e->chi2()>7.815 || !e->isDepthPositive())
        {
            KeyFrame* pKFi = vpEdgeKFStereo[i];
            vToErase.push_back(make_pair(pKFi,pMP));
        }
    }

    // Get Map Mutex
    unique_lock<mutex> lock(pMap->mMutexMapUpdate);

    //13.删除outlier
    if(!vToErase.empty())
    {
        for(size_t i=0;i<vToErase.size();i++)
        {
            KeyFrame* pKFi = vToErase[i].first;
            MapPoint* pMPi = vToErase[i].second;
            pKFi->EraseMapPointMatch(pMPi);
            pMPi->EraseObservation(pKFi);
        }
    }

    // Recover optimized data
    //14.恢复LocalKeyFrame和LocalMapPoint的Pose
    for(list<KeyFrame*>::iterator lit=lLocalKeyFrames.begin(), lend=lLocalKeyFrames.end(); lit!=lend; lit++)
    {
        KeyFrame* pKF = *lit;
        g2o::VertexSE3Expmap* vSE3 = static_cast<g2o::VertexSE3Expmap*>(optimizer.vertex(pKF->mnId));
        g2o::SE3Quat SE3quat = vSE3->estimate();
        pKF->SetPose(Converter::toCvMat(SE3quat));
    }

    //Points
    for(list<MapPoint*>::iterator lit=lLocalMapPoints.begin(), lend=lLocalMapPoints.end(); lit!=lend; lit++)
    {
        MapPoint* pMP = *lit;
        g2o::VertexSBAPointXYZ* vPoint = static_cast<g2o::VertexSBAPointXYZ*>(optimizer.vertex(pMP->mnId+maxKFid+1));
        pMP->SetWorldPos(Converter::toCvMat(vPoint->estimate()));
        pMP->UpdateNormalAndDepth();
    }
}


void Optimizer::OptimizeEssentialGraph(Map* pMap, KeyFrame* pLoopKF, KeyFrame* pCurKF,
                                       const LoopClosing::KeyFrameAndPose &NonCorrectedSim3,
                                       const LoopClosing::KeyFrameAndPose &CorrectedSim3,
                                       const map<KeyFrame *, set<KeyFrame *> > &LoopConnections, const bool &bFixScale)
{
    // Setup optimizer
    //1.设置优化器
    g2o::SparseOptimizer optimizer;
    optimizer.setVerbose(false);
    //7: 7 freedom, 3: 3D pose
    g2o::BlockSolver_7_3::LinearSolverType * linearSolver =
           new g2o::LinearSolverEigen<g2o::BlockSolver_7_3::PoseMatrixType>();
    g2o::BlockSolver_7_3 * solver_ptr= new g2o::BlockSolver_7_3(linearSolver);
    g2o::OptimizationAlgorithmLevenberg* solver = new g2o::OptimizationAlgorithmLevenberg(solver_ptr);

    solver->setUserLambdaInit(1e-16);
    optimizer.setAlgorithm(solver);

    //2.获取所有的关键帧和MapPoint
    const vector<KeyFrame*> vpKFs = pMap->GetAllKeyFrames();
    const vector<MapPoint*> vpMPs = pMap->GetAllMapPoints();

    const unsigned int nMaxKFid = pMap->GetMaxKFid();

    vector<g2o::Sim3,Eigen::aligned_allocator<g2o::Sim3> > vScw(nMaxKFid+1);
    vector<g2o::Sim3,Eigen::aligned_allocator<g2o::Sim3> > vCorrectedSwc(nMaxKFid+1);
    vector<g2o::VertexSim3Expmap*> vpVertices(nMaxKFid+1);

    const int minFeat = 100;

    // Set KeyFrame vertices
    //3.将地图中所有的关键帧设置为优化顶点
    for(size_t i=0, iend=vpKFs.size(); i<iend;i++)
    {
        KeyFrame* pKF = vpKFs[i];
        if(pKF->isBad())
            continue;
        g2o::VertexSim3Expmap* VSim3 = new g2o::VertexSim3Expmap();

        const int nIDi = pKF->mnId;
        //在CorrectedSim3找到这个KeyFrame
        LoopClosing::KeyFrameAndPose::const_iterator it = CorrectedSim3.find(pKF);

        if(it!=CorrectedSim3.end())
        {   
            //保存它的Pose
            vScw[nIDi] = it->second;
            //设置Sim3顶点的Pose初始值为关键帧的Pose
            VSim3->setEstimate(it->second);
        }
        else
        {   //如果在CorrectedSim3中没有找到这个KeyFrame
            Eigen::Matrix<double,3,3> Rcw = Converter::toMatrix3d(pKF->GetRotation());
            Eigen::Matrix<double,3,1> tcw = Converter::toVector3d(pKF->GetTranslation());
            g2o::Sim3 Siw(Rcw,tcw,1.0);
            vScw[nIDi] = Siw;
            VSim3->setEstimate(Siw);
        }

