ia_fpcs.hpp

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#ifndef PCL_REGISTRATION_IMPL_IA_FPCS_H_
#define PCL_REGISTRATION_IMPL_IA_FPCS_H_
 
#include <pcl/common/distances.h>
#include <pcl/common/time.h>
#include <pcl/common/utils.h>
#include <pcl/filters/random_sample.h>
#include <pcl/registration/ia_fpcs.h>
#include <pcl/registration/transformation_estimation_3point.h>
#include <pcl/sample_consensus/sac_model_plane.h>
#include <pcl/search/auto.h>
 
#include <limits>
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointT>
inline float
pcl::getMeanPointDensity(const typename pcl::PointCloud<PointT>::ConstPtr& cloud,
                         float max_dist,
                         int nr_threads)
{
  const float max_dist_sqr = max_dist * max_dist;
  const std::size_t s = cloud->size();
 
  typename pcl::search::Search<PointT>::Ptr tree(pcl::search::autoSelectMethod<PointT>(
      cloud, true, pcl::search::Purpose::many_knn_search));
 
  float mean_dist = 0.f;
  int num = 0;
  pcl::Indices ids(2);
  std::vector<float> dists_sqr(2);
 
  pcl::utils::ignore(nr_threads);
#pragma omp parallel for default(none) shared(tree, cloud)                             \
    firstprivate(ids, dists_sqr) reduction(+ : mean_dist, num)                         \
    firstprivate(s, max_dist_sqr) num_threads(nr_threads)
  for (int i = 0; i < 1000; i++) {
    tree->nearestKSearch((*cloud)[rand() % s], 2, ids, dists_sqr);
    if (dists_sqr[1] < max_dist_sqr) {
      mean_dist += std::sqrt(dists_sqr[1]);
      num++;
    }
  }
 
  return (mean_dist / num);
};
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointT>
inline float
pcl::getMeanPointDensity(const typename pcl::PointCloud<PointT>::ConstPtr& cloud,
                         const pcl::Indices& indices,
                         float max_dist,
                         int nr_threads)
{
  const float max_dist_sqr = max_dist * max_dist;
  const std::size_t s = indices.size();
 
  typename pcl::search::Search<PointT>::Ptr tree(pcl::search::autoSelectMethod<PointT>(
      cloud, true, pcl::search::Purpose::many_knn_search));
 
  float mean_dist = 0.f;
  int num = 0;
  pcl::Indices ids(2);
  std::vector<float> dists_sqr(2);
 
  pcl::utils::ignore(nr_threads);
#if OPENMP_LEGACY_CONST_DATA_SHARING_RULE
#pragma omp parallel for default(none) shared(tree, cloud, indices)                    \
    firstprivate(ids, dists_sqr) reduction(+ : mean_dist, num) num_threads(nr_threads)
#else
#pragma omp parallel for default(none) shared(tree, cloud, indices, s, max_dist_sqr)   \
    firstprivate(ids, dists_sqr) reduction(+ : mean_dist, num) num_threads(nr_threads)
#endif
  for (int i = 0; i < 1000; i++) {
    tree->nearestKSearch((*cloud)[indices[rand() % s]], 2, ids, dists_sqr);
    if (dists_sqr[1] < max_dist_sqr) {
      mean_dist += std::sqrt(dists_sqr[1]);
      num++;
    }
  }
 
  return (mean_dist / num);
};
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointSource, typename PointTarget, typename NormalT, typename Scalar>
pcl::registration::FPCSInitialAlignment<PointSource, PointTarget, NormalT, Scalar>::
    FPCSInitialAlignment()
: source_normals_()
, target_normals_()
, score_threshold_(std::numeric_limits<float>::max())
, fitness_score_(std::numeric_limits<float>::max())
{
  reg_name_ = "pcl::registration::FPCSInitialAlignment";
  max_iterations_ = 0;
  ransac_iterations_ = 1000;
  transformation_estimation_.reset(
      new pcl::registration::TransformationEstimation3Point<PointSource, PointTarget>);
}
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointSource, typename PointTarget, typename NormalT, typename Scalar>
void
pcl::registration::FPCSInitialAlignment<PointSource, PointTarget, NormalT, Scalar>::
    computeTransformation(PointCloudSource& output, const Eigen::Matrix4f& guess)
{
  if (!initCompute())
    return;
 
  final_transformation_ = guess;
  bool abort = false;
  std::vector<MatchingCandidates> all_candidates(max_iterations_);
  pcl::StopWatch timer;
 
