SLAM实践：3D—2D：PnP

1. 理论知识

1. PnP——直接线性变换DLT
2. P3P

2. 相关代码

3D2D部分代码解读

 Mat r, t;
 solvePnP(pts_3d, pts_2d, K, Mat(), r, t, false); // 调用OpenCV 的 PnP 求解，可选择EPNP，DLS等方法
 Mat R;
 cv::Rodrigues(r, R); // r为旋转向量形式，用Rodrigues公式转换为矩阵
 cout << "R=" << endl << R << endl;
 cout << "t=" << endl << t << endl

高斯牛顿法PnP

void bundleAdjustmentGaussNewton(
  const VecVector3d &points_3d,
  const VecVector2d &points_2d,
  const Mat &K,
  Sophus::SE3d &pose) {
  typedef Eigen::Matrix<double, 6, 1> Vector6d;
  const int iterations = 10;
  double cost = 0, lastCost = 0;
  double fx = K.at<double>(0, 0);
  double fy = K.at<double>(1, 1);
  double cx = K.at<double>(0, 2);
  double cy = K.at<double>(1, 2);

  for (int iter = 0; iter < iterations; iter++) { // 初始化
    Eigen::Matrix<double, 6, 6> H = Eigen::Matrix<double, 6, 6>::Zero();
    Vector6d b = Vector6d::Zero();

    cost = 0;
    // compute cost
    for (int i = 0; i < points_3d.size(); i++) {
      Eigen::Vector3d pc = pose * points_3d[i]; // 世界坐标系转换成相机坐标系
      double inv_z = 1.0 / pc[2];
      double inv_z2 = inv_z * inv_z;
      Eigen::Vector2d proj(fx * pc[0] / pc[2] + cx, fy * pc[1] / pc[2] + cy); //相机坐标系转换成像素坐标（估计的）

      Eigen::Vector2d e = points_2d[i] - proj; // 误差

      cost += e.squaredNorm();
      Eigen::Matrix<double, 2, 6> J;
      J << -fx * inv_z, 
        0,
        fx * pc[0] * inv_z2,
        fx * pc[0] * pc[1] * inv_z2,
        -fx - fx * pc[0] * pc[0] * inv_z2,
        fx * pc[1] * inv_z,
        0,
        -fy * inv_z,
        fy * pc[1] * inv_z,
        fy + fy * pc[1] * pc[1] * inv_z2,
        -fy * pc[0] * pc[1] * inv_z2,
        -fy * pc[0] * inv_z; // 雅可比矩阵：重投影误差关于相机位姿李代数的一阶变化关系

      H += J.transpose() * J;
      b += -J.transpose() * e;
    }

    Vector6d dx;
    dx = H.ldlt().solve(b); //高斯牛顿法

    if (isnan(dx[0])) {
      cout << "result is nan!" << endl;
      break;
    }

    if (iter > 0 && cost >= lastCost) {
      // cost increase, update is not good
      cout << "cost: " << cost << ", last cost: " << lastCost << endl;
      break;
    }

    // update your estimation
    pose = Sophus::SE3d::exp(dx) * pose;
    lastCost = cost;

    cout << "iteration " << iter << " cost=" << cout.precision(12) << cost << endl;
    if (dx.norm() < 1e-6) {
      // converge
      break;
    }
  }

  cout << "pose by g-n: \n" << pose.matrix() << endl;
}

3. 实验结果