        //如果关键帧是参与回环检测的帧,,就固定,不优化Pose
        if(pKF==pLoopKF)
            VSim3->setFixed(true);

        VSim3->setId(nIDi);
        VSim3->setMarginalized(false);//不参与边缘化
        VSim3->_fix_scale = bFixScale;

        optimizer.addVertex(VSim3);//添加顶点

        vpVertices[nIDi]=VSim3;//保存顶点
    }


    set<pair<long unsigned int,long unsigned int> > sInsertedEdges;

    const Eigen::Matrix<double,7,7> matLambda = Eigen::Matrix<double,7,7>::Identity();

    // Set Loop edges
    //设置回环的边
    for(map<KeyFrame *, set<KeyFrame *> >::const_iterator mit = LoopConnections.begin(), mend=LoopConnections.end(); mit!=mend; mit++)
    {
        KeyFrame* pKF = mit->first;
        const long unsigned int nIDi = pKF->mnId;
        const set<KeyFrame*> &spConnections = mit->second;
        //获取Sim的Pose
        const g2o::Sim3 Siw = vScw[nIDi];
        const g2o::Sim3 Swi = Siw.inverse();

        for(set<KeyFrame*>::const_iterator sit=spConnections.begin(), send=spConnections.end(); sit!=send; sit++)
        {
            const long unsigned int nIDj = (*sit)->mnId;
            /**1.不是当前帧;
             * 2.不是回环帧;
             * 3.pKF和sit两帧之间的图权重小于minFeat
             */
            if((nIDi!=pCurKF->mnId || nIDj!=pLoopKF->mnId) && pKF->GetWeight(*sit)<minFeat)
                continue;
            
            //获取Sim的Pose
            const g2o::Sim3 Sjw = vScw[nIDj];
            //两帧之间的Pose
            const g2o::Sim3 Sji = Sjw * Swi;

            //在两个关键帧之间添加边
            g2o::EdgeSim3* e = new g2o::EdgeSim3();
            e->setVertex(1, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(nIDj)));
            e->setVertex(0, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(nIDi)));
            e->setMeasurement(Sji);

            e->information() = matLambda;

            optimizer.addEdge(e);

            sInsertedEdges.insert(make_pair(min(nIDi,nIDj),max(nIDi,nIDj)));
        }
    }

    // Set normal edges
    for(size_t i=0, iend=vpKFs.size(); i<iend; i++)
    {
        KeyFrame* pKF = vpKFs[i];

        const int nIDi = pKF->mnId;

        g2o::Sim3 Swi;

        LoopClosing::KeyFrameAndPose::const_iterator iti = NonCorrectedSim3.find(pKF);

        if(iti!=NonCorrectedSim3.end())
            Swi = (iti->second).inverse();
        else
            Swi = vScw[nIDi].inverse();

        KeyFrame* pParentKF = pKF->GetParent();

        // Spanning tree edge
        //在pKF帧和parent帧之间添加边
        if(pParentKF)
        {
            int nIDj = pParentKF->mnId;

            g2o::Sim3 Sjw;

            LoopClosing::KeyFrameAndPose::const_iterator itj = NonCorrectedSim3.find(pParentKF);

            if(itj!=NonCorrectedSim3.end())
                Sjw = itj->second;
            else
                Sjw = vScw[nIDj];

            g2o::Sim3 Sji = Sjw * Swi;

            g2o::EdgeSim3* e = new g2o::EdgeSim3();
            e->setVertex(1, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(nIDj)));
            e->setVertex(0, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(nIDi)));
            e->setMeasurement(Sji);

            e->information() = matLambda;
            optimizer.addEdge(e);
        }

        // Loop edges
        //在pKF和其sLoopEdges之间添加边
        const set<KeyFrame*> sLoopEdges = pKF->GetLoopEdges();
        for(set<KeyFrame*>::const_iterator sit=sLoopEdges.begin(), send=sLoopEdges.end(); sit!=send; sit++)
        {
            KeyFrame* pLKF = *sit;
            if(pLKF->mnId<pKF->mnId)
            {
                g2o::Sim3 Slw;