#pragma omp parallel default(none) shared(abort, all_candidates, timer)                \
    num_threads(nr_threads_)
  {
#ifdef _OPENMP
    const unsigned int seed =
        static_cast<unsigned int>(std::time(nullptr)) ^ omp_get_thread_num();
    std::srand(seed);
    PCL_DEBUG("[%s::computeTransformation] Using seed=%u\n", reg_name_.c_str(), seed);
#pragma omp for schedule(dynamic)
#endif
    for (int i = 0; i < max_iterations_; i++) {
#pragma omp flush(abort)
 
      MatchingCandidates candidates(1);
      pcl::Indices base_indices(4);
      all_candidates[i] = candidates;
 
      if (!abort) {
        float ratio[2];
        // select four coplanar point base
        if (selectBase(base_indices, ratio) == 0) {
          // calculate candidate pair correspondences using diagonal lengths of base
          pcl::Correspondences pairs_a, pairs_b;
          if (bruteForceCorrespondences(base_indices[0], base_indices[1], pairs_a) ==
                  0 &&
              bruteForceCorrespondences(base_indices[2], base_indices[3], pairs_b) ==
                  0) {
            // determine candidate matches by combining pair correspondences based on
            // segment distances
            std::vector<pcl::Indices> matches;
            if (determineBaseMatches(base_indices, matches, pairs_a, pairs_b, ratio) ==
                0) {
              // check and evaluate candidate matches and store them
              handleMatches(base_indices, matches, candidates);
              if (!candidates.empty())
                all_candidates[i] = candidates;
            }
          }
        }
 
        // check terminate early (time or fitness_score threshold reached)
        if (!candidates.empty() && candidates[0].fitness_score < score_threshold_) {
          PCL_DEBUG("[%s::computeTransformation] Terminating because fitness score "
                    "(%g) is below threshold (%g).\n",
                    reg_name_.c_str(),
                    candidates[0].fitness_score,
                    score_threshold_);
          abort = true;
        }
        else if (timer.getTimeSeconds() > max_runtime_) {
          PCL_DEBUG("[%s::computeTransformation] Terminating because time exceeded.\n",
                    reg_name_.c_str());
          abort = true;
        }
 
#pragma omp flush(abort)
      }
    }
  }
 
  // determine best match over all tries
  finalCompute(all_candidates);
 
  // apply the final transformation
  pcl::transformPointCloud(*input_, output, final_transformation_);
 
  deinitCompute();
}
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointSource, typename PointTarget, typename NormalT, typename Scalar>
bool
pcl::registration::FPCSInitialAlignment<PointSource, PointTarget, NormalT, Scalar>::
    initCompute()
{
  const unsigned int seed = std::time(nullptr);
  std::srand(seed);
  PCL_DEBUG("[%s::initCompute] Using seed=%u\n", reg_name_.c_str(), seed);
 
  // basic pcl initialization
  if (!pcl::PCLBase<PointSource>::initCompute())
    return (false);
 
  // check if source and target are given
  if (!input_ || !target_) {
    PCL_ERROR("[%s::initCompute] Source or target dataset not given!\n",
              reg_name_.c_str());
    return (false);
  }
 
  if (!target_indices_ || target_indices_->empty()) {
    target_indices_.reset(new pcl::Indices(target_->size()));
    int index = 0;
    for (auto& target_index : *target_indices_)
      target_index = index++;
    target_cloud_updated_ = true;
  }
 
  // if a sample size for the point clouds is given; preferably no sampling of target
  // cloud
  if (nr_samples_ > 0 && static_cast<std::size_t>(nr_samples_) < indices_->size()) {
    source_indices_ = pcl::IndicesPtr(new pcl::Indices);
    pcl::RandomSample<PointSource> random_sampling;
    random_sampling.setInputCloud(input_);
    random_sampling.setIndices(indices_);
    random_sampling.setSample(nr_samples_);
    random_sampling.setSeed(seed);
    random_sampling.filter(*source_indices_);
  }
  else
    source_indices_ = indices_;
 
  // check usage of normals
  if (source_normals_ && target_normals_ && source_normals_->size() == input_->size() &&
      target_normals_->size() == target_->size())
    use_normals_ = true;
 
  // set up tree structures
  if (target_cloud_updated_) {
    tree_->setInputCloud(target_, target_indices_);
    target_cloud_updated_ = false;
  }
 
