实践：g2o求解BA(2)

实现代码
g2o使用步骤：

• 创建线性求解器LinearSolver;
• 创建BlockSolver,用于上面定义的线性求解器初始化；
• 创建总求解器solver,使用GN/LM/DogLey任意一种增量求解方法；
• 创建图优化核心：稀疏优化器；
• 定义节点和边，并添加到稀疏优化器中；
• 设置优化参数，开始优化；

#include 
#include 
#include 
#include 
#include 
#include 
#include 

#include "common.h"
#include "sophus/se3.hpp"

using namespace Sophus;
using namespace Eigen;
using namespace std;

/// 姿态和内参的结构
struct PoseAndIntrinsics {
    PoseAndIntrinsics() {}

    /// set from given data address
    explicit PoseAndIntrinsics(double *data_addr) {
        rotation = SO3d::exp(Vector3d(data_addr[0], data_addr[1], data_addr[2]));
        translation = Vector3d(data_addr[3], data_addr[4], data_addr[5]);
        focal = data_addr[6];
        k1 = data_addr[7];
        k2 = data_addr[8];
    }

    /// 将估计值放入内存
    void set_to(double *data_addr) {
        auto r = rotation.log();
        for (int i = 0; i < 3; ++i) data_addr[i] = r[i];
        for (int i = 0; i < 3; ++i) data_addr[i + 3] = translation[i];
        data_addr[6] = focal;
        data_addr[7] = k1;
        data_addr[8] = k2;
    }

    SO3d rotation;
    Vector3d translation = Vector3d::Zero();
    double focal = 0;
    double k1 = 0, k2 = 0;
};

/// 位姿加相机内参的顶点，9维，前三维为so3，接下去为t, f, k1, k2
class VertexPoseAndIntrinsics : public g2o::BaseVertex<9, PoseAndIntrinsics> {
public:
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW;

    VertexPoseAndIntrinsics() {}

    virtual void setToOriginImpl() override {
        _estimate = PoseAndIntrinsics();
    }

    virtual void oplusImpl(const double *update) override {
        _estimate.rotation = SO3d::exp(Vector3d(update[0], update[1], update[2])) * _estimate.rotation;
        _estimate.translation += Vector3d(update[3], update[4], update[5]);
        _estimate.focal += update[6];
        _estimate.k1 += update[7];
        _estimate.k2 += update[8];
    }

    /// 根据估计值投影一个点
    Vector2d project(const Vector3d &point) {
        Vector3d pc = _estimate.rotation * point + _estimate.translation;
        pc = -pc / pc[2];
        double r2 = pc.squaredNorm();
        double distortion = 1.0 + r2 * (_estimate.k1 + _estimate.k2 * r2);
        return Vector2d(_estimate.focal * distortion * pc[0],
                        _estimate.focal * distortion * pc[1]);
    }

    virtual bool read(istream &in) {}

    virtual bool write(ostream &out) const {}
};

class VertexPoint : public g2o::BaseVertex<3, Vector3d> {
public:
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW;

    VertexPoint() {}

    virtual void setToOriginImpl() override {
        _estimate = Vector3d(0, 0, 0);  //顶点重置函数，把估计值置0即可
    }

    //顶点更新函数，优化过程最重要的增量计算，xk+1 = xk + 增量
    virtual void oplusImpl(const double *update) override {
        _estimate += Vector3d(update[0], update[1], update[2]);
    }

    virtual bool read(istream &in) {}

    virtual bool write(ostream &out) const {}
};

class EdgeProjection :
    public g2o::BaseBinaryEdge<2, Vector2d, VertexPoseAndIntrinsics, VertexPoint> {
public:
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW;

    //边的误差计算函数，该函数取出边所连接的顶点的当前估计值，它与观测值比较。
    virtual void computeError() override {
        auto v0 = (VertexPoseAndIntrinsics *) _vertices[0];
        auto v1 = (VertexPoint *) _vertices[1];
        auto proj = v0->project(v1->estimate());
        _error = proj - _measurement;
    }

    // use numeric derivatives
    virtual bool read(istream &in) {}

    virtual bool write(ostream &out) const {}

};

void SolveBA(BALProblem &bal_problem);

