利用ICP把两个数据集对齐

        在实际当中，我们经常需要比较两条轨迹之间的误差。但是，由于 ground-truth 轨迹与相机轨迹很可能不在一个参考系中，它们得到的轨迹并不能直接比较。这时，我们可以用 ICP 来计算两条轨迹之间的相对旋转与平移，从而估计出两个参考系之间的差异。设真实轨迹为 Tg，估计轨迹为 Te，二者皆以 TW C 格式存储。但是真实轨迹的坐标原点定义于外部某参考系中，而估计
轨迹则以相机出发点为参考系。由于这个原因，理论上的真实轨迹点与估计轨迹点应满足：

                                                                                 

        从而：                                                           

        其中 i 表示轨迹中的第 i 条记录， Tge为两个坐标系之间的变换矩阵，该矩阵在整条轨迹中保持不变。 Tge 可以通过两条轨迹数据估计得到，我们把两条轨迹的平移部分看作点集，然后求点集之间的 ICP，得到两组点之间的变换。

        轨迹文件为：compare.txt，格式为：

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1305031547.744332 -0.963581026 0.684470177 -0.429666400 -0.117340922 -0.025876738 -0.069295891 0.990333080 1305031547.742800 0.8929 -0.1386 1.2441 0.9011 0.2307 -0.1025 -0.3526
1305031547.776390 -0.964229822 0.688230872 -0.429996789 -0.114284322 -0.024022026 -0.070344165 0.990663290 1305031547.772700 0.8935 -0.1379 1.2440 0.9008 0.2318 -0.1015 -0.3529
1305031547.812317 -0.964506626 0.684349477 -0.429410160 -0.117394648 -0.022055248 -0.071717598 0.990246713 1305031547.812700 0.8942 -0.1371 1.2441 0.9011 0.2310 -0.0996 -0.3532
1305031547.844564 -0.962979019 0.686277032 -0.429381162 -0.114744045 -0.021526016 -0.070772044 0.990637004 1305031547.842800 0.8946 -0.1365 1.2442 0.9008 0.2305 -0.0994 -0.3543
1305031547.876362 -0.963006616 0.688939631 -0.429479182 -0.113952808 -0.021306587 -0.070929334 0.990721881 1305031547.872800 0.8950 -0.1360 1.2442 0.9016 0.2311 -0.0993 -0.3520
1305031547.912744 -0.960898936 0.685296535 -0.428291798 -0.116005875 -0.021983700 -0.069795489 0.990549266 1305031547.912800 0.8956 -0.1352 1.2445 0.9016 0.2297 -0.0992 -0.3529
1305031547.944304 -0.960632503 0.685537279 -0.428972363 -0.115375742 -0.021099383 -0.069957919 0.990630627 1305031547.943100 0.8959 -0.1347 1.2447 0.9019 0.2297 -0.0988 -0.3522

对准前：

对准后：

代码：

#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
using namespace std;
using namespace cv;
using namespace Sophus;

//pangolin画图
void DrawTrajectory(vector> poses1,vector> poses2) {
    if (poses1.empty()||poses2.empty()) {
        cerr << "Trajectory is empty!" << endl;
        return;
    }
    // create pangolin window and plot the trajectory
    pangolin::CreateWindowAndBind("Trajectory Viewer", 1024, 768);
    glEnable(GL_DEPTH_TEST);
    glEnable(GL_BLEND);
    glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);

    pangolin::OpenGlRenderState s_cam(
            pangolin::ProjectionMatrix(1024, 768, 500, 500, 512, 389, 0.1, 1000),
            pangolin::ModelViewLookAt(0, -0.1, -1.8, 0, 0, 0, 0.0, -1.0, 0.0)
    );

    pangolin::View &d_cam = pangolin::CreateDisplay()
            .SetBounds(0.0, 1.0, pangolin::Attach::Pix(175), 1.0, -1024.0f / 768.0f)
            .SetHandler(new pangolin::Handler3D(s_cam));

    while (pangolin::ShouldQuit() == false) {
        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

        d_cam.Activate(s_cam);
        glClearColor(1.0f, 1.0f, 1.0f, 1.0f);

        glLineWidth(2);
        for (size_t i = 0; i < poses1.size() - 1; i++) {
            //glColor3f(1 - (float) i / poses1.size(), 0.0f, (float) i / poses1.size());
            glColor3f(1.0f, 0.0f, 0.0f);
            glBegin(GL_LINES);
            auto p1 = poses1[i], p2 = poses1[i + 1];
            glVertex2d(p1.translation()[0], p1.translation()[1]);//p1.translation()[2]
            glVertex2d(p2.translation()[0], p2.translation()[1]);//p2.translation()[2]
            glEnd();
        }
        for (size_t i = 0; i < poses2.size() - 1; i++) {
            //glColor3f(1 - (float) i / poses2.size(), 0.0f, (float) i / poses2.size());
            glColor3f(0.0f, 0.0f, 0.0f);
            glBegin(GL_LINES);
            auto p1 = poses2[i], p2 = poses2[i + 1];
            glVertex2d(p1.translation()[0], p1.translation()[1]);//p1.translation()[2]
            glVertex2d(p2.translation()[0], p2.translation()[1]);//p2.translation()[2]
            glEnd();
        }
        pangolin::FinishFrame();
        usleep(5000);   // sleep 5 ms
    }
}
int main ( int argc, char** argv )
{
    vector> ps1,ps2;
    ifstream file("../compare.txt");
    string line;
    vector pEstimated,pGroundTruth;
    while(getline(file,line))
    {
        stringstream record(line);
        vector vTmp(16,0);
        for(auto &v:vTmp)
            record>>v;
        Point3d p1{vTmp[1],vTmp[2],vTmp[3]};//位置
        Eigen::Quaterniond q1{vTmp[4],vTmp[5],vTmp[6],vTmp[7]};//旋转四元数
        Sophus::SE3 SE3_qt1(q1,Eigen::Vector3d(p1.x,p1.y,p1.z));//组成李群（欧式变换群）--estimated
        Point3d p2{vTmp[9],vTmp[10],vTmp[11]};
        Eigen::Quaterniond q2{vTmp[12],vTmp[13],vTmp[14],vTmp[15]};
        Sophus::SE3 SE3_qt2(q2,Eigen::Vector3d(p2.x,p2.y,p2.z));//组成李群（欧式变换群）--groundtruth
        pEstimated.push_back(p1);//求估计到真实的变换矩阵只需要用到位置
        pGroundTruth.push_back(p2);
        ps1.push_back(SE3_qt1);
        ps2.push_back(SE3_qt2);
    }
    //下面是ICP过程，p1=Rp2+t，即为真实到估计之间的变换，之后取逆即为估计到真实之间的变换
    Point3d pMid1, pMid2;     // center of mass
    int N = pEstimated.size();
    for ( int i=0; i     q1 ( N ), q2 ( N ); // remove the center
    for ( int i=0; i