  // set predefined variables
  constexpr int min_iterations = 4;
  constexpr float diameter_fraction = 0.3f;
 
  // get diameter of input cloud (distance between farthest points)
  Eigen::Vector4f pt_min, pt_max;
  pcl::getMinMax3D(*target_, *target_indices_, pt_min, pt_max);
  diameter_ = (pt_max - pt_min).norm();
 
  // derive the limits for the random base selection
  float max_base_diameter = diameter_ * approx_overlap_ * 2.f;
  max_base_diameter_sqr_ = max_base_diameter * max_base_diameter;
 
#ifdef _OPENMP
  if (nr_threads_ < 1) {
    nr_threads_ = omp_get_num_procs();
    PCL_DEBUG("[%s::initCompute] Setting number of threads to %i.\n",
              reg_name_.c_str(),
              nr_threads_);
  }
#endif // _OPENMP
 
  // normalize the delta
  if (normalize_delta_) {
    float mean_dist = getMeanPointDensity<PointTarget>(
        target_, *target_indices_, 0.05f * diameter_, nr_threads_);
    delta_ *= mean_dist;
  }
 
  // heuristic determination of number of trials to have high probability of finding a
  // good solution
  if (max_iterations_ == 0) {
    float first_est = std::log(small_error_) /
                      std::log(1.0 - std::pow(static_cast<double>(approx_overlap_),
                                              static_cast<double>(min_iterations)));
    max_iterations_ =
        static_cast<int>(first_est / (diameter_fraction * approx_overlap_ * 2.f));
    PCL_DEBUG("[%s::initCompute] Estimated max iterations as %i\n",
              reg_name_.c_str(),
              max_iterations_);
  }
 
  // set further parameter
  if (score_threshold_ == std::numeric_limits<float>::max())
    score_threshold_ = 1.f - approx_overlap_;
 
  if (max_iterations_ < 4)
    max_iterations_ = 4;
 
  if (max_runtime_ < 1)
    max_runtime_ = std::numeric_limits<int>::max();
 
  // calculate internal parameters based on the the estimated point density
  max_pair_diff_ = delta_ * 2.f;
  max_edge_diff_ = delta_ * 4.f;
  coincidation_limit_ = delta_ * 2.f; // EDITED: originally std::sqrt (delta_ * 2.f)
  max_mse_ = powf(delta_ * 2.f, 2.f);
  max_inlier_dist_sqr_ = powf(delta_ * 2.f, 2.f);
  PCL_DEBUG("[%s::initCompute] delta_=%g, max_inlier_dist_sqr_=%g, "
            "coincidation_limit_=%g, max_edge_diff_=%g, max_pair_diff_=%g\n",
            reg_name_.c_str(),
            delta_,
            max_inlier_dist_sqr_,
            coincidation_limit_,
            max_edge_diff_,
            max_pair_diff_);
 
  // reset fitness_score
  fitness_score_ = std::numeric_limits<float>::max();
 
  return (true);
}
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointSource, typename PointTarget, typename NormalT, typename Scalar>
int
pcl::registration::FPCSInitialAlignment<PointSource, PointTarget, NormalT, Scalar>::
    selectBase(pcl::Indices& base_indices, float (&ratio)[2])
{
  const float too_close_sqr = max_base_diameter_sqr_ * 0.01;
 
  Eigen::VectorXf coefficients(4);
  pcl::SampleConsensusModelPlane<PointTarget> plane(target_);
  plane.setIndices(target_indices_);
  Eigen::Vector4f centre_pt;
  float nearest_to_plane = std::numeric_limits<float>::max();
 
  // repeat base search until valid quadruple was found or ransac_iterations_ number of
  // tries were unsuccessful
  for (int i = 0; i < ransac_iterations_; i++) {
    // random select an appropriate point triple
    if (selectBaseTriangle(base_indices) < 0)
      continue;
 
    pcl::Indices base_triple(base_indices.begin(), base_indices.end() - 1);
    plane.computeModelCoefficients(base_triple, coefficients);
    pcl::compute3DCentroid(*target_, base_triple, centre_pt);
 
    // loop over all points in source cloud to find most suitable fourth point
    const PointTarget* pt1 = &((*target_)[base_indices[0]]);
    const PointTarget* pt2 = &((*target_)[base_indices[1]]);
    const PointTarget* pt3 = &((*target_)[base_indices[2]]);
 
    for (const auto& target_index : *target_indices_) {
      const PointTarget* pt4 = &((*target_)[target_index]);
 
      float d1 = pcl::squaredEuclideanDistance(*pt4, *pt1);
      float d2 = pcl::squaredEuclideanDistance(*pt4, *pt2);
      float d3 = pcl::squaredEuclideanDistance(*pt4, *pt3);
      float d4 = (pt4->getVector3fMap() - centre_pt.head<3>()).squaredNorm();
 