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

    if (argc != 2) {
        cout << "usage: bundle_adjustment_g2o bal_data.txt" << endl;
        return 1;
    }

    BALProblem bal_problem(argv[1]);
    bal_problem.Normalize();
    bal_problem.Perturb(0.1, 0.5, 0.5);
    bal_problem.WriteToPLYFile("initial.ply");
    SolveBA(bal_problem);
    bal_problem.WriteToPLYFile("final.ply");

    return 0;
}

void SolveBA(BALProblem &bal_problem) {
    const int point_block_size = bal_problem.point_block_size();
    const int camera_block_size = bal_problem.camera_block_size();
    double *points = bal_problem.mutable_points();
    double *cameras = bal_problem.mutable_cameras();

    // pose dimension 9, landmark is 3
    //构建图优化，每个误差项优化变变量相机9个，路标点3个
    typedef g2o::BlockSolver<g2o::BlockSolverTraits<9, 3>> BlockSolverType;
    //线性求解器
    typedef g2o::LinearSolverCSparse<BlockSolverType::PoseMatrixType> LinearSolverType;
    // 梯度下降方法选LM
    auto solver = new g2o::OptimizationAlgorithmLevenberg(
        g2o::make_unique<BlockSolverType>(g2o::make_unique<LinearSolverType>()));
    g2o::SparseOptimizer optimizer; // 图模型
    optimizer.setAlgorithm(solver);  //设置求解器
    optimizer.setVerbose(true);  //打开调试输出

    /// build g2o problem
    const double *observations = bal_problem.observations();
    // vertex
    vector<VertexPoseAndIntrinsics *> vertex_pose_intrinsics;  
    vector<VertexPoint *> vertex_points;
    //往图中添加相机的优化变量顶点
    for (int i = 0; i < bal_problem.num_cameras(); ++i) {
        VertexPoseAndIntrinsics *v = new VertexPoseAndIntrinsics();  //往图中增加相机的优化变量(顶点)
        double *camera = cameras + camera_block_size * i;
        v->setId(i);
        v->setEstimate(PoseAndIntrinsics(camera));
        optimizer.addVertex(v);
        vertex_pose_intrinsics.push_back(v);
    }
    //往图中添加路标点的顶点
    for (int i = 0; i < bal_problem.num_points(); ++i) {
        VertexPoint *v = new VertexPoint();
        double *point = points + point_block_size * i;
        v->setId(i + bal_problem.num_cameras());
        v->setEstimate(Vector3d(point[0], point[1], point[2]));
        // g2o在BA中需要手动设置待Marg的顶点，BA中的系数性，边缘哪部分。
        v->setMarginalized(true);
        optimizer.addVertex(v);
        vertex_points.push_back(v);
    }

    // 往图中添加边
    for (int i = 0; i < bal_problem.num_observations(); ++i) {
        EdgeProjection *edge = new EdgeProjection;
        edge->setVertex(0, vertex_pose_intrinsics[bal_problem.camera_index()[i]]); //设置连接的顶点
        edge->setVertex(1, vertex_points[bal_problem.point_index()[i]]);  //设置连接的顶点
        edge->setMeasurement(Vector2d(observations[2 * i + 0], observations[2 * i + 1]));   //观测的数值
        edge->setInformation(Matrix2d::Identity()); //信息矩阵，协方差矩阵之逆
        edge->setRobustKernel(new g2o::RobustKernelHuber());
        optimizer.addEdge(edge);
    }

    //执行优化
    optimizer.initializeOptimization();
    optimizer.optimize(40);

    // set to bal problem
    for (int i = 0; i < bal_problem.num_cameras(); ++i) {
        double *camera = cameras + camera_block_size * i;
        auto vertex = vertex_pose_intrinsics[i];
        auto estimate = vertex->estimate();
        estimate.set_to(camera);
    }
    for (int i = 0; i < bal_problem.num_points(); ++i) {
        double *point = points + point_block_size * i;
        auto vertex = vertex_points[i];
        for (int k = 0; k < 3; ++k) point[k] = vertex->estimate()[k];
    }
}

运行结果：