V-LOAM源码解析（二）

转载请注明出处：本文转自zhch_pan的博客http://www.cnblogs.com/zhchp-blog/

本博客为本人之前做项目时做的源码阅读工作，po到网上希望帮助其他人更好的理解V-LOAM的工程实现，有些地方代码做了修改，可能和原工程有出入，但对于该工程的整体流程理解没有妨碍。

源码下载链接：https://github.com/Jinqiang/demo_lidar

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节点：visualOdometry

功能：订阅"/image_points_last"和"/depth_cloud"消息，将图像特征与三维点云匹配，获得图像特征点深度值，然后采用非线性优化的方法迭代收敛得到两帧图像之间的变换矩阵，即融合了三维点云信息的视觉里程计。

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <ros/ros.h>

#include <nav_msgs/Odometry.h>
#include <sensor_msgs/Imu.h>

#include <tf/transform_datatypes.h>
#include <tf/transform_listener.h>
#include <tf/transform_broadcaster.h>

#include "cameraParameters.h"
#include "pointDefinition.h"

const double PI = 3.1415926;

pcl::PointCloud<ImagePoint>::Ptr imagePointsCur(new pcl::PointCloud<ImagePoint>());
pcl::PointCloud<ImagePoint>::Ptr imagePointsLast(new pcl::PointCloud<ImagePoint>());
pcl::PointCloud<ImagePoint>::Ptr startPointsCur(new pcl::PointCloud<ImagePoint>());
pcl::PointCloud<ImagePoint>::Ptr startPointsLast(new pcl::PointCloud<ImagePoint>());
pcl::PointCloud<pcl::PointXYZHSV>::Ptr startTransCur(new pcl::PointCloud<pcl::PointXYZHSV>());
pcl::PointCloud<pcl::PointXYZHSV>::Ptr startTransLast(new pcl::PointCloud<pcl::PointXYZHSV>());
pcl::PointCloud<pcl::PointXYZHSV>::Ptr ipRelations(new pcl::PointCloud<pcl::PointXYZHSV>());
pcl::PointCloud<pcl::PointXYZHSV>::Ptr ipRelations2(new pcl::PointCloud<pcl::PointXYZHSV>());
pcl::PointCloud<pcl::PointXYZ>::Ptr imagePointsProj(new pcl::PointCloud<pcl::PointXYZ>());
pcl::PointCloud<DepthPoint>::Ptr depthPointsCur(new pcl::PointCloud<DepthPoint>());
pcl::PointCloud<DepthPoint>::Ptr depthPointsLast(new pcl::PointCloud<DepthPoint>());
pcl::PointCloud<DepthPoint>::Ptr depthPointsSend(new pcl::PointCloud<DepthPoint>());

std::vector<int> ipInd;
std::vector<float> ipy2;

std::vector<float>* ipDepthCur = new std::vector<float>();
std::vector<float>* ipDepthLast = new std::vector<float>();

double imagePointsCurTime;
double imagePointsLastTime;

int imagePointsCurNum = 0;
int imagePointsLastNum = 0;

int depthPointsCurNum = 0;
int depthPointsLastNum = 0;

pcl::PointCloud<pcl::PointXYZI>::Ptr depthCloud(new pcl::PointCloud<pcl::PointXYZI>());
pcl::KdTreeFLANN<pcl::PointXYZI>::Ptr kdTree(new pcl::KdTreeFLANN<pcl::PointXYZI>());

double depthCloudTime;
int depthCloudNum = 0;

std::vector<int> pointSearchInd;
std::vector<float> pointSearchSqrDis;

double transformSum[6] = {0};
double angleSum[3] = {0};

int imuPointerFront = 0;
int imuPointerLast = -1;
const int imuQueLength = 200;
bool imuInited = false;

double imuRollCur = 0, imuPitchCur = 0, imuYawCur = 0;
double imuRollLast = 0, imuPitchLast = 0, imuYawLast = 0;

double imuYawInit = 0;
double imuTime[imuQueLength] = {0};
double imuRoll[imuQueLength] = {0};
double imuPitch[imuQueLength] = {0};
double imuYaw[imuQueLength] = {0};

ros::Publisher *voDataPubPointer = NULL;
tf::TransformBroadcaster *tfBroadcasterPointer = NULL;
ros::Publisher *depthPointsPubPointer = NULL;
ros::Publisher *imagePointsProjPubPointer = NULL;
ros::Publisher *imageShowPubPointer;

const int showDSRate = 2;

void accumulateRotation(double cx, double cy, double cz, double lx, double ly, double lz, 
                        double &ox, double &oy, double &oz)
{
    /*R_wl=[ccy 0 scy;0 1 0;-scy 0 ccy]*[1 0 0;0 ccx -scx;0 scx ccx]*[ccz -scz 0;scz ccz 0;0 0 1];（表示以world为参考坐标系）
     *R_cl=[clz -slz 0;slz clz 0;0 0 1]*[1 0 0;0 clx -slx;0 slx clx]*[cly 0 sly;0 1 0;-sly 0 cly];（表示以current为参考坐标系）
     *R_wc=R_wl*(R_cl).';
     *最后求出来(-sin(rx))=cos(cx)*cos(cz)*sin(lx) - cos(lx)*cos(ly)*sin(cx) - cos(cx)*cos(lx)*sin(cz)*sin(ly)
     *而程序中是(-sin(rx))= cos(lx)*cos(cx)*sin(ly)*sin(cz) - cos(cx)*cos(cz)*sin(lx) - cos(lx)*cos(ly)*sin(cx);（程序里的srx=(-sin(rx))）
     *可以发现两个公式之间差了lx,ly,lz的负号，所以accumulateRotation()函数传入的是transform[0]~[2]的负值
     *至于为什么-sinx等于上式，可以通过看R_wl，发现第二行第三列的元素为-sinx，因此两个旋转矩阵相乘后，对应位置上的元素就对应着新的pitch角的sin 值
    */
  double srx = cos(lx)*cos(cx)*sin(ly)*sin(cz) - cos(cx)*cos(cz)*sin(lx) - cos(lx)*cos(ly)*sin(cx);
  ox = -asin(srx);