      // check distance between points w.r.t minimum sampling distance; EDITED -> 4th
      // point now also limited by max base line
      if (d1 < too_close_sqr || d2 < too_close_sqr || d3 < too_close_sqr ||
          d4 < too_close_sqr || d1 > max_base_diameter_sqr_ ||
          d2 > max_base_diameter_sqr_ || d3 > max_base_diameter_sqr_)
        continue;
 
      // check distance to plane to get point closest to plane
      float dist_to_plane = pcl::pointToPlaneDistance(*pt4, coefficients);
      if (dist_to_plane < nearest_to_plane) {
        base_indices[3] = target_index;
        nearest_to_plane = dist_to_plane;
      }
    }
 
    // check if at least one point fulfilled the conditions
    if (nearest_to_plane != std::numeric_limits<float>::max()) {
      // order points to build largest quadrangle and calculate intersection ratios of
      // diagonals
      setupBase(base_indices, ratio);
      return (0);
    }
  }
 
  // return unsuccessful if no quadruple was selected
  return (-1);
}
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointSource, typename PointTarget, typename NormalT, typename Scalar>
int
pcl::registration::FPCSInitialAlignment<PointSource, PointTarget, NormalT, Scalar>::
    selectBaseTriangle(pcl::Indices& base_indices)
{
  const auto nr_points = target_indices_->size();
  float best_t = 0.f;
 
  // choose random first point
  base_indices[0] = (*target_indices_)[rand() % nr_points];
  auto* index1 = base_indices.data();
 
  // random search for 2 other points (as far away as overlap allows)
  for (int i = 0; i < ransac_iterations_; i++) {
    auto* index2 = &(*target_indices_)[rand() % nr_points];
    auto* index3 = &(*target_indices_)[rand() % nr_points];
 
    Eigen::Vector3f u =
        (*target_)[*index2].getVector3fMap() - (*target_)[*index1].getVector3fMap();
    Eigen::Vector3f v =
        (*target_)[*index3].getVector3fMap() - (*target_)[*index1].getVector3fMap();
    float t =
        u.cross(v).squaredNorm(); // triangle area (0.5 * sqrt(t)) should be maximal
 
    // check for most suitable point triple
    if (t > best_t && u.squaredNorm() < max_base_diameter_sqr_ &&
        v.squaredNorm() < max_base_diameter_sqr_) {
      best_t = t;
      base_indices[1] = *index2;
      base_indices[2] = *index3;
    }
  }
 
  // return if a triplet could be selected
  return (best_t == 0.f ? -1 : 0);
}
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointSource, typename PointTarget, typename NormalT, typename Scalar>
void
pcl::registration::FPCSInitialAlignment<PointSource, PointTarget, NormalT, Scalar>::
    setupBase(pcl::Indices& base_indices, float (&ratio)[2])
{
  float best_t = std::numeric_limits<float>::max();
  const pcl::Indices copy(base_indices.begin(), base_indices.end());
  pcl::Indices temp(base_indices.begin(), base_indices.end());
 
  // loop over all combinations of base points
  for (auto i = copy.begin(), i_e = copy.end(); i != i_e; ++i)
    for (auto j = copy.begin(), j_e = copy.end(); j != j_e; ++j) {
      if (i == j)
        continue;
 
      for (auto k = copy.begin(), k_e = copy.end(); k != k_e; ++k) {
        if (k == j || k == i)
          continue;
 
        auto l = copy.begin();
        while (l == i || l == j || l == k)
          ++l;
 
        temp[0] = *i;
        temp[1] = *j;
        temp[2] = *k;
        temp[3] = *l;
 
