basalt/src/vi_estimator/ba_base.cpp

/**
BSD 3-Clause License

This file is part of the Basalt project.
https://gitlab.com/VladyslavUsenko/basalt.git

Copyright (c) 2019, Vladyslav Usenko and Nikolaus Demmel.
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

* Redistributions of source code must retain the above copyright notice, this
  list of conditions and the following disclaimer.

* Redistributions in binary form must reproduce the above copyright notice,
  this list of conditions and the following disclaimer in the documentation
  and/or other materials provided with the distribution.

* Neither the name of the copyright holder nor the names of its
  contributors may be used to endorse or promote products derived from
  this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/

#include <basalt/vi_estimator/ba_base.h>

#include <tbb/parallel_for.h>

namespace basalt {

Sophus::SE3d BundleAdjustmentBase::computeRelPose(const Sophus::SE3d& T_w_i_h,
                                                  const Sophus::SE3d& T_i_c_h,
                                                  const Sophus::SE3d& T_w_i_t,
                                                  const Sophus::SE3d& T_i_c_t,
                                                  Sophus::Matrix6d* d_rel_d_h,
                                                  Sophus::Matrix6d* d_rel_d_t) {
  Sophus::SE3d tmp2 = (T_i_c_t).inverse();

  Sophus::SE3d T_t_i_h_i;
  T_t_i_h_i.so3() = T_w_i_t.so3().inverse() * T_w_i_h.so3();
  T_t_i_h_i.translation() =
      T_w_i_t.so3().inverse() * (T_w_i_h.translation() - T_w_i_t.translation());

  Sophus::SE3d tmp = tmp2 * T_t_i_h_i;
  Sophus::SE3d res = tmp * T_i_c_h;

  if (d_rel_d_h) {
    Eigen::Matrix3d R = T_w_i_h.so3().inverse().matrix();

    Sophus::Matrix6d RR;
    RR.setZero();
    RR.topLeftCorner<3, 3>() = R;
    RR.bottomRightCorner<3, 3>() = R;

    *d_rel_d_h = tmp.Adj() * RR;
  }

  if (d_rel_d_t) {
    Eigen::Matrix3d R = T_w_i_t.so3().inverse().matrix();

    Sophus::Matrix6d RR;
    RR.setZero();
    RR.topLeftCorner<3, 3>() = R;
    RR.bottomRightCorner<3, 3>() = R;

    *d_rel_d_t = -tmp2.Adj() * RR;
  }

  return res;
}

void BundleAdjustmentBase::updatePoints(const AbsOrderMap& aom,
                                        const RelLinData& rld,
                                        const Eigen::VectorXd& inc) {
  Eigen::VectorXd rel_inc;
  rel_inc.setZero(rld.order.size() * POSE_SIZE);
  for (size_t i = 0; i < rld.order.size(); i++) {
    const TimeCamId& tcid_h = rld.order[i].first;
    const TimeCamId& tcid_t = rld.order[i].second;

    if (tcid_h.first != tcid_t.first) {
      int abs_h_idx = aom.abs_order_map.at(tcid_h.first).first;
      int abs_t_idx = aom.abs_order_map.at(tcid_t.first).first;

      rel_inc.segment<POSE_SIZE>(i * POSE_SIZE) =
          rld.d_rel_d_h[i] * inc.segment<POSE_SIZE>(abs_h_idx) +
          rld.d_rel_d_t[i] * inc.segment<POSE_SIZE>(abs_t_idx);
    }
  }

  for (const auto& kv : rld.lm_to_obs) {
    int lm_idx = kv.first;
    const auto& other_obs = kv.second;

    Eigen::Vector3d H_l_p_x;
    H_l_p_x.setZero();

    for (size_t k = 0; k < other_obs.size(); k++) {
      int rel_idx = other_obs[k].first;
      const FrameRelLinData& frld_other = rld.Hpppl.at(rel_idx);

      Eigen::Matrix<double, 3, POSE_SIZE> H_l_p_other =
          frld_other.Hpl[other_obs[k].second].transpose();