  double srycrx = sin(lx)*(cos(cy)*sin(cz) - cos(cz)*sin(cx)*sin(cy)) + cos(lx)*sin(ly)*(cos(cy)*cos(cz) 
                + sin(cx)*sin(cy)*sin(cz)) + cos(lx)*cos(ly)*cos(cx)*sin(cy);
  double crycrx = cos(lx)*cos(ly)*cos(cx)*cos(cy) - cos(lx)*sin(ly)*(cos(cz)*sin(cy) 
                - cos(cy)*sin(cx)*sin(cz)) - sin(lx)*(sin(cy)*sin(cz) + cos(cy)*cos(cz)*sin(cx));
  oy = atan2(srycrx / cos(ox), crycrx / cos(ox));

  double srzcrx = sin(cx)*(cos(lz)*sin(ly) - cos(ly)*sin(lx)*sin(lz)) + cos(cx)*sin(cz)*(cos(ly)*cos(lz) 
                + sin(lx)*sin(ly)*sin(lz)) + cos(lx)*cos(cx)*cos(cz)*sin(lz);
  double crzcrx = cos(lx)*cos(lz)*cos(cx)*cos(cz) - cos(cx)*sin(cz)*(cos(ly)*sin(lz) 
                - cos(lz)*sin(lx)*sin(ly)) - sin(cx)*(sin(ly)*sin(lz) + cos(ly)*cos(lz)*sin(lx));
  oz = atan2(srzcrx / cos(ox), crzcrx / cos(ox));
}

void diffRotation(double cx, double cy, double cz, double lx, double ly, double lz, 
                  double &ox, double &oy, double &oz)
{
  double srx = cos(cx)*cos(cy)*(sin(ly)*sin(lz) + cos(ly)*cos(lz)*sin(lx)) 
             - cos(cx)*sin(cy)*(cos(ly)*sin(lz) - cos(lz)*sin(lx)*sin(ly)) - cos(lx)*cos(lz)*sin(cx);
  ox = -asin(srx);

  double srycrx = cos(cx)*sin(cy)*(cos(ly)*cos(lz) + sin(lx)*sin(ly)*sin(lz)) 
                - cos(cx)*cos(cy)*(cos(lz)*sin(ly) - cos(ly)*sin(lx)*sin(lz)) - cos(lx)*sin(cx)*sin(lz);
  double crycrx = sin(cx)*sin(lx) + cos(cx)*cos(cy)*cos(lx)*cos(ly) + cos(cx)*cos(lx)*sin(cy)*sin(ly);
  oy = atan2(srycrx / cos(ox), crycrx / cos(ox));

  double srzcrx = cos(cx)*cos(lx)*cos(lz)*sin(cz) - (cos(cz)*sin(cy) 
                - cos(cy)*sin(cx)*sin(cz))*(sin(ly)*sin(lz) + cos(ly)*cos(lz)*sin(lx)) 
                - (cos(cy)*cos(cz) + sin(cx)*sin(cy)*sin(cz))*(cos(ly)*sin(lz) - cos(lz)*sin(lx)*sin(ly));
  double crzcrx = (sin(cy)*sin(cz) + cos(cy)*cos(cz)*sin(cx))*(sin(ly)*sin(lz) 
                + cos(ly)*cos(lz)*sin(lx)) + (cos(cy)*sin(cz) - cos(cz)*sin(cx)*sin(cy))*(cos(ly)*sin(lz) 
                - cos(lz)*sin(lx)*sin(ly)) + cos(cx)*cos(cz)*cos(lx)*cos(lz);
  oz = atan2(srzcrx / cos(ox), crzcrx / cos(ox));
}

void imagePointsHandler(const sensor_msgs::PointCloud2ConstPtr& imagePoints2)
{
  imagePointsLastTime = imagePointsCurTime;
  imagePointsCurTime = imagePoints2->header.stamp.toSec();

  imuRollLast = imuRollCur;
  imuPitchLast = imuPitchCur;
  imuYawLast = imuYawCur;
  //transform用于记录帧与帧之间的转移矩阵，transformSum记录当前帧与初始帧的转移矩阵,
  double transform[6] = {0};
  if (imuPointerLast >= 0) {
      //将该帧图像到来之前的所有IMU信息提取出来
    while (imuPointerFront != imuPointerLast) {
      if (imagePointsCurTime < imuTime[imuPointerFront]) {
        break;
      }
      imuPointerFront = (imuPointerFront + 1) % imuQueLength;
    }

    if (imagePointsCurTime > imuTime[imuPointerFront]) {
      imuRollCur = imuRoll[imuPointerFront];
      imuPitchCur = imuPitch[imuPointerFront];
      imuYawCur = imuYaw[imuPointerFront];
    } else {
      int imuPointerBack = (imuPointerFront + imuQueLength - 1) % imuQueLength;
      double ratioFront = (imagePointsCurTime - imuTime[imuPointerBack]) 
                        / (imuTime[imuPointerFront] - imuTime[imuPointerBack]);
      double ratioBack = (imuTime[imuPointerFront] - imagePointsCurTime) 
                       / (imuTime[imuPointerFront] - imuTime[imuPointerBack]);

      //通过插值得到img时刻的roll,pitch,yaw值
      imuRollCur = imuRoll[imuPointerFront] * ratioFront + imuRoll[imuPointerBack] * ratioBack;
      imuPitchCur = imuPitch[imuPointerFront] * ratioFront + imuPitch[imuPointerBack] * ratioBack;
      if (imuYaw[imuPointerFront] - imuYaw[imuPointerBack] > PI) {
        imuYawCur = imuYaw[imuPointerFront] * ratioFront + (imuYaw[imuPointerBack] + 2 * PI) * ratioBack;
      } else if (imuYaw[imuPointerFront] - imuYaw[imuPointerBack] < -PI) {
        imuYawCur = imuYaw[imuPointerFront] * ratioFront + (imuYaw[imuPointerBack] - 2 * PI) * ratioBack;
      } else {
        imuYawCur = imuYaw[imuPointerFront] * ratioFront + imuYaw[imuPointerBack] * ratioBack;
      }
    }

    if (imuInited) {
      //transform[0] -= imuPitchCur - imuPitchLast;
      //transform[1] -= imuYawCur - imuYawLast;
      //transform[2] -= imuRollCur - imuRollLast;
    }
  }

  pcl::PointCloud<ImagePoint>::Ptr imagePointsTemp = imagePointsLast;
  imagePointsLast = imagePointsCur;
  imagePointsCur = imagePointsTemp;

  imagePointsCur->clear();
  pcl::fromROSMsg(*imagePoints2, *imagePointsCur);

  imagePointsLastNum = imagePointsCurNum;
  imagePointsCurNum = imagePointsCur->points.size();

  pcl::PointCloud<ImagePoint>::Ptr startPointsTemp = startPointsLast;
  startPointsLast = startPointsCur;
  startPointsCur = startPointsTemp;

  pcl::PointCloud<pcl::PointXYZHSV>::Ptr startTransTemp = startTransLast;
  startTransLast = startTransCur;
  startTransCur = startTransTemp;

  std::vector<float>* ipDepthTemp = ipDepthLast;
  ipDepthLast = ipDepthCur;
  ipDepthCur = ipDepthTemp;

  int j = 0;
  pcl::PointXYZI ips;
  pcl::PointXYZHSV ipr;
  ipRelations->clear();
  ipInd.clear();