        // calculate diagonal intersection ratios and check for suitable segment to
        // segment distances
        float ratio_temp[2];
        float t = segmentToSegmentDist(temp, ratio_temp);
        if (t < best_t) {
          best_t = t;
          ratio[0] = ratio_temp[0];
          ratio[1] = ratio_temp[1];
          base_indices = temp;
        }
      }
    }
}
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointSource, typename PointTarget, typename NormalT, typename Scalar>
float
pcl::registration::FPCSInitialAlignment<PointSource, PointTarget, NormalT, Scalar>::
    segmentToSegmentDist(const pcl::Indices& base_indices, float (&ratio)[2])
{
  // get point vectors
  Eigen::Vector3f u = (*target_)[base_indices[1]].getVector3fMap() -
                      (*target_)[base_indices[0]].getVector3fMap();
  Eigen::Vector3f v = (*target_)[base_indices[3]].getVector3fMap() -
                      (*target_)[base_indices[2]].getVector3fMap();
  Eigen::Vector3f w = (*target_)[base_indices[0]].getVector3fMap() -
                      (*target_)[base_indices[2]].getVector3fMap();
 
  // calculate segment distances
  float a = u.dot(u);
  float b = u.dot(v);
  float c = v.dot(v);
  float d = u.dot(w);
  float e = v.dot(w);
  float D = a * c - b * b;
  float sN = 0.f, sD = D;
  float tN = 0.f, tD = D;
 
  // check segments
  if (D < small_error_) {
    sN = 0.f;
    sD = 1.f;
    tN = e;
    tD = c;
  }
  else {
    sN = (b * e - c * d);
    tN = (a * e - b * d);
 
    if (sN < 0.f) {
      sN = 0.f;
      tN = e;
      tD = c;
    }
    else if (sN > sD) {
      sN = sD;
      tN = e + b;
      tD = c;
    }
  }
 
  if (tN < 0.f) {
    tN = 0.f;
 
    if (-d < 0.f)
      sN = 0.f;
 
    else if (-d > a)
      sN = sD;
 
    else {
      sN = -d;
      sD = a;
    }
  }
 
  else if (tN > tD) {
    tN = tD;
 
    if ((-d + b) < 0.f)
      sN = 0.f;
 
    else if ((-d + b) > a)
      sN = sD;
 
    else {
      sN = (-d + b);
      sD = a;
    }
  }
 
  // set intersection ratios
  ratio[0] = (std::abs(sN) < small_error_) ? 0.f : sN / sD;
  ratio[1] = (std::abs(tN) < small_error_) ? 0.f : tN / tD;
 
  Eigen::Vector3f x = w + (ratio[0] * u) - (ratio[1] * v);
  return (x.norm());
}
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointSource, typename PointTarget, typename NormalT, typename Scalar>
int
pcl::registration::FPCSInitialAlignment<PointSource, PointTarget, NormalT, Scalar>::
    bruteForceCorrespondences(int idx1, int idx2, pcl::Correspondences& pairs)
{
  const float max_norm_diff = 0.5f * max_norm_diff_ * M_PI / 180.f;
 
  // calculate reference segment distance and normal angle
  float ref_dist = pcl::euclideanDistance((*target_)[idx1], (*target_)[idx2]);
  float ref_norm_angle =
      (use_normals_ ? ((*target_normals_)[idx1].getNormalVector3fMap() -
                       (*target_normals_)[idx2].getNormalVector3fMap())
                          .norm()
                    : 0.f);
 
  // loop over all pairs of points in source point cloud
  auto it_out = source_indices_->begin(), it_out_e = source_indices_->end() - 1;
  auto it_in_e = source_indices_->end();
  for (; it_out != it_out_e; it_out++) {
    auto it_in = it_out + 1;
    const PointSource* pt1 = &(*input_)[*it_out];
    for (; it_in != it_in_e; it_in++) {
      const PointSource* pt2 = &(*input_)[*it_in];
 
      // check point distance compared to reference dist (from base)
      float dist = pcl::euclideanDistance(*pt1, *pt2);
      if (std::abs(dist - ref_dist) < max_pair_diff_) {
        // add here normal evaluation if normals are given
        if (use_normals_) {
          const NormalT* pt1_n = &((*source_normals_)[*it_out]);
          const NormalT* pt2_n = &((*source_normals_)[*it_in]);
 
          float norm_angle_1 =
              (pt1_n->getNormalVector3fMap() - pt2_n->getNormalVector3fMap()).norm();
          float norm_angle_2 =
              (pt1_n->getNormalVector3fMap() + pt2_n->getNormalVector3fMap()).norm();
 
          float norm_diff = std::min<float>(std::abs(norm_angle_1 - ref_norm_angle),
                                            std::abs(norm_angle_2 - ref_norm_angle));
          if (norm_diff > max_norm_diff)
            continue;
        }
 
        pairs.emplace_back(*it_in, *it_out, dist);
        pairs.emplace_back(*it_out, *it_in, dist);
      }
    }
  }
 
