sac_model_cylinder.hpp

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#ifndef PCL_SAMPLE_CONSENSUS_IMPL_SAC_MODEL_CYLINDER_H_
#define PCL_SAMPLE_CONSENSUS_IMPL_SAC_MODEL_CYLINDER_H_
 
#include <unsupported/Eigen/NonLinearOptimization> // for LevenbergMarquardt
#include <pcl/sample_consensus/sac_model_cylinder.h>
#include <pcl/common/common.h> // for getAngle3D
#include <pcl/common/concatenate.h>
 
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointT, typename PointNT> bool
pcl::SampleConsensusModelCylinder<PointT, PointNT>::isSampleGood (const Indices &samples) const
{
  if (samples.size () != sample_size_)
  {
    PCL_ERROR ("[pcl::SampleConsensusModelCylinder::isSampleGood] Wrong number of samples (is %lu, should be %lu)!\n", samples.size (), sample_size_);
    return (false);
  }
 
  // Make sure that the two sample points are not identical
  if (
      std::abs ((*input_)[samples[0]].x - (*input_)[samples[1]].x) <= std::numeric_limits<float>::epsilon ()
    &&
      std::abs ((*input_)[samples[0]].y - (*input_)[samples[1]].y) <= std::numeric_limits<float>::epsilon ()
    &&
      std::abs ((*input_)[samples[0]].z - (*input_)[samples[1]].z) <= std::numeric_limits<float>::epsilon ())
  {
    PCL_ERROR ("[pcl::SampleConsensusModelCylinder::isSampleGood] The two sample points are (almost) identical!\n");
    return (false);
  }
 
  return (true);
}
 
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointT, typename PointNT> bool
pcl::SampleConsensusModelCylinder<PointT, PointNT>::computeModelCoefficients (
      const Indices &samples, Eigen::VectorXf &model_coefficients) const
{
  // Make sure that the samples are valid
  if (!isSampleGood (samples))
  {
    PCL_ERROR ("[pcl::SampleConsensusModelCylinder::computeModelCoefficients] Invalid set of samples given!\n");
    return (false);
  }
 
  if (!normals_)
  {
    PCL_ERROR ("[pcl::SampleConsensusModelCylinder::computeModelCoefficients] No input dataset containing normals was given!\n");
    return (false);
  }
 
  Eigen::Vector4f p1 ((*input_)[samples[0]].x, (*input_)[samples[0]].y, (*input_)[samples[0]].z, 0.0f);
  Eigen::Vector4f p2 ((*input_)[samples[1]].x, (*input_)[samples[1]].y, (*input_)[samples[1]].z, 0.0f);
 
  Eigen::Vector4f n1 ((*normals_)[samples[0]].normal[0], (*normals_)[samples[0]].normal[1], (*normals_)[samples[0]].normal[2], 0.0f);
  Eigen::Vector4f n2 ((*normals_)[samples[1]].normal[0], (*normals_)[samples[1]].normal[1], (*normals_)[samples[1]].normal[2], 0.0f);
  Eigen::Vector4f w = n1 + p1 - p2;
 
  float a = n1.dot (n1);
  float b = n1.dot (n2);
  float c = n2.dot (n2);
  float d = n1.dot (w);
  float e = n2.dot (w);
  float denominator = a*c - b*b;
  float sc, tc;
  // Compute the line parameters of the two closest points
  if (denominator < 1e-8)          // The lines are almost parallel
  {
    sc = 0.0f;
    tc = (b > c ? d / b : e / c);  // Use the largest denominator
  }
  else
  {
    sc = (b*e - c*d) / denominator;
    tc = (a*e - b*d) / denominator;
  }
 
  // point_on_axis, axis_direction
  Eigen::Vector4f line_pt  = p1 + n1 + sc * n1;
  Eigen::Vector4f line_dir = p2 + tc * n2 - line_pt;
  line_dir.normalize ();
 
  model_coefficients.resize (model_size_);
  // model_coefficients.template head<3> ()    = line_pt.template head<3> ();
  model_coefficients[0] = line_pt[0];
  model_coefficients[1] = line_pt[1];
  model_coefficients[2] = line_pt[2];
  // model_coefficients.template segment<3> (3) = line_dir.template head<3> ();
  model_coefficients[3] = line_dir[0];
  model_coefficients[4] = line_dir[1];
  model_coefficients[5] = line_dir[2];
  // cylinder radius
  model_coefficients[6] = static_cast<float> (sqrt (pcl::sqrPointToLineDistance (p1, line_pt, line_dir)));
 
  if (model_coefficients[6] > radius_max_ || model_coefficients[6] < radius_min_)
    return (false);
 
  PCL_DEBUG ("[pcl::SampleConsensusModelCylinder::computeModelCoefficients] Model is (%g,%g,%g,%g,%g,%g,%g).\n",
             model_coefficients[0], model_coefficients[1], model_coefficients[2], model_coefficients[3],
             model_coefficients[4], model_coefficients[5], model_coefficients[6]);
  return (true);
}
 
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointT, typename PointNT> void
pcl::SampleConsensusModelCylinder<PointT, PointNT>::getDistancesToModel (
      const Eigen::VectorXf &model_coefficients, std::vector<double> &distances) const
{
  // Check if the model is valid given the user constraints
  if (!isModelValid (model_coefficients))
  {
    distances.clear ();
    return;
  }
 
  distances.resize (indices_->size ());
 
  Eigen::Vector4f line_pt  (model_coefficients[0], model_coefficients[1], model_coefficients[2], 0.0f);
  Eigen::Vector4f line_dir (model_coefficients[3], model_coefficients[4], model_coefficients[5], 0.0f);
  float ptdotdir = line_pt