      H_l_p_x += H_l_p_other * rel_inc.segment<POSE_SIZE>(rel_idx * POSE_SIZE);

      // std::cerr << "inc_p " << inc_p.transpose() << std::endl;
    }

    Eigen::Vector3d inc_p = rld.Hll.at(lm_idx) * (rld.bl.at(lm_idx) - H_l_p_x);

    KeypointPosition& kpt = kpts[lm_idx];
    kpt.dir -= inc_p.head<2>();
    kpt.id -= inc_p[2];

    kpt.id = std::max(0., kpt.id);
  }
}

void BundleAdjustmentBase::computeError(double& error) const {
  error = 0;

  for (const auto& kv : obs) {
    const TimeCamId& tcid_h = kv.first;

    for (const auto& obs_kv : kv.second) {
      const TimeCamId& tcid_t = obs_kv.first;

      if (tcid_h != tcid_t) {
        PoseStateWithLin state_h = getPoseStateWithLin(tcid_h.first);
        PoseStateWithLin state_t = getPoseStateWithLin(tcid_t.first);

        Sophus::SE3d T_t_h_sophus =
            computeRelPose(state_h.getPose(), calib.T_i_c[tcid_h.second],
                           state_t.getPose(), calib.T_i_c[tcid_t.second]);

        Eigen::Matrix4d T_t_h = T_t_h_sophus.matrix();

        std::visit(
            [&](const auto& cam) {
              for (size_t i = 0; i < obs_kv.second.size(); i++) {
                const KeypointObservation& kpt_obs = obs_kv.second[i];
                const KeypointPosition& kpt_pos = kpts.at(kpt_obs.kpt_id);

                Eigen::Vector2d res;

                bool valid = linearizePoint(kpt_obs, kpt_pos, T_t_h, cam, res);

                if (valid) {
                  double e = res.norm();
                  double huber_weight =
                      e < huber_thresh ? 1.0 : huber_thresh / e;
                  double obs_weight =
                      huber_weight / (obs_std_dev * obs_std_dev);

                  error +=
                      (2 - huber_weight) * obs_weight * res.transpose() * res;
                }
              }
            },
            calib.intrinsics[tcid_t.second].variant);

      } else {
        // target and host are the same
        // residual does not depend on the pose
        // it just depends on the point

        std::visit(
            [&](const auto& cam) {
              for (size_t i = 0; i < obs_kv.second.size(); i++) {
                const KeypointObservation& kpt_obs = obs_kv.second[i];
                const KeypointPosition& kpt_pos = kpts.at(kpt_obs.kpt_id);

                Eigen::Vector2d res;

                bool valid = linearizePoint(kpt_obs, kpt_pos, cam, res);
                if (valid) {
                  double e = res.norm();
                  double huber_weight =
                      e < huber_thresh ? 1.0 : huber_thresh / e;
                  double obs_weight =
                      huber_weight / (obs_std_dev * obs_std_dev);

                  error +=
                      (2 - huber_weight) * obs_weight * res.transpose() * res;
                }
              }
            },
            calib.intrinsics[tcid_t.second].variant);
      }
    }
  }
}

void BundleAdjustmentBase::linearizeHelper(
    Eigen::vector<RelLinData>& rld_vec,
    const Eigen::map<TimeCamId,
                     Eigen::map<TimeCamId, Eigen::vector<KeypointObservation>>>&
        obs_to_lin,
    double& error) const {
  error = 0;

  rld_vec.clear();

  std::vector<TimeCamId> obs_tcid_vec;
  for (const auto& kv : obs_to_lin) {
    obs_tcid_vec.emplace_back(kv.first);
    rld_vec.emplace_back(kpts.size(), kv.second.size());
  }

  tbb::parallel_for(
      tbb::blocked_range<size_t>(0, obs_tcid_vec.size()),
      [&](const tbb::blocked_range<size_t>& range) {
        for (size_t r = range.begin(); r != range.end(); ++r) {
          auto kv = obs_to_lin.find(obs_tcid_vec[r]);