  // return success if at least one correspondence was found
  return (pairs.empty() ? -1 : 0);
}
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointSource, typename PointTarget, typename NormalT, typename Scalar>
int
pcl::registration::FPCSInitialAlignment<PointSource, PointTarget, NormalT, Scalar>::
    determineBaseMatches(const pcl::Indices& base_indices,
                         std::vector<pcl::Indices>& matches,
                         const pcl::Correspondences& pairs_a,
                         const pcl::Correspondences& pairs_b,
                         const float (&ratio)[2])
{
  // calculate edge lengths of base
  float dist_base[4];
  dist_base[0] =
      pcl::euclideanDistance((*target_)[base_indices[0]], (*target_)[base_indices[2]]);
  dist_base[1] =
      pcl::euclideanDistance((*target_)[base_indices[0]], (*target_)[base_indices[3]]);
  dist_base[2] =
      pcl::euclideanDistance((*target_)[base_indices[1]], (*target_)[base_indices[2]]);
  dist_base[3] =
      pcl::euclideanDistance((*target_)[base_indices[1]], (*target_)[base_indices[3]]);
 
  // loop over first point pair correspondences and store intermediate points 'e' in new
  // point cloud
  PointCloudSourcePtr cloud_e(new PointCloudSource);
  cloud_e->resize(pairs_a.size() * 2);
  auto it_pt = cloud_e->begin();
  for (const auto& pair : pairs_a) {
    const PointSource* pt1 = &((*input_)[pair.index_match]);
    const PointSource* pt2 = &((*input_)[pair.index_query]);
 
    // calculate intermediate points using both ratios from base (r1,r2)
    for (int i = 0; i < 2; i++, it_pt++) {
      it_pt->x = pt1->x + ratio[i] * (pt2->x - pt1->x);
      it_pt->y = pt1->y + ratio[i] * (pt2->y - pt1->y);
      it_pt->z = pt1->z + ratio[i] * (pt2->z - pt1->z);
    }
  }
 
  // initialize new kd tree of intermediate points from first point pair correspondences
  KdTreeReciprocalPtr tree_e(new KdTreeReciprocal);
  tree_e->setInputCloud(cloud_e);
 
  pcl::Indices ids;
  std::vector<float> dists_sqr;
 
  // loop over second point pair correspondences
  for (const auto& pair : pairs_b) {
    const PointTarget* pt1 = &((*input_)[pair.index_match]);
    const PointTarget* pt2 = &((*input_)[pair.index_query]);
 
    // calculate intermediate points using both ratios from base (r1,r2)
    for (const float& r : ratio) {
      PointTarget pt_e;
      pt_e.x = pt1->x + r * (pt2->x - pt1->x);
      pt_e.y = pt1->y + r * (pt2->y - pt1->y);
      pt_e.z = pt1->z + r * (pt2->z - pt1->z);
 
      // search for corresponding intermediate points
      tree_e->radiusSearch(pt_e, coincidation_limit_, ids, dists_sqr);
      for (const auto& id : ids) {
        pcl::Indices match_indices(4);
 
        match_indices[0] =
            pairs_a[static_cast<int>(std::floor((id / 2.f)))].index_match;
        match_indices[1] =
            pairs_a[static_cast<int>(std::floor((id / 2.f)))].index_query;
        match_indices[2] = pair.index_match;
        match_indices[3] = pair.index_query;
        if (match_indices[0] == match_indices[2] ||
            match_indices[0] == match_indices[3] ||
            match_indices[1] == match_indices[2] ||
            match_indices[1] == match_indices[3])
          continue;
 
        // EDITED: added coarse check of match based on edge length (due to rigid-body )
        if (checkBaseMatch(match_indices, dist_base) < 0)
          continue;
 
        matches.push_back(match_indices);
      }
    }
  }
 
  // return unsuccessful if no match was found
  if (matches.empty()) {
    PCL_DEBUG("[%s::determineBaseMatches] no matches found\n", reg_name_.c_str());
    return -1;
  }
  else {
    PCL_DEBUG("[%s::determineBaseMatches] found %zu matches\n",
              reg_name_.c_str(),
              matches.size());
    return 0;
  }
}
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointSource, typename PointTarget, typename NormalT, typename Scalar>
int
pcl::registration::FPCSInitialAlignment<PointSource, PointTarget, NormalT, Scalar>::
    checkBaseMatch(const pcl::Indices& match_indices, const float (&dist_ref)[4])
{
  float d0 =
      pcl::euclideanDistance((*input_)[match_indices[0]], (*input_)[match_indices[2]]);
  float d1 =
      pcl::euclideanDistance((*input_)[match_indices[0]], (*input_)[match_indices[3]]);
  float d2 =
      pcl::euclideanDistance((*input_)[match_indices[1]], (*input_)[match_indices[2]]);
  float d3 =
      pcl::euclideanDistance((*input_)[match_indices[1]], (*input_)[match_indices[3]]);
 
