《視覺SLAM十四講》slambook/ch7/gpose_estimation_3d3d更改成只用Eigen不用非線性優化

例子運行方法：
siat@hzt:~/Documents/slambook/ch7$ ./build/pose_estimation_3d3d 1.png 2.png 1_depth.png 2_depth.png

因我具體的問題是3點到3點的ICP匹配求相機姿態，所以SVD就夠了，不用非線性優化（因裏面有g2o庫還需要再下載一個，挺大的吧，各種不想用），自己刪除了此文件中非線性相關代碼，併成功編譯使用SVD（前提是裝OPENCV，Eigen 頭文件庫）。新建gpose_estimation_3_3d3d.cpp內容如下：
#include
#include <opencv2/core/core.hpp>
#include <opencv2/features2d/features2d.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/calib3d/calib3d.hpp>
#include <Eigen/Core>
#include <Eigen/Geometry>
#include <Eigen/SVD>
#include <g2o/core/base_vertex.h>
#include <g2o/core/base_unary_edge.h>
#include <g2o/core/block_solver.h>
#include <g2o/core/optimization_algorithm_gauss_newton.h>
#include <g2o/solvers/eigen/linear_solver_eigen.h>
#include <g2o/types/sba/types_six_dof_expmap.h>
#include

using namespace std;
using namespace cv;

void pose_estimation_3d3d (
const vector& pts1,
const vector& pts2,
Mat& R, Mat& t
);

void bundleAdjustment(
const vector& points_3d,
const vector& points_2d,
Mat& R, Mat& t
);

// g2o edge
class EdgeProjectXYZRGBDPoseOnly : public g2o::BaseUnaryEdge<3, Eigen::Vector3d, g2o::VertexSE3Expmap>
{
public:
EIGEN_MAKE_ALIGNED_OPERATOR_NEW;
EdgeProjectXYZRGBDPoseOnly( const Eigen::Vector3d& point ) : _point(point) {}

virtual void computeError()
{
    const g2o::VertexSE3Expmap* pose = static_cast<const g2o::VertexSE3Expmap*> ( _vertices[0] );
    // measurement is p, point is p'
    _error = _measurement - pose->estimate().map( _point );
}

virtual void linearizeOplus()
{
    g2o::VertexSE3Expmap* pose = static_cast<g2o::VertexSE3Expmap *>(_vertices[0]);
    g2o::SE3Quat T(pose->estimate());
    Eigen::Vector3d xyz_trans = T.map(_point);
    double x = xyz_trans[0];
    double y = xyz_trans[1];
    double z = xyz_trans[2];

    _jacobianOplusXi(0,0) = 0;
    _jacobianOplusXi(0,1) = -z;
    _jacobianOplusXi(0,2) = y;
    _jacobianOplusXi(0,3) = -1;
    _jacobianOplusXi(0,4) = 0;
    _jacobianOplusXi(0,5) = 0;

    _jacobianOplusXi(1,0) = z;
    _jacobianOplusXi(1,1) = 0;
    _jacobianOplusXi(1,2) = -x;
    _jacobianOplusXi(1,3) = 0;
    _jacobianOplusXi(1,4) = -1;
    _jacobianOplusXi(1,5) = 0;

    _jacobianOplusXi(2,0) = -y;
    _jacobianOplusXi(2,1) = x;
    _jacobianOplusXi(2,2) = 0;
    _jacobianOplusXi(2,3) = 0;
    _jacobianOplusXi(2,4) = 0;
    _jacobianOplusXi(2,5) = -1;
}

bool read ( istream& in ) {}
bool write ( ostream& out ) const {}

protected:
Eigen::Vector3d _point;
};

int main ( int argc, char** argv )
{

vector<Point3f> pts1, pts2;

float x1=43,y1=7,z1=404;
float x2=-38,y2=6,z2=384;
float x3=-52,y3=2,z3=382;
float xo1=78,yo1=6,zo1=416;
float xo2=6,yo2=7,zo2=372;
float xo3=-7,yo3=2,zo3=367;
pts1.push_back ( Point3f (x1, y1, z1));
pts2.push_back ( Point3f (xo1, yo1,zo1));
pts1.push_back ( Point3f (x2, y2, z2));
pts2.push_back ( Point3f (xo2, yo2,zo2));
pts1.push_back ( Point3f (x3, y3, z3));
pts2.push_back ( Point3f (xo3, yo3,zo3));
cout<<"3d-3d pairs: "<<pts1.size() <<endl;
Mat R, t;
pose_estimation_3d3d ( pts1, pts2, R, t );
cout<<"ICP via SVD results: "<<endl;
cout<<"R = "<<R<<endl;
cout<<"t = "<<t<<endl;
cout<<"R_inv = "<<R.t() <<endl;
cout<<"t_inv = "<<-R.t() *t<<endl;

cout<<"calling bundle adjustment"<<endl;

bundleAdjustment( pts1, pts2, R, t );

// verify p1 = R*p2 + t
for ( int i=0; i<3; i++ )
{
    cout<<"p1 = "<<pts1[i]<<endl;
    cout<<"p2 = "<<pts2[i]<<endl;
    cout<<"(R*p2+t) = "<<
        R * (Mat_<double>(3,1)<<pts2[i].x, pts2[i].y, pts2[i].z) + t
        <<endl;
    cout<<endl;
}