  //这里是以imagePointsLast为基准进行查找，有些imagePointsCur中的点不会被查询到
  for (int i = 0; i < imagePointsLastNum; i++) {
    bool ipFound = false;
    //查找是否有匹配到的特征点
    for (; j < imagePointsCurNum; j++) {
      if (imagePointsCur->points[j].ind == imagePointsLast->points[i].ind) {
        ipFound = true;
      }
      if (imagePointsCur->points[j].ind >= imagePointsLast->points[i].ind) {
        break;
      }
    }

    //如果发现匹配的特征点，尝试获取深度信息
    if (ipFound) {
      ipr.x = imagePointsLast->points[i].u;
      ipr.y = imagePointsLast->points[i].v;
      ipr.z = imagePointsCur->points[j].u;
      ipr.h = imagePointsCur->points[j].v;

      ips.x = 10 * ipr.x;
      ips.y = 10 * ipr.y;
      ips.z = 10;
      
      if (depthCloudNum > 10) {
        kdTree->nearestKSearch(ips, 3, pointSearchInd, pointSearchSqrDis);

        double minDepth, maxDepth;
        if (pointSearchSqrDis[0] < 0.5 && pointSearchInd.size() == 3) {
          pcl::PointXYZI depthPoint = depthCloud->points[pointSearchInd[0]];
          double x1 = depthPoint.x * depthPoint.intensity / 10;
          double y1 = depthPoint.y * depthPoint.intensity / 10;
          double z1 = depthPoint.intensity;
          minDepth = z1;
          maxDepth = z1;

          depthPoint = depthCloud->points[pointSearchInd[1]];
          double x2 = depthPoint.x * depthPoint.intensity / 10;
          double y2 = depthPoint.y * depthPoint.intensity / 10;
          double z2 = depthPoint.intensity;
          minDepth = (z2 < minDepth)? z2 : minDepth;
          maxDepth = (z2 > maxDepth)? z2 : maxDepth;

          depthPoint = depthCloud->points[pointSearchInd[2]];
          double x3 = depthPoint.x * depthPoint.intensity / 10;
          double y3 = depthPoint.y * depthPoint.intensity / 10;
          double z3 = depthPoint.intensity;
          minDepth = (z3 < minDepth)? z3 : minDepth;
          maxDepth = (z3 > maxDepth)? z3 : maxDepth;
          //目前只知道该特征点在相机坐标系下的归一化坐标[u,v]（即[X/Z,Y/Z,1]），
          //通过计算ipr.s获得对应于该特征点的深度值,即系数Z，则Z*u和Z*v就可获得该特征点在相机坐标系下实际的X,Y,Z坐标
          double u = ipr.x;
          double v = ipr.y;
          ipr.s = (x1*y2*z3 - x1*y3*z2 - x2*y1*z3 + x2*y3*z1 + x3*y1*z2 - x3*y2*z1) 
                / (x1*y2 - x2*y1 - x1*y3 + x3*y1 + x2*y3 - x3*y2 + u*y1*z2 - u*y2*z1
                - v*x1*z2 + v*x2*z1 - u*y1*z3 + u*y3*z1 + v*x1*z3 - v*x3*z1 + u*y2*z3 
                - u*y3*z2 - v*x2*z3 + v*x3*z2);
          ipr.v = 1;

          if (maxDepth - minDepth > 2) {
            ipr.s = 0;
            ipr.v = 0;
          } else if (ipr.s - maxDepth > 0.2) {
            ipr.s = maxDepth;
          } else if (ipr.s - minDepth < -0.2) {
            ipr.s = minDepth;
          }
        } else {
          ipr.s = 0;
          ipr.v = 0;
        }
      } else {
        ipr.s = 0;
        ipr.v = 0;
      }
      //如果无法从点云获取深度信息，三角测量？
      if (fabs(ipr.v) < 0.5) {
        double disX = transformSum[3] - startTransLast->points[i].h;
        double disY = transformSum[4] - startTransLast->points[i].s;
        double disZ = transformSum[5] - startTransLast->points[i].v;
        //若移动距离大于1m
        if (sqrt(disX * disX + disY * disY + disZ * disZ) > 1) {

          double u0 = startPointsLast->points[i].u;
          double v0 = startPointsLast->points[i].v;
          double u1 = ipr.x;
          double v1 = ipr.y;

          double srx0 = sin(-startTransLast->points[i].x);
          double crx0 = cos(-startTransLast->points[i].x);
          double sry0 = sin(-startTransLast->points[i].y);
          double cry0 = cos(-startTransLast->points[i].y);
          double srz0 = sin(-startTransLast->points[i].z);
          double crz0 = cos(-startTransLast->points[i].z);

          double srx1 = sin(-transformSum[0]);
          double crx1 = cos(-transformSum[0]);
          double sry1 = sin(-transformSum[1]);
          double cry1 = cos(-transformSum[1]);
          double srz1 = sin(-transformSum[2]);
          double crz1 = cos(-transformSum[2]);

          double tx0 = -startTransLast->points[i].h;
          double ty0 = -startTransLast->points[i].s;
          double tz0 = -startTransLast->points[i].v;

          double tx1 = -transformSum[3];
          double ty1 = -transformSum[4];
          double tz1 = -transformSum[5];

          double x1 = crz0 * u0 + srz0 * v0;
          double y1 = -srz0 * u0 + crz0 * v0;
          double z1 = 1;