  // check edge distances of match w.r.t the base
  return (std::abs(d0 - dist_ref[0]) < max_edge_diff_ &&
          std::abs(d1 - dist_ref[1]) < max_edge_diff_ &&
          std::abs(d2 - dist_ref[2]) < max_edge_diff_ &&
          std::abs(d3 - dist_ref[3]) < max_edge_diff_)
             ? 0
             : -1;
}
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointSource, typename PointTarget, typename NormalT, typename Scalar>
void
pcl::registration::FPCSInitialAlignment<PointSource, PointTarget, NormalT, Scalar>::
    handleMatches(const pcl::Indices& base_indices,
                  std::vector<pcl::Indices>& matches,
                  MatchingCandidates& candidates)
{
  candidates.resize(1);
  float fitness_score = std::numeric_limits<float>::max();
 
  // loop over all Candidate matches
  for (auto& match : matches) {
    Eigen::Matrix4f transformation_temp;
    pcl::Correspondences correspondences_temp;
    correspondences_temp.emplace_back(match[0], base_indices[0], 0.0);
    correspondences_temp.emplace_back(match[1], base_indices[1], 0.0);
    correspondences_temp.emplace_back(match[2], base_indices[2], 0.0);
    correspondences_temp.emplace_back(match[3], base_indices[3], 0.0);
 
    // check match based on residuals of the corresponding points after
    if (validateMatch(base_indices, match, correspondences_temp, transformation_temp) <
        0)
      continue;
 
    // check resulting  using a sub sample of the source point cloud and compare to
    // previous matches
    if (validateTransformation(transformation_temp, fitness_score) < 0)
      continue;
 
    // store best match as well as associated fitness_score and transformation
    candidates[0].fitness_score = fitness_score;
    candidates[0].transformation = transformation_temp;
    correspondences_temp.erase(correspondences_temp.end() - 1);
    candidates[0].correspondences = correspondences_temp;
  }
}
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointSource, typename PointTarget, typename NormalT, typename Scalar>
void
pcl::registration::FPCSInitialAlignment<PointSource, PointTarget, NormalT, Scalar>::
    linkMatchWithBase(const pcl::Indices& base_indices,
                      pcl::Indices& match_indices,
                      pcl::Correspondences& correspondences)
{
  // calculate centroid of base and target
  Eigen::Vector4f centre_base{0, 0, 0, 0}, centre_match{0, 0, 0, 0};
  pcl::compute3DCentroid(*target_, base_indices, centre_base);
  pcl::compute3DCentroid(*input_, match_indices, centre_match);
 
  PointTarget centre_pt_base;
  centre_pt_base.x = centre_base[0];
  centre_pt_base.y = centre_base[1];
  centre_pt_base.z = centre_base[2];
 
  PointSource centre_pt_match;
  centre_pt_match.x = centre_match[0];
  centre_pt_match.y = centre_match[1];
  centre_pt_match.z = centre_match[2];
 
  // find corresponding points according to their distance to the centroid
  pcl::Indices copy = match_indices;
 
  auto it_match_orig = match_indices.begin();
  for (auto it_base = base_indices.cbegin(), it_base_e = base_indices.cend();
       it_base != it_base_e;
       it_base++, it_match_orig++) {
    float dist_sqr_1 =
        pcl::squaredEuclideanDistance((*target_)[*it_base], centre_pt_base);
    float best_diff_sqr = std::numeric_limits<float>::max();
    int best_index = -1;
 
    for (const auto& match_index : copy) {
      // calculate difference of distances to centre point
      float dist_sqr_2 =
          pcl::squaredEuclideanDistance((*input_)[match_index], centre_pt_match);
      float diff_sqr = std::abs(dist_sqr_1 - dist_sqr_2);
 
      if (diff_sqr < best_diff_sqr) {
        best_diff_sqr = diff_sqr;
        best_index = match_index;
      }
    }
 