                LoopClosing::KeyFrameAndPose::const_iterator itl = NonCorrectedSim3.find(pLKF);

                if(itl!=NonCorrectedSim3.end())
                    Slw = itl->second;
                else
                    Slw = vScw[pLKF->mnId];

                g2o::Sim3 Sli = Slw * Swi;
                g2o::EdgeSim3* el = new g2o::EdgeSim3();
                el->setVertex(1, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(pLKF->mnId)));
                el->setVertex(0, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(nIDi)));
                el->setMeasurement(Sli);
                el->information() = matLambda;
                optimizer.addEdge(el);
            }
        }

        // Covisibility graph edges
        //在pKF帧和其vpConnectedKFs帧之间添加边
        const vector<KeyFrame*> vpConnectedKFs = pKF->GetCovisiblesByWeight(minFeat);
        for(vector<KeyFrame*>::const_iterator vit=vpConnectedKFs.begin(); vit!=vpConnectedKFs.end(); vit++)
        {
            KeyFrame* pKFn = *vit;
            if(pKFn && pKFn!=pParentKF && !pKF->hasChild(pKFn) && !sLoopEdges.count(pKFn))
            {
                if(!pKFn->isBad() && pKFn->mnId<pKF->mnId)
                {
                    if(sInsertedEdges.count(make_pair(min(pKF->mnId,pKFn->mnId),max(pKF->mnId,pKFn->mnId))))
                        continue;

                    g2o::Sim3 Snw;

                    LoopClosing::KeyFrameAndPose::const_iterator itn = NonCorrectedSim3.find(pKFn);

                    if(itn!=NonCorrectedSim3.end())
                        Snw = itn->second;
                    else
                        Snw = vScw[pKFn->mnId];

                    g2o::Sim3 Sni = Snw * Swi;

                    g2o::EdgeSim3* en = new g2o::EdgeSim3();
                    en->setVertex(1, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(pKFn->mnId)));
                    en->setVertex(0, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(nIDi)));
                    en->setMeasurement(Sni);
                    en->information() = matLambda;
                    optimizer.addEdge(en);
                }
            }
        }
    }//for

    // Optimize!
    //优化
    optimizer.initializeOptimization();
    optimizer.optimize(20);

    unique_lock<mutex> lock(pMap->mMutexMapUpdate);

    // SE3 Pose Recovering. Sim3:[sR t;0 1] -> SE3:[R t/s;0 1]
    //从Sim3 Pose恢复出关键帧的SE3Pose
    for(size_t i=0;i<vpKFs.size();i++)
    {
        KeyFrame* pKFi = vpKFs[i];

        const int nIDi = pKFi->mnId;

        g2o::VertexSim3Expmap* VSim3 = static_cast<g2o::VertexSim3Expmap*>(optimizer.vertex(nIDi));
        g2o::Sim3 CorrectedSiw =  VSim3->estimate();
        vCorrectedSwc[nIDi]=CorrectedSiw.inverse();
        Eigen::Matrix3d eigR = CorrectedSiw.rotation().toRotationMatrix();
        Eigen::Vector3d eigt = CorrectedSiw.translation();
        double s = CorrectedSiw.scale();

        eigt *=(1./s); //[R t/s;0 1]

        cv::Mat Tiw = Converter::toCvSE3(eigR,eigt);

        pKFi->SetPose(Tiw);
    }

    // Correct points. Transform to "non-optimized" reference keyframe pose and transform back with optimized pose
    //纠正MapPoint,用没有优化的参考帧的Pose转换到相机坐标系,然后用优化后的参考帧的Pose转换回世界坐标系
    for(size_t i=0, iend=vpMPs.size(); i<iend; i++)
    {
        MapPoint* pMP = vpMPs[i];

        if(pMP->isBad())
            continue;

        int nIDr;
        if(pMP->mnCorrectedByKF==pCurKF->mnId)
        {
            nIDr = pMP->mnCorrectedReference;
        }
        else
        {
            KeyFrame* pRefKF = pMP->GetReferenceKeyFrame();
            nIDr = pRefKF->mnId;
        }


        g2o::Sim3 Srw = vScw[nIDr];
        g2o::Sim3 correctedSwr = vCorrectedSwc[nIDr];

        cv::Mat P3Dw = pMP->GetWorldPos();
        Eigen::Matrix<double,3,1> eigP3Dw = Converter::toVector3d(P3Dw);
        Eigen::Matrix<double,3,1> eigCorrectedP3Dw = correctedSwr.map(Srw.map(eigP3Dw));