          RelLinData& rld = rld_vec[r];

          rld.error = 0;

          const TimeCamId& tcid_h = kv->first;

          for (const auto& obs_kv : kv->second) {
            const TimeCamId& tcid_t = obs_kv.first;
            if (tcid_h != tcid_t) {
              // target and host are not the same
              rld.order.emplace_back(std::make_pair(tcid_h, tcid_t));

              PoseStateWithLin state_h = getPoseStateWithLin(tcid_h.first);
              PoseStateWithLin state_t = getPoseStateWithLin(tcid_t.first);

              Sophus::Matrix6d d_rel_d_h, d_rel_d_t;

              Sophus::SE3d T_t_h_sophus = computeRelPose(
                  state_h.getPoseLin(), calib.T_i_c[tcid_h.second],
                  state_t.getPoseLin(), calib.T_i_c[tcid_t.second], &d_rel_d_h,
                  &d_rel_d_t);

              rld.d_rel_d_h.emplace_back(d_rel_d_h);
              rld.d_rel_d_t.emplace_back(d_rel_d_t);

              if (state_h.isLinearized() || state_t.isLinearized()) {
                T_t_h_sophus = computeRelPose(
                    state_h.getPose(), calib.T_i_c[tcid_h.second],
                    state_t.getPose(), calib.T_i_c[tcid_t.second]);
              }

              Eigen::Matrix4d T_t_h = T_t_h_sophus.matrix();

              FrameRelLinData frld;

              std::visit(
                  [&](const auto& cam) {
                    for (size_t i = 0; i < obs_kv.second.size(); i++) {
                      const KeypointObservation& kpt_obs = obs_kv.second[i];
                      const KeypointPosition& kpt_pos = kpts.at(kpt_obs.kpt_id);

                      Eigen::Vector2d res;
                      Eigen::Matrix<double, 2, POSE_SIZE> d_res_d_xi;
                      Eigen::Matrix<double, 2, 3> d_res_d_p;

                      bool valid = linearizePoint(kpt_obs, kpt_pos, T_t_h, cam,
                                                  res, &d_res_d_xi, &d_res_d_p);

                      if (valid) {
                        double e = res.norm();
                        double huber_weight =
                            e < huber_thresh ? 1.0 : huber_thresh / e;
                        double obs_weight =
                            huber_weight / (obs_std_dev * obs_std_dev);

                        rld.error += (2 - huber_weight) * obs_weight *
                                     res.transpose() * res;

                        if (rld.Hll.count(kpt_obs.kpt_id) == 0) {
                          rld.Hll[kpt_obs.kpt_id].setZero();
                          rld.bl[kpt_obs.kpt_id].setZero();
                        }

                        rld.Hll[kpt_obs.kpt_id] +=
                            obs_weight * d_res_d_p.transpose() * d_res_d_p;
                        rld.bl[kpt_obs.kpt_id] +=
                            obs_weight * d_res_d_p.transpose() * res;

                        frld.Hpp +=
                            obs_weight * d_res_d_xi.transpose() * d_res_d_xi;
                        frld.bp += obs_weight * d_res_d_xi.transpose() * res;
                        frld.Hpl.emplace_back(
                            obs_weight * d_res_d_xi.transpose() * d_res_d_p);
                        frld.lm_id.emplace_back(kpt_obs.kpt_id);

                        rld.lm_to_obs[kpt_obs.kpt_id].emplace_back(
                            rld.Hpppl.size(), frld.lm_id.size() - 1);
                      }
                    }
                  },
                  calib.intrinsics[tcid_t.second].variant);

              rld.Hpppl.emplace_back(frld);

            } else {
              // target and host are the same
              // residual does not depend on the pose
              // it just depends on the point

              std::visit(
                  [&](const auto& cam) {
                    for (size_t i = 0; i < obs_kv.second.size(); i++) {
                      const KeypointObservation& kpt_obs = obs_kv.second[i];
                      const KeypointPosition& kpt_pos = kpts.at(kpt_obs.kpt_id);