    // assign new correspondence and update indices of matched targets
    correspondences.emplace_back(best_index, *it_base, best_diff_sqr);
    *it_match_orig = best_index;
  }
}
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointSource, typename PointTarget, typename NormalT, typename Scalar>
int
pcl::registration::FPCSInitialAlignment<PointSource, PointTarget, NormalT, Scalar>::
    validateMatch(const pcl::Indices& base_indices,
                  const pcl::Indices& match_indices,
                  const pcl::Correspondences& correspondences,
                  Eigen::Matrix4f& transformation)
{
  // only use triplet of points to simplify process (possible due to planar case)
  pcl::Correspondences correspondences_temp = correspondences;
  correspondences_temp.erase(correspondences_temp.end() - 1);
 
  // estimate transformation between correspondence set
  transformation_estimation_->estimateRigidTransformation(
      *input_, *target_, correspondences_temp, transformation);
 
  // transform base points
  PointCloudSource match_transformed;
  pcl::transformPointCloud(*input_, match_indices, match_transformed, transformation);
 
  // calculate residuals of transformation and check against maximum threshold
  std::size_t nr_points = correspondences_temp.size();
  float mse = 0.f;
  for (std::size_t i = 0; i < nr_points; i++)
    mse += pcl::squaredEuclideanDistance(match_transformed.points[i],
                                         target_->points[base_indices[i]]);
 
  mse /= nr_points;
  return (mse < max_mse_ ? 0 : -1);
}
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointSource, typename PointTarget, typename NormalT, typename Scalar>
int
pcl::registration::FPCSInitialAlignment<PointSource, PointTarget, NormalT, Scalar>::
    validateTransformation(Eigen::Matrix4f& transformation, float& fitness_score)
{
  // transform source point cloud
  PointCloudSource source_transformed;
  pcl::transformPointCloud(
      *input_, *source_indices_, source_transformed, transformation);
 
  std::size_t nr_points = source_transformed.size();
  std::size_t terminate_value =
      fitness_score > 1 ? 0
                        : static_cast<std::size_t>((1.f - fitness_score) * nr_points);
 
  float inlier_score_temp = 0;
  pcl::Indices ids(1);
  std::vector<float> dists_sqr(1);
  auto it = source_transformed.begin();
 
  for (std::size_t i = 0; i < nr_points; it++, i++) {
    // search for nearest point using kd tree search
    tree_->nearestKSearch(*it, 1, ids, dists_sqr);
    inlier_score_temp += (dists_sqr[0] < max_inlier_dist_sqr_ ? 1 : 0);
 
    // early terminating
    if (nr_points - i + inlier_score_temp < terminate_value)
      break;
  }
 
  // check current costs and return unsuccessful if larger than previous ones
  inlier_score_temp /= static_cast<float>(nr_points);
  float fitness_score_temp = 1.f - inlier_score_temp;
 
  if (fitness_score_temp > fitness_score)
    return (-1);
 
  fitness_score = fitness_score_temp;
  return (0);
}
 
///////////////////////////////////////////////////////////////////////////////////////////
template <typename PointSource, typename PointTarget, typename NormalT, typename Scalar>
void
pcl::registration::FPCSInitialAlignment<PointSource, PointTarget, NormalT, Scalar>::
    finalCompute(const std::vector<MatchingCandidates>& candidates)
{
  // get best fitness_score over all tries
  int nr_candidates = static_cast<int>(candidates.size());
  int best_index = -1;
  float best_score = std::numeric_limits<float>::max();
  for (int i = 0; i < nr_candidates; i++) {
    const float& fitness_score = candidates[i][0].fitness_score;
    if (fitness_score < best_score) {
      best_score = fitness_score;
      best_index = i;
    }
  }
  PCL_DEBUG(
      "[%s::finalCompute] best score is %g (iteration %i), out of %zu iterations.\n",
      reg_name_.c_str(),
      best_score,
      best_index,
      candidates.size());
 
  // check if a valid candidate was available
  if (!(best_index < 0)) {
    fitness_score_ = candidates[best_index][0].fitness_score;
    final_transformation_ = candidates[best_index][0].transformation;
    *correspondences_ = candidates[best_index][0].correspondences;
 
    // here we define convergence if resulting fitness_score is below 1-threshold
    converged_ = fitness_score_ < score_threshold_;
  }
}
 
///////////////////////////////////////////////////////////////////////////////////////////
 
#endif // PCL_REGISTRATION_IMPL_IA_4PCS_H_