        cv::Mat cvCorrectedP3Dw = Converter::toCvMat(eigCorrectedP3Dw);
        pMP->SetWorldPos(cvCorrectedP3Dw);

        pMP->UpdateNormalAndDepth();
    }
}

int Optimizer::OptimizeSim3(KeyFrame *pKF1, KeyFrame *pKF2, vector<MapPoint *> &vpMatches1, g2o::Sim3 &g2oS12, const float th2, const bool bFixScale)
{
    //1.设置优化器
    g2o::SparseOptimizer optimizer;
    g2o::BlockSolverX::LinearSolverType * linearSolver;

    linearSolver = new g2o::LinearSolverDense<g2o::BlockSolverX::PoseMatrixType>();

    g2o::BlockSolverX * solver_ptr = new g2o::BlockSolverX(linearSolver);

    g2o::OptimizationAlgorithmLevenberg* solver = new g2o::OptimizationAlgorithmLevenberg(solver_ptr);
    optimizer.setAlgorithm(solver);

    // Calibration
    const cv::Mat &K1 = pKF1->mK;
    const cv::Mat &K2 = pKF2->mK;

    // Camera poses
    const cv::Mat R1w = pKF1->GetRotation();
    const cv::Mat t1w = pKF1->GetTranslation();
    const cv::Mat R2w = pKF2->GetRotation();
    const cv::Mat t2w = pKF2->GetTranslation();

    // Set Sim3 vertex
    //2.设置Sim3顶点,该顶点为pKF1和pKF2之间的Sim3 相对Pose
    g2o::VertexSim3Expmap * vSim3 = new g2o::VertexSim3Expmap();    
    vSim3->_fix_scale=bFixScale;
    vSim3->setEstimate(g2oS12);
    vSim3->setId(0);
    vSim3->setFixed(false);
    vSim3->_principle_point1[0] = K1.at<float>(0,2);
    vSim3->_principle_point1[1] = K1.at<float>(1,2);
    vSim3->_focal_length1[0] = K1.at<float>(0,0);
    vSim3->_focal_length1[1] = K1.at<float>(1,1);
    vSim3->_principle_point2[0] = K2.at<float>(0,2);
    vSim3->_principle_point2[1] = K2.at<float>(1,2);
    vSim3->_focal_length2[0] = K2.at<float>(0,0);
    vSim3->_focal_length2[1] = K2.at<float>(1,1);
    optimizer.addVertex(vSim3);

    // Set MapPoint vertices
    //3.设置MapPoint顶点
    const int N = vpMatches1.size();
    const vector<MapPoint*> vpMapPoints1 = pKF1->GetMapPointMatches();
    vector<g2o::EdgeSim3ProjectXYZ*> vpEdges12;
    vector<g2o::EdgeInverseSim3ProjectXYZ*> vpEdges21;
    vector<size_t> vnIndexEdge;

    vnIndexEdge.reserve(2*N);
    vpEdges12.reserve(2*N);
    vpEdges21.reserve(2*N);

    const float deltaHuber = sqrt(th2);

    int nCorrespondences = 0;
    //遍历N对匹配点
    for(int i=0; i<N; i++)
    {
        if(!vpMatches1[i])
            continue;

        MapPoint* pMP1 = vpMapPoints1[i];
        MapPoint* pMP2 = vpMatches1[i];

        const int id1 = 2*i+1;
        const int id2 = 2*(i+1);

        const int i2 = pMP2->GetIndexInKeyFrame(pKF2);

        if(pMP1 && pMP2)
        {
            if(!pMP1->isBad() && !pMP2->isBad() && i2>=0)
            {
                g2o::VertexSBAPointXYZ* vPoint1 = new g2o::VertexSBAPointXYZ();
                cv::Mat P3D1w = pMP1->GetWorldPos();
                cv::Mat P3D1c = R1w*P3D1w + t1w;//从世界坐标系转换到pKF1相机坐标系
                vPoint1->setEstimate(Converter::toVector3d(P3D1c));
                vPoint1->setId(id1);
                vPoint1->setFixed(true);
                optimizer.addVertex(vPoint1);//添加顶点

                g2o::VertexSBAPointXYZ* vPoint2 = new g2o::VertexSBAPointXYZ();
                cv::Mat P3D2w = pMP2->GetWorldPos();
                cv::Mat P3D2c = R2w*P3D2w + t2w;//从世界坐标系转换到pKF2相机坐标系
                vPoint2->setEstimate(Converter::toVector3d(P3D2c));
                vPoint2->setId(id2);
                vPoint2->setFixed(true);
                optimizer.addVertex(vPoint2);
            }
            else
                continue;
        }
        else
            continue;

        nCorrespondences++;