          double x2 = x1;
          double y2 = crx0 * y1 + srx0 * z1;
          double z2 = -srx0 * y1 + crx0 * z1;

          double x3 = cry0 * x2 - sry0 * z2;
          double y3 = y2;
          double z3 = sry0 * x2 + cry0 * z2;

          double x4 = cry1 * x3 + sry1 * z3;
          double y4 = y3;
          double z4 = -sry1 * x3 + cry1 * z3;

          double x5 = x4;
          double y5 = crx1 * y4 - srx1 * z4;
          double z5 = srx1 * y4 + crx1 * z4;

          double x6 = crz1 * x5 - srz1 * y5;
          double y6 = srz1 * x5 + crz1 * y5;
          double z6 = z5;

          u0 = x6 / z6;
          v0 = y6 / z6;

          x1 = cry1 * (tx1 - tx0) + sry1 * (tz1 - tz0);
          y1 = ty1 - ty0;
          z1 = -sry1 * (tx1 - tx0) + cry1 * (tz1 - tz0);

          x2 = x1;
          y2 = crx1 * y1 - srx1 * z1;
          z2 = srx1 * y1 + crx1 * z1;

          double tx = crz1 * x2 - srz1 * y2;
          double ty = srz1 * x2 + crz1 * y2;
          double tz = z2;

          double delta = sqrt((v0 - v1) * (v0 - v1) + (u0 - u1) * (u0 - u1))
                       * cos(atan2(tz * v1 - ty, tz * u1 - tx) - atan2(v0 - v1, u0 - u1));
          double depth = sqrt((tz * u0 - tx) * (tz * u0 - tx) + (tz * v0 - ty) * (tz * v0 - ty)) / delta;

          if (depth > 0.5 && depth < 100) {
            ipr.s = depth;
            ipr.v = 2;
          }
        }

        //每一个匹配上的特征点对都会被打上一个ipr.v标签，ipr.v＝０代表未从点云获得深度，ipr.v＝１
        //代表从点云获得深度，ipr.v＝２代表此时可以通过三角测量获得该特征点的深度值。
        /*
         *ipDepthLast)[i]存储的是第i个特征点的三角测量值，若该特征点从未被三角测量过，
         *ipDepthLast)[i]＝－１；若该特征点在一段时间内能一直被观测到，且没有从点云中获得
         *深度信息，则不断通过三角测量的融合收敛该特征点的深度值；若在这个过程中某几帧中能从
         *点云获得该特征点的深度，则使用点云的深度信息，三角测量的结果仍通过计算出的转移矩阵
         *进行维护，仍然存储在*ipDepthLast)[i]中，一旦无法从点云获得深度，则仍使用
         *ipDepthLast)[i]中保存的三角测量进行融合
         */
        if (ipr.v == 2) {
          if ((*ipDepthLast)[i] > 0) {
              //这一步进行的是多次三角测量的融合,低通滤波
            ipr.s = 3 * ipr.s * (*ipDepthLast)[i] / (ipr.s + 2 * (*ipDepthLast)[i]);
          }
          (*ipDepthLast)[i] = ipr.s;
        } else if ((*ipDepthLast)[i] > 0) {
          ipr.s = (*ipDepthLast)[i];
          ipr.v = 2;
        }
      }

      ipRelations->push_back(ipr);
      ipInd.push_back(imagePointsLast->points[i].ind);
    }
  }

  //迭代收敛获得两帧图像间的转移矩阵
  int iterNum = 100;
  pcl::PointXYZHSV ipr2, ipr3, ipr4;
  int ipRelationsNum = ipRelations->points.size();
  int ptNumNoDepthRec = 0;
  int ptNumWithDepthRec = 0;
  double meanValueWithDepthRec = 100000;
  for (int iterCount = 0; iterCount < iterNum; iterCount++) {
    ipRelations2->clear();
    ipy2.clear();
    int ptNumNoDepth = 0;
    int ptNumWithDepth = 0;
    double meanValueNoDepth = 0;
    double meanValueWithDepth = 0;
    for (int i = 0; i < ipRelationsNum; i++) {
      ipr = ipRelations->points[i];

      double u0 = ipr.x;
      double v0 = ipr.y;
      double u1 = ipr.z;
      double v1 = ipr.h;

      double srx = sin(transform[0]);
      double crx = cos(transform[0]);
      double sry = sin(transform[1]);
      double cry = cos(transform[1]);
      double srz = sin(transform[2]);
      double crz = cos(transform[2]);
      double tx = transform[3];
      double ty = transform[4];
      double tz = transform[5];

      if (fabs(ipr.v) < 0.5) {
    /*
     * 这里R矩阵使用欧拉角roll,pitch yaw来表示的，下面六个公式是论文公式（6）在对roll,pitch,yaw和tx,ty,tz求偏导
     *transform[0]存储的是绕x轴旋转的角度，transform[1]存绕y轴角度，transform[2]存绕z轴角度
     *这里计算的R、T矩阵是k-1时刻旋转到k时刻的R、T矩阵，注意这个主次关系,参考坐标系是current,即k时刻坐标系
     *从k-1旋转到k的顺序是：z轴->x轴->y轴，注意顺序
     *R_cl=[crz -srz 0;srz crz 0;0 0 1]*[1 0 0;0 crx -srx;0 srx crx]*[cry 0 sry;0 1 0;-sry 0 cry];
    */
        ipr2.x = v0*(crz*srx*(tx - tz*u1) - crx*(ty*u1 - tx*v1) + srz*srx*(ty - tz*v1)) 
               - u0*(sry*srx*(ty*u1 - tx*v1) + crz*sry*crx*(tx - tz*u1) + sry*srz*crx*(ty - tz*v1)) 
               + cry*srx*(ty*u1 - tx*v1) + cry*crz*crx*(tx - tz*u1) + cry*srz*crx*(ty - tz*v1);

        ipr2.y = u0*((tx - tz*u1)*(srz*sry - crz*srx*cry) - (ty - tz*v1)*(crz*sry + srx*srz*cry) 
               + crx*cry*(ty*u1 - tx*v1)) - (tx - tz*u1)*(srz*cry + crz*srx*sry) 
               + (ty - tz*v1)*(crz*cry - srx*srz*sry) + crx*sry*(ty*u1 - tx*v1);