}

void pose_estimation_3d3d (
const vector& pts1,
const vector& pts2,
Mat& R, Mat& t
)
{
Point3f p1, p2; // center of mass
int N = pts1.size();
for ( int i=0; i<N; i++ )
{
p1 += pts1[i];
p2 += pts2[i];
}
p1 = Point3f( Vec3f(p1) / N);
p2 = Point3f( Vec3f(p2) / N);
vector q1 ( N ), q2 ( N ); // remove the center
for ( int i=0; i<N; i++ )
{
q1[i] = pts1[i] - p1;
q2[i] = pts2[i] - p2;
}

// compute q1*q2^T
Eigen::Matrix3d W = Eigen::Matrix3d::Zero();
for ( int i=0; i<N; i++ )
{
    W += Eigen::Vector3d ( q1[i].x, q1[i].y, q1[i].z ) * Eigen::Vector3d ( q2[i].x, q2[i].y, q2[i].z ).transpose();
}
cout<<"W="<<W<<endl;

// SVD on W
Eigen::JacobiSVD<Eigen::Matrix3d> svd ( W, Eigen::ComputeFullU|Eigen::ComputeFullV );
Eigen::Matrix3d U = svd.matrixU();
Eigen::Matrix3d V = svd.matrixV();

if (U.determinant() * V.determinant() < 0)
{
    for (int x = 0; x < 3; ++x)
    {
        U(x, 2) *= -1;
    }
}

cout<<"U="<<U<<endl;
cout<<"V="<<V<<endl;

Eigen::Matrix3d R_ = U* ( V.transpose() );
Eigen::Vector3d t_ = Eigen::Vector3d ( p1.x, p1.y, p1.z ) - R_ * Eigen::Vector3d ( p2.x, p2.y, p2.z );

// convert to cv::Mat
R = ( Mat_<double> ( 3,3 ) <<
      R_ ( 0,0 ), R_ ( 0,1 ), R_ ( 0,2 ),
      R_ ( 1,0 ), R_ ( 1,1 ), R_ ( 1,2 ),
      R_ ( 2,0 ), R_ ( 2,1 ), R_ ( 2,2 )
    );
t = ( Mat_<double> ( 3,1 ) << t_ ( 0,0 ), t_ ( 1,0 ), t_ ( 2,0 ) );

}

void bundleAdjustment (
const vector< Point3f >& pts1,
const vector< Point3f >& pts2,
Mat& R, Mat& t )
{
// 初始化g2o
typedef g2o::BlockSolver< g2o::BlockSolverTraits<6,3> > Block; // pose維度爲 6, landmark 維度爲 3
Block::LinearSolverType* linearSolver = new g2o::LinearSolverEigenBlock::PoseMatrixType(); // 線性方程求解器
Block* solver_ptr = new Block( linearSolver ); // 矩陣塊求解器
g2o::OptimizationAlgorithmGaussNewton* solver = new g2o::OptimizationAlgorithmGaussNewton( solver_ptr );
g2o::SparseOptimizer optimizer;
optimizer.setAlgorithm( solver );

// vertex
g2o::VertexSE3Expmap* pose = new g2o::VertexSE3Expmap(); // camera pose
pose->setId(0);
pose->setEstimate( g2o::SE3Quat(
    Eigen::Matrix3d::Identity(),
    Eigen::Vector3d( 0,0,0 )
) );
optimizer.addVertex( pose );

// edges
int index = 1;
vector<EdgeProjectXYZRGBDPoseOnly*> edges;
for ( size_t i=0; i<pts1.size(); i++ )
{
    EdgeProjectXYZRGBDPoseOnly* edge = new EdgeProjectXYZRGBDPoseOnly(
        Eigen::Vector3d(pts2[i].x, pts2[i].y, pts2[i].z) );
    edge->setId( index );
    edge->setVertex( 0, dynamic_cast<g2o::VertexSE3Expmap*> (pose) );
    edge->setMeasurement( Eigen::Vector3d(
        pts1[i].x, pts1[i].y, pts1[i].z) );
    edge->setInformation( Eigen::Matrix3d::Identity()*1e4 );
    optimizer.addEdge(edge);
    index++;
    edges.push_back(edge);
}

chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
optimizer.setVerbose( true );
optimizer.initializeOptimization();
optimizer.optimize(10);
chrono::steady_clock::time_point t2 = chrono::steady_clock::now();
chrono::duration<double> time_used = chrono::duration_cast<chrono::duration<double>>(t2-t1);
cout<<"optimization costs time: "<<time_used.count()<<" seconds."<<endl;

cout<<endl<<"after optimization:"<<endl;
cout<<"T="<<endl<<Eigen::Isometry3d( pose->estimate() ).matrix()<<endl;

}
然後在同一級的CMakeLists.txt文件中（末尾）加入一段編譯信息：
add_executable( pose_estimation_3_3d3d pose_estimation_3_3d3d.cpp )
target_link_libraries( pose_estimation_3_3d3d
${OpenCV_LIBS}
g2o_core g2o_stuff g2o_types_sba g2o_csparse_extension
${CSPARSE_LIBRARY} ) 然後進入build目錄開始編譯： siat@hzt:~/Documents/slambook/ch7$ cd build
siat@hzt:~/Documents/slambook/ch7/build$ cmake …（注意…前有一個空格）
siat@hzt:~/Documents/slambook/ch7/build$ cmake…
過幾分鐘編譯完生產可執行文件pose_estimation_3_3d3d，
就可以運行了：
siat@hzt:~/Documents/slambook/ch7/build$ ./pose_estimation_3_3d3d