                      Eigen::Vector2d res;
                      Eigen::Matrix<double, 2, 3> d_res_d_p;

                      bool valid = linearizePoint(kpt_obs, kpt_pos, cam, res,
                                                  &d_res_d_p);

                      if (valid) {
                        double e = res.norm();
                        double huber_weight =
                            e < huber_thresh ? 1.0 : huber_thresh / e;
                        double obs_weight =
                            huber_weight / (obs_std_dev * obs_std_dev);

                        rld.error += (2 - huber_weight) * obs_weight *
                                     res.transpose() * res;

                        if (rld.Hll.count(kpt_obs.kpt_id) == 0) {
                          rld.Hll[kpt_obs.kpt_id].setZero();
                          rld.bl[kpt_obs.kpt_id].setZero();
                        }

                        rld.Hll[kpt_obs.kpt_id] +=
                            obs_weight * d_res_d_p.transpose() * d_res_d_p;
                        rld.bl[kpt_obs.kpt_id] +=
                            obs_weight * d_res_d_p.transpose() * res;
                      }
                    }
                  },
                  calib.intrinsics[tcid_t.second].variant);
            }
          }
        }
      });

  for (const auto& rld : rld_vec) error += rld.error;
}

void BundleAdjustmentBase::linearizeRel(const RelLinData& rld,
                                        Eigen::MatrixXd& H,
                                        Eigen::VectorXd& b) {
  //  std::cout << "linearizeRel: KF " << frame_states.size() << " obs "
  //            << obs.size() << std::endl;

  // Do schur complement
  size_t msize = rld.order.size();
  H.setZero(POSE_SIZE * msize, POSE_SIZE * msize);
  b.setZero(POSE_SIZE * msize);

  for (size_t i = 0; i < rld.order.size(); i++) {
    const FrameRelLinData& frld = rld.Hpppl.at(i);

    H.block<POSE_SIZE, POSE_SIZE>(POSE_SIZE * i, POSE_SIZE * i) += frld.Hpp;
    b.segment<POSE_SIZE>(POSE_SIZE * i) += frld.bp;

    for (size_t j = 0; j < frld.lm_id.size(); j++) {
      Eigen::Matrix<double, POSE_SIZE, 3> H_pl_H_ll_inv;
      int lm_id = frld.lm_id[j];

      H_pl_H_ll_inv = frld.Hpl[j] * rld.Hll.at(lm_id);
      b.segment<POSE_SIZE>(POSE_SIZE * i) -= H_pl_H_ll_inv * rld.bl.at(lm_id);

      const auto& other_obs = rld.lm_to_obs.at(lm_id);
      for (size_t k = 0; k < other_obs.size(); k++) {
        const FrameRelLinData& frld_other = rld.Hpppl.at(other_obs[k].first);
        int other_i = other_obs[k].first;

        Eigen::Matrix<double, 3, POSE_SIZE> H_l_p_other =
            frld_other.Hpl[other_obs[k].second].transpose();

        H.block<POSE_SIZE, POSE_SIZE>(POSE_SIZE * i, POSE_SIZE * other_i) -=
            H_pl_H_ll_inv * H_l_p_other;
      }
    }
  }
}

void BundleAdjustmentBase::get_current_points(
    Eigen::vector<Eigen::Vector3d>& points, std::vector<int>& ids) const {
  points.clear();
  ids.clear();

  for (const auto& kv_kpt : kpts) {
    Eigen::Vector3d pt_cam =
        StereographicParam<double>::unproject(kv_kpt.second.dir).head<3>();
    pt_cam /= kv_kpt.second.id;

    Sophus::SE3d T_w_i;

    int64_t id = kv_kpt.second.kf_id.first;
    if (frame_states.count(id) > 0) {
      PoseVelBiasStateWithLin state = frame_states.at(id);
      T_w_i = state.getState().T_w_i;
    } else if (frame_poses.count(id) > 0) {
      PoseStateWithLin state = frame_poses.at(id);

      T_w_i = state.getPose();
    } else {
      std::cout << "Unknown frame id: " << id << std::endl;
      std::abort();
    }

    const Sophus::SE3d& T_i_c = calib.T_i_c[kv_kpt.second.kf_id.second];