        ipr2.z = -u0*((tx - tz*u1)*(cry*crz - srx*sry*srz) + (ty - tz*v1)*(cry*srz + srx*sry*crz)) 
               - (tx - tz*u1)*(sry*crz + cry*srx*srz) - (ty - tz*v1)*(sry*srz - cry*srx*crz) 
               - v0*(crx*crz*(ty - tz*v1) - crx*srz*(tx - tz*u1));

        ipr2.h = cry*crz*srx - v0*(crx*crz - srx*v1) - u0*(cry*srz + crz*srx*sry + crx*sry*v1) 
               - sry*srz + crx*cry*v1;

        ipr2.s = crz*sry - v0*(crx*srz + srx*u1) + u0*(cry*crz + crx*sry*u1 - srx*sry*srz) 
               - crx*cry*u1 + cry*srx*srz;

        ipr2.v = u1*(sry*srz - cry*crz*srx) - v1*(crz*sry + cry*srx*srz) + u0*(u1*(cry*srz + crz*srx*sry) 
               - v1*(cry*crz - srx*sry*srz)) + v0*(crx*crz*u1 + crx*srz*v1);
    //将六个变量值代入论文（公式6）计算得到残差值
        double y2 = (ty - tz*v1)*(crz*sry + cry*srx*srz) - (tx - tz*u1)*(sry*srz - cry*crz*srx) 
                  - v0*(srx*(ty*u1 - tx*v1) + crx*crz*(tx - tz*u1) + crx*srz*(ty - tz*v1)) 
                  + u0*((ty - tz*v1)*(cry*crz - srx*sry*srz) - (tx - tz*u1)*(cry*srz + crz*srx*sry) 
                  + crx*sry*(ty*u1 - tx*v1)) - crx*cry*(ty*u1 - tx*v1);

        if (ptNumNoDepthRec < 50 || iterCount < 25 || fabs(y2) < 2 * meanValueWithDepthRec / 10000) {
          double scale = 100;
          ipr2.x *= scale;
          ipr2.y *= scale;
          ipr2.z *= scale;
          ipr2.h *= scale;
          ipr2.s *= scale;
          ipr2.v *= scale;
          y2 *= scale;

          ipRelations2->push_back(ipr2);
          ipy2.push_back(y2);

          ptNumNoDepth++;
        } else {
          ipRelations->points[i].v = -1;
        }
      } else if (fabs(ipr.v - 1) < 0.5 || fabs(ipr.v - 2) < 0.5) {

        double d0 = ipr.s;

        ipr3.x = d0*(cry*srz*crx + cry*u1*srx) - d0*u0*(sry*srz*crx + sry*u1*srx) 
               - d0*v0*(u1*crx - srz*srx);

        ipr3.y = d0*(crz*cry + crx*u1*sry - srx*srz*sry) - d0*u0*(crz*sry - crx*u1*cry + srx*srz*cry);

        ipr3.z = -d0*(sry*srz - cry*srx*crz) - d0*u0*(cry*srz + srx*sry*crz) - crx*d0*v0*crz;

        ipr3.h = 1;

        ipr3.s = 0;

        ipr3.v = -u1;

        double y3 = tx - tz*u1 + d0*(crz*sry - crx*cry*u1 + cry*srx*srz) - d0*v0*(crx*srz + srx*u1) 
                  + d0*u0*(cry*crz + crx*sry*u1 - srx*sry*srz);

        ipr4.x = d0*(cry*v1*srx - cry*crz*crx) + d0*u0*(crz*sry*crx - sry*v1*srx) 
               - d0*v0*(crz*srx + v1*crx);

        ipr4.y = d0*(srz*cry + crz*srx*sry + crx*v1*sry) + d0*u0*(crz*srx*cry - srz*sry + crx*v1*cry);

        ipr4.z = d0*(sry*crz + cry*srx*srz) + d0*u0*(cry*crz - srx*sry*srz) - crx*d0*v0*srz;

        ipr4.h = 0;

        ipr4.s = 1;

        ipr4.v = -v1;

        double y4 = ty - tz*v1 - d0*(cry*crz*srx - sry*srz + crx*cry*v1) + d0*v0*(crx*crz - srx*v1) 
                  + d0*u0*(cry*srz + crz*srx*sry + crx*sry*v1);

        if (ptNumWithDepthRec < 50 || iterCount < 25 || 
            sqrt(y3 * y3 + y4 * y4) < 2 * meanValueWithDepthRec) {
          ipRelations2->push_back(ipr3);
          ipy2.push_back(y3);

          ipRelations2->push_back(ipr4);
          ipy2.push_back(y4);

          ptNumWithDepth++;
          meanValueWithDepth += sqrt(y3 * y3 + y4 * y4);
        } else {
          ipRelations->points[i].v = -1;
        }
      }
    }
    //加 0.01 是为了防止 ptNumWithDepth 为 0
    meanValueWithDepth /= (ptNumWithDepth + 0.01);
    ptNumNoDepthRec = ptNumNoDepth;
    ptNumWithDepthRec = ptNumWithDepth;
    meanValueWithDepthRec = meanValueWithDepth;

    int ipRelations2Num = ipRelations2->points.size();
    if (ipRelations2Num > 10) {
      cv::Mat matA(ipRelations2Num, 6, CV_32F, cv::Scalar::all(0));
      cv::Mat matAt(6, ipRelations2Num, CV_32F, cv::Scalar::all(0));
      cv::Mat matAtA(6, 6, CV_32F, cv::Scalar::all(0));
      cv::Mat matB(ipRelations2Num, 1, CV_32F, cv::Scalar::all(0));
      cv::Mat matAtB(6, 1, CV_32F, cv::Scalar::all(0));
      cv::Mat matX(6, 1, CV_32F, cv::Scalar::all(0));

      for (int i = 0; i < ipRelations2Num; i++) {
        ipr2 = ipRelations2->points[i];

        matA.at<float>(i, 0) = ipr2.x;
        matA.at<float>(i, 1) = ipr2.y;
        matA.at<float>(i, 2) = ipr2.z;
        matA.at<float>(i, 3) = ipr2.h;
        matA.at<float>(i, 4) = ipr2.s;
        matA.at<float>(i, 5) = ipr2.v;
        matB.at<float>(i, 0) = -0.2 * ipy2[i];
      }
      cv::transpose(matA, matAt);
      matAtA = matAt * matA;
      matAtB = matAt * matB;
      //根据《14讲》式（6.21），这里用的是高斯牛顿法而不是LM算法
      cv::solve(matAtA, matAtB, matX, cv::DECOMP_QR);