        // Set edge x1 = S12*X2
        //特征点的像素坐标
        Eigen::Matrix<double,2,1> obs1;
        const cv::KeyPoint &kpUn1 = pKF1->mvKeysUn[i];
        obs1 << kpUn1.pt.x, kpUn1.pt.y;

        //添加边e12
        g2o::EdgeSim3ProjectXYZ* e12 = new g2o::EdgeSim3ProjectXYZ();
        e12->setVertex(0, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(id2)));
        e12->setVertex(1, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(0)));
        e12->setMeasurement(obs1);
        const float &invSigmaSquare1 = pKF1->mvInvLevelSigma2[kpUn1.octave];
        e12->setInformation(Eigen::Matrix2d::Identity()*invSigmaSquare1);

        g2o::RobustKernelHuber* rk1 = new g2o::RobustKernelHuber;
        e12->setRobustKernel(rk1);
        rk1->setDelta(deltaHuber);
        optimizer.addEdge(e12);

        // Set edge x2 = S21*X1
        Eigen::Matrix<double,2,1> obs2;
        const cv::KeyPoint &kpUn2 = pKF2->mvKeysUn[i2];
        obs2 << kpUn2.pt.x, kpUn2.pt.y;

        g2o::EdgeInverseSim3ProjectXYZ* e21 = new g2o::EdgeInverseSim3ProjectXYZ();

        e21->setVertex(0, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(id1)));
        e21->setVertex(1, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(0)));
        e21->setMeasurement(obs2);
        float invSigmaSquare2 = pKF2->mvInvLevelSigma2[kpUn2.octave];
        e21->setInformation(Eigen::Matrix2d::Identity()*invSigmaSquare2);

        g2o::RobustKernelHuber* rk2 = new g2o::RobustKernelHuber;
        e21->setRobustKernel(rk2);
        rk2->setDelta(deltaHuber);
        optimizer.addEdge(e21);

        vpEdges12.push_back(e12);
        vpEdges21.push_back(e21);
        vnIndexEdge.push_back(i);
    }

    // Optimize!
    //优化
    optimizer.initializeOptimization();
    optimizer.optimize(5);

    // Check inliers
    int nBad=0;
    for(size_t i=0; i<vpEdges12.size();i++)
    {
        g2o::EdgeSim3ProjectXYZ* e12 = vpEdges12[i];
        g2o::EdgeInverseSim3ProjectXYZ* e21 = vpEdges21[i];
        if(!e12 || !e21)
            continue;

        //如果卡方值超过阈值,则移除这条边
        if(e12->chi2()>th2 || e21->chi2()>th2)
        {
            size_t idx = vnIndexEdge[i];
            vpMatches1[idx]=static_cast<MapPoint*>(NULL);
            optimizer.removeEdge(e12);
            optimizer.removeEdge(e21);
            vpEdges12[i]=static_cast<g2o::EdgeSim3ProjectXYZ*>(NULL);
            vpEdges21[i]=static_cast<g2o::EdgeInverseSim3ProjectXYZ*>(NULL);
            nBad++;
        }
    }

    int nMoreIterations;
    if(nBad>0)
        nMoreIterations=10;
    else
        nMoreIterations=5;

    if(nCorrespondences-nBad<10)
        return 0;

    // Optimize again only with inliers
    //再次优化
    optimizer.initializeOptimization();
    optimizer.optimize(nMoreIterations);

    int nIn = 0;
    for(size_t i=0; i<vpEdges12.size();i++)
    {
        g2o::EdgeSim3ProjectXYZ* e12 = vpEdges12[i];
        g2o::EdgeInverseSim3ProjectXYZ* e21 = vpEdges21[i];
        if(!e12 || !e21)
            continue;

        //如果卡方值超过阈值,则移除pKF2中的地图点
        if(e12->chi2()>th2 || e21->chi2()>th2)
        {
            size_t idx = vnIndexEdge[i];
            vpMatches1[idx]=static_cast<MapPoint*>(NULL);
        }
        else
            nIn++;
    }

    // Recover optimized Sim3
    g2o::VertexSim3Expmap* vSim3_recov = static_cast<g2o::VertexSim3Expmap*>(optimizer.vertex(0));
    g2oS12= vSim3_recov->estimate();

    return nIn;
}


} //namespace ORB_SLAM