    // std::cerr << "T_w_i\n" << T_w_i.matrix() << std::endl;

    points.emplace_back(T_w_i * T_i_c * pt_cam);

    ids.emplace_back(kv_kpt.first);
  }
}

Eigen::Vector4d BundleAdjustmentBase::triangulate(const Eigen::Vector3d& p0_3d,
                                                  const Eigen::Vector3d& p1_3d,
                                                  const Sophus::SE3d& T_0_1) {
  Eigen::Vector3d p1_3d_unrotated = T_0_1.so3() * p1_3d;
  Eigen::Vector2d b;
  b[0] = T_0_1.translation().dot(p0_3d);
  b[1] = T_0_1.translation().dot(p1_3d_unrotated);
  Eigen::Matrix2d A;
  A(0, 0) = p0_3d.dot(p0_3d);
  A(1, 0) = p0_3d.dot(p1_3d_unrotated);
  A(0, 1) = -A(1, 0);
  A(1, 1) = -p1_3d_unrotated.dot(p1_3d_unrotated);
  Eigen::Vector2d lambda = A.inverse() * b;
  Eigen::Vector3d xm = lambda[0] * p0_3d;
  Eigen::Vector3d xn = T_0_1.translation() + lambda[1] * p1_3d_unrotated;

  Eigen::Vector4d p0_triangulated;
  p0_triangulated.head<3>() = (xm + xn) / 2;
  p0_triangulated[3] = 0;

  return p0_triangulated;
}

void BundleAdjustmentBase::marginalizeHelper(Eigen::MatrixXd& abs_H,
                                             Eigen::VectorXd& abs_b,
                                             const std::set<int>& idx_to_keep,
                                             const std::set<int>& idx_to_marg,
                                             Eigen::MatrixXd& marg_H,
                                             Eigen::VectorXd& marg_b) {
  int keep_size = idx_to_keep.size();
  int marg_size = idx_to_marg.size();

  BASALT_ASSERT(keep_size + marg_size == abs_H.cols());

  // Fill permutation matrix
  Eigen::Matrix<int, Eigen::Dynamic, 1> indices(idx_to_keep.size() +
                                                idx_to_marg.size());

  {
    auto it = idx_to_keep.begin();
    for (size_t i = 0; i < idx_to_keep.size(); i++) {
      indices[i] = *it;
      it++;
    }
  }

  {
    auto it = idx_to_marg.begin();
    for (size_t i = 0; i < idx_to_marg.size(); i++) {
      indices[idx_to_keep.size() + i] = *it;
      it++;
    }
  }

  const Eigen::PermutationWrapper<Eigen::Matrix<int, Eigen::Dynamic, 1>> p(
      indices);

  const Eigen::PermutationMatrix<Eigen::Dynamic> pt = p.transpose();

  abs_b.applyOnTheLeft(pt);
  abs_H.applyOnTheLeft(pt);
  abs_H.applyOnTheRight(p);

  Eigen::MatrixXd H_mm_inv;
  //  H_mm_inv.setIdentity(marg_size, marg_size);
  //  abs_H.bottomRightCorner(marg_size,
  //  marg_size).ldlt().solveInPlace(H_mm_inv);

  H_mm_inv = abs_H.bottomRightCorner(marg_size, marg_size)
                 .fullPivLu()
                 .solve(Eigen::MatrixXd::Identity(marg_size, marg_size));

  //  H_mm_inv = abs_H.bottomRightCorner(marg_size, marg_size)
  //                 .fullPivHouseholderQr()
  //                 .solve(Eigen::MatrixXd::Identity(marg_size, marg_size));

  abs_H.topRightCorner(keep_size, marg_size) *= H_mm_inv;

  marg_H = abs_H.topLeftCorner(keep_size, keep_size);
  marg_b = abs_b.head(keep_size);

  marg_H -= abs_H.topRightCorner(keep_size, marg_size) *
            abs_H.bottomLeftCorner(marg_size, keep_size);
  marg_b -= abs_H.topRightCorner(keep_size, marg_size) * abs_b.tail(marg_size);

  abs_H.resize(0, 0);
  abs_b.resize(0);
}
}  // namespace basalt