      //if (fabs(matX.at<float>(0, 0)) < 0.1 && fabs(matX.at<float>(1, 0)) < 0.1 && 
      //    fabs(matX.at<float>(2, 0)) < 0.1) {
        transform[0] += matX.at<float>(0, 0);
        transform[1] += matX.at<float>(1, 0);
        transform[2] += matX.at<float>(2, 0);
        transform[3] += matX.at<float>(3, 0);
        transform[4] += matX.at<float>(4, 0);
        transform[5] += matX.at<float>(5, 0);
      //}

      float deltaR = sqrt(matX.at<float>(0, 0) * 180 / PI * matX.at<float>(0, 0) * 180 / PI
                   + matX.at<float>(1, 0) * 180 / PI * matX.at<float>(1, 0) * 180 / PI
                   + matX.at<float>(2, 0) * 180 / PI * matX.at<float>(2, 0) * 180 / PI);
      float deltaT = sqrt(matX.at<float>(3, 0) * 100 * matX.at<float>(3, 0) * 100
                   + matX.at<float>(4, 0) * 100 * matX.at<float>(4, 0) * 100
                   + matX.at<float>(5, 0) * 100 * matX.at<float>(5, 0) * 100);

      if (deltaR < 0.00001 && deltaT < 0.00001) {
        break;
      }

      //ROS_INFO ("iter: %d, deltaR: %f, deltaT: %f", iterCount, deltaR, deltaT);
    }
  }

  if (!imuInited) {
    imuYawInit = imuYawCur;
    transform[0] -= imuPitchCur;
    transform[2] -= imuRollCur;

    imuInited = true;
  }

  //rx,ry,rz表示当前帧与初始帧的pitch,yaw，roll角度
  double rx, ry, rz;
  accumulateRotation(transformSum[0], transformSum[1], transformSum[2], 
                    -transform[0], -transform[1], -transform[2], rx, ry, rz);

  if (imuPointerLast >= 0) {
    double drx, dry, drz;
    diffRotation(imuPitchCur, imuYawCur - imuYawInit, imuRollCur, rx, ry, rz, drx, dry, drz);

    transform[0] -= 0.1 * drx;
    /*if (dry > PI) {
      transform[1] -= 0.1 * (dry - 2 * PI);
    } else if (imuYawCur - imuYawInit - ry < -PI) {
      transform[1] -= 0.1 * (dry + 2 * PI);
    } else {
      transform[1] -= 0.1 * dry;
    }*/
    transform[2] -= 0.1 * drz;

    accumulateRotation(transformSum[0], transformSum[1], transformSum[2], 
                      -transform[0], -transform[1], -transform[2], rx, ry, rz);
  }

  double x1 = cos(rz) * transform[3] - sin(rz) * transform[4];
  double y1 = sin(rz) * transform[3] + cos(rz) * transform[4];
  double z1 = transform[5];

  double x2 = x1;
  double y2 = cos(rx) * y1 - sin(rx) * z1;
  double z2 = sin(rx) * y1 + cos(rx) * z1;

  //当前帧与上一帧的位移量通过rx,ry,rz的旋转，计算当前帧和初始帧的位移增量，叠加到transformSum[]中
  //该增量计算得到的是last帧相对于current帧在世界坐标系下的位移,所以current相对于Last在世界坐标系下的位移为负值,所以是减去
  double tx = transformSum[3] - (cos(ry) * x2 + sin(ry) * z2);
  double ty = transformSum[4] - y2;
  double tz = transformSum[5] - (-sin(ry) * x2 + cos(ry) * z2);
  //当前帧与初始帧的转移矩阵保存在transformSum中,transformSum中存的是将当前帧旋转到起始帧的旋转矩阵
  transformSum[0] = rx;
  transformSum[1] = ry;
  transformSum[2] = rz;
  transformSum[3] = tx;
  transformSum[4] = ty;
  transformSum[5] = tz;

  pcl::PointXYZHSV spc;
  spc.x = transformSum[0];
  spc.y = transformSum[1];
  spc.z = transformSum[2];
  spc.h = transformSum[3];
  spc.s = transformSum[4];
  spc.v = transformSum[5];

  double crx = cos(transform[0]);
  double srx = sin(transform[0]);
  double cry = cos(transform[1]);
  double sry = sin(transform[1]);

  j = 0;
  //这里是以imagePointsCur为基准进行查找，会遍历imagePointsCur中的每一个点
  for (int i = 0; i < imagePointsCurNum; i++) {
    bool ipFound = false;
    for (; j < imagePointsLastNum; j++) {
      if (imagePointsLast->points[j].ind == imagePointsCur->points[i].ind) {
        ipFound = true;
      }
      if (imagePointsLast->points[j].ind >= imagePointsCur->points[i].ind) {
        break;
      }
    }

    if (ipFound) {
      /*
        *如果在连续的多帧特征图像之间，imagePointsCur中的某个特征点能够与上一帧
        *imagePointsLast匹配到，代表该特征点能够被连续观测到，则将该特征点第一次出现在这些连续帧
        *的坐标以及该坐标相对于初始帧的转移矩阵保存在startPointsCur中，用作三角测量时的第一帧
        *特征点；若该特征点一旦与前一帧匹配失败，就表示该特征点为一系列特征点帧中的一个新出现的
        *特征点，则将该特征点当前的坐标与转移矩阵保存在startPointsCur，认为它第一次出现，并在后续帧中
        *若能一直观测到该特征点，startPointsCur中仍保存第一次出现的坐标与转移矩阵
       */
      startPointsCur->push_back(startPointsLast->points[j]);
      startTransCur->push_back(startTransLast->points[j]);

      if ((*ipDepthLast)[j] > 0) {
      /*
      *transform[]里存的就是T_cl,所以将Last坐标系的点按照zxy(从右往左看)的顺序旋转,再加上位移就变换到了current坐标系
      *而R_lc就是把transform[0]~transform[2]的pitch,yaw,roll角取负值然后按照yxz(从右往左看)的顺序变换就可得到
      *这里有一点注意的是,将transform[0]~[2]按照yxz相乘得到的R_lc和直接将R_cl取转置得到的R_lc差了三个角度的负值
      *所以通过旋转相乘得到R_lc时transform[0]~[2]要先取负值
      */
        double ipz = (*ipDepthLast)[j];
        double ipx = imagePointsLast->points[j].u * ipz;
        double ipy = imagePointsLast->points[j].v * ipz;

        x1 = cry * ipx + sry * ipz;
        y1 = ipy;
        z1 = -sry * ipx + cry * ipz;

        x2 = x1;
        y2 = crx * y1 - srx * z1;
        z2 = srx * y1 + crx * z1;

        ipDepthCur->push_back(z2 + transform[5]);
      } else {
        ipDepthCur->push_back(-1);
      }
    } else {
      startPointsCur->push_back(imagePointsCur->points[i]);
      startTransCur->push_back(spc);
      ipDepthCur->push_back(-1);
    }
  }
  startPointsLast->clear();
  startTransLast->clear();
  ipDepthLast->clear();

  angleSum[0] -= transform[0];
  angleSum[1] -= transform[1];
  angleSum[2] -= transform[2];

  /* rz,rx,ry分别对应着标准右手坐标系中的roll,pitch,yaw角,通过查看createQuaternionMsgFromRollPitchYaw()的函数定义可以发现.
   * 当pitch和yaw角给负值后,四元数中的y和z会变成负值,x和w不受影响.由四元数定义可以知道,x,y,z是指旋转轴在三个轴上的投影,w影响
   * 旋转角度,所以由createQuaternionMsgFromRollPitchYaw()计算得到四元数后,其在一般右手坐标系中的x,y,z分量对应到该应用场景下
   * 的坐标系中,geoQuat.x对应实际坐标系下的z轴分量,geoQuat.y对应x轴分量,geoQuat.z对应实际的y轴分量,而由于rx和ry在计算四元数
   * 时给的是负值,所以geoQuat.y和geoQuat.z取负值,这样就等于没变
  */

  geometry_msgs::Quaternion geoQuat = tf::createQuaternionMsgFromRollPitchYaw(rz, -rx, -ry);
  //geometry_msgs::Quaternion geoQuat = tf::createQuaternionMsgFromRollPitchYaw(rz, rx, ry);

  nav_msgs::Odometry voData;
  voData.header.frame_id = "/camera_init";
  voData.child_frame_id = "/camera";
  voData.header.stamp = imagePoints2->header.stamp;
  voData.pose.pose.orientation.x = -geoQuat.y;
  voData.pose.pose.orientation.y = -geoQuat.z;
  //voData.pose.pose.orientation.x = geoQuat.y;
  //voData.pose.pose.orientation.y = geoQuat.z;
  voData.pose.pose.orientation.z = geoQuat.x;
  voData.pose.pose.orientation.w = geoQuat.w;
  voData.pose.pose.position.x = tx;
  voData.pose.pose.position.y = ty;
  voData.pose.pose.position.z = tz;
  voData.twist.twist.angular.x = angleSum[0];
  voData.twist.twist.angular.y = angleSum[1];
  voData.twist.twist.angular.z = angleSum[2];
  voDataPubPointer->publish(voData);

  tf::StampedTransform voTrans;
  voTrans.frame_id_ = "/camera_init";
  voTrans.child_frame_id_ = "/camera";
  voTrans.stamp_ = imagePoints2->header.stamp;
  voTrans.setRotation(tf::Quaternion(-geoQuat.y, -geoQuat.z, geoQuat.x, geoQuat.w));
  //voTrans.setRotation(tf::Quaternion(geoQuat.y, geoQuat.z, geoQuat.x, geoQuat.w));
  voTrans.setOrigin(tf::Vector3(tx, ty, tz));
  tfBroadcasterPointer->sendTransform(voTrans);

  pcl::PointCloud<DepthPoint>::Ptr depthPointsTemp = depthPointsLast;
  depthPointsLast = depthPointsCur;
  depthPointsCur = depthPointsTemp;

  DepthPoint ipd;
  depthPointsCur->clear();

  ipd.u = transformSum[0];
  ipd.v = transformSum[1];
  ipd.depth = transformSum[2];
  ipd.ind = -2;
  depthPointsCur->push_back(ipd);

  ipd.u = transformSum[3];
  ipd.v = transformSum[4];
  ipd.depth = transformSum[5];
  ipd.ind = -1;
  depthPointsCur->push_back(ipd);

  depthPointsLastNum = depthPointsCurNum;
  depthPointsCurNum = 2;

  j = 0;
  pcl::PointXYZ ipp;
  depthPointsSend->clear();
  imagePointsProj->clear();
  for (int i = 0; i < ipRelationsNum; i++) {
    if (fabs(ipRelations->points[i].v - 1) < 0.5 || fabs(ipRelations->points[i].v - 2) < 0.5) {

      ipd.u = ipRelations->points[i].z;
      ipd.v = ipRelations->points[i].h;
      //这一步是对标号为ind的特征点深度进行的一个粗略估计,后面如果该特征点可以直接从点云或者三角测量获得深度值,
      //则这个估计值失效,如果后面不能得到该特征深度值,则仍使用该估计值
      ////////////////////////////////////////////////////////////////////
      /*double ipz = ipRelations->points[i].s;
      double ipx = ipRelations->points[i].x * ipz;
      double ipy = ipRelations->points[i].y * ipz;

      double x1 = cry * ipx + sry * ipz;
      double y1 = ipy;
      double z1 = -sry * ipx + cry * ipz;

      double x2 = x1;
      double y2 = crx * y1 - srx * z1;
      double z2 = srx * y1 + crx * z1;
      ipd.depth = z2 + transform[5];
      */
      ////////////////////////////////////////////////////////////////////

      ipd.depth = ipRelations->points[i].s + transform[5];
      ipd.label = ipRelations->points[i].v;
      ipd.ind = ipInd[i];

      depthPointsCur->push_back(ipd);
      depthPointsCurNum++;

      for (; j < depthPointsLastNum; j++) {
        if (depthPointsLast->points[j].ind < ipInd[i]) {
          depthPointsSend->push_back(depthPointsLast->points[j]);
        } else if (depthPointsLast->points[j].ind > ipInd[i]) {
          break;
        }
      }

      ipd.u = ipRelations->points[i].x;
      ipd.v = ipRelations->points[i].y;
      ipd.depth = ipRelations->points[i].s;

      //现在有Last帧和Cur帧，depthPointsSend中存储的是对Last帧中特征点深度的估计和确切计算到的深度
      depthPointsSend->push_back(ipd);

      ipp.x = ipRelations->points[i].x * ipRelations->points[i].s;
      ipp.y = ipRelations->points[i].y * ipRelations->points[i].s;
      ipp.z = ipRelations->points[i].s;

      imagePointsProj->push_back(ipp);
    }
  }

  sensor_msgs::PointCloud2 depthPoints2;
  pcl::toROSMsg(*depthPointsSend, depthPoints2);
  depthPoints2.header.frame_id = "camera2";
  depthPoints2.header.stamp = ros::Time().fromSec(imagePointsLastTime);
  depthPointsPubPointer->publish(depthPoints2);

  sensor_msgs::PointCloud2 imagePointsProj2;
  pcl::toROSMsg(*imagePointsProj, imagePointsProj2);
  imagePointsProj2.header.frame_id = "camera2";
  imagePointsProj2.header.stamp = ros::Time().fromSec(imagePointsLastTime);
  imagePointsProjPubPointer->publish(imagePointsProj2);
}

void depthCloudHandler(const sensor_msgs::PointCloud2ConstPtr& depthCloud2)
{
  depthCloudTime = depthCloud2->header.stamp.toSec();

  depthCloud->clear();
  pcl::fromROSMsg(*depthCloud2, *depthCloud);
  depthCloudNum = depthCloud->points.size();
  //将整个点云投影到焦距为单位距离=10的平面上
  if (depthCloudNum > 10) {
    for (int i = 0; i < depthCloudNum; i++) {
      depthCloud->points[i].intensity = depthCloud->points[i].z;
      depthCloud->points[i].x *= 10 / depthCloud->points[i].z;
      depthCloud->points[i].y *= 10 / depthCloud->points[i].z;
      depthCloud->points[i].z = 10;
    }

    kdTree->setInputCloud(depthCloud);
  }
}

void imuDataHandler(const sensor_msgs::Imu::ConstPtr& imuData)
{
  double roll, pitch, yaw;
  tf::Quaternion orientation;
  tf::quaternionMsgToTF(imuData->orientation, orientation);
  tf::Matrix3x3(orientation).getRPY(roll, pitch, yaw);

  imuPointerLast = (imuPointerLast + 1) % imuQueLength;

  imuTime[imuPointerLast] = imuData->header.stamp.toSec() - 0.1068;
  imuRoll[imuPointerLast] = roll;
  imuPitch[imuPointerLast] = pitch;
  imuYaw[imuPointerLast] = yaw;
}

void imageDataHandler(const sensor_msgs::Image::ConstPtr& imageData) 
{
  cv_bridge::CvImagePtr bridge = cv_bridge::toCvCopy(imageData, "bgr8");

  int ipRelationsNum = ipRelations->points.size();
  for (int i = 0; i < ipRelationsNum; i++) {
    if (fabs(ipRelations->points[i].v) < 0.5) {
        //这里运用《14讲》公式5.5将归一化坐标平面上的点变换到图像平面，这里的相减是因为在featureTrack部分将图像坐标
        //变到归一化图像平面时加了个负号,又考虑到显示的图像是缩小一倍后的，所以要再除以showDSRate
      cv::circle(bridge->image, cv::Point((kImage[2] - ipRelations->points[i].z * kImage[0]) / showDSRate,
                (kImage[5] - ipRelations->points[i].h * kImage[4]) / showDSRate), 1, CV_RGB(255, 0, 0), 2);
    } else if (fabs(ipRelations->points[i].v - 1) < 0.5) {
      cv::circle(bridge->image, cv::Point((kImage[2] - ipRelations->points[i].z * kImage[0]) / showDSRate,
                (kImage[5] - ipRelations->points[i].h * kImage[4]) / showDSRate), 1, CV_RGB(0, 255, 0), 2);
    } else if (fabs(ipRelations->points[i].v - 2) < 0.5) {
      cv::circle(bridge->image, cv::Point((kImage[2] - ipRelations->points[i].z * kImage[0]) / showDSRate,
                (kImage[5] - ipRelations->points[i].h * kImage[4]) / showDSRate), 1, CV_RGB(0, 0, 255), 2);
    } /*else {
      cv::circle(bridge->image, cv::Point((kImage[2] - ipRelations->points[i].z * kImage[0]) / showDSRate,
                (kImage[5] - ipRelations->points[i].h * kImage[4]) / showDSRate), 1, CV_RGB(0, 0, 0), 2);
    }*/
  }

  sensor_msgs::Image::Ptr imagePointer = bridge->toImageMsg();
  imageShowPubPointer->publish(imagePointer);
}

int main(int argc, char** argv)
{
  ros::init(argc, argv, "visualOdometry");
  ros::NodeHandle nh;

  ros::Subscriber imagePointsSub = nh.subscribe<sensor_msgs::PointCloud2>
                                   ("/image_points_last", 5, imagePointsHandler);

  ros::Subscriber depthCloudSub = nh.subscribe<sensor_msgs::PointCloud2> 
                                  ("/depth_cloud", 5, depthCloudHandler);

  /*
   * whether you need IMU information
  */
  //ros::Subscriber imuDataSub = nh.subscribe<sensor_msgs::Imu> ("/imu/data", 5, imuDataHandler);

  ros::Publisher voDataPub = nh.advertise<nav_msgs::Odometry> ("/cam_to_init", 5);
  voDataPubPointer = &voDataPub;

  tf::TransformBroadcaster tfBroadcaster;
  tfBroadcasterPointer = &tfBroadcaster;

  ros::Publisher depthPointsPub = nh.advertise<sensor_msgs::PointCloud2> ("/depth_points_last", 5);
  depthPointsPubPointer = &depthPointsPub;

  ros::Publisher imagePointsProjPub = nh.advertise<sensor_msgs::PointCloud2> ("/image_points_proj", 1);
  imagePointsProjPubPointer = &imagePointsProjPub;

  ros::Subscriber imageDataSub = nh.subscribe<sensor_msgs::Image>("/image/show", 1, imageDataHandler);

  ros::Publisher imageShowPub = nh.advertise<sensor_msgs::Image>("/image/show_2", 1);
  imageShowPubPointer = &imageShowPub;

  ros::spin();

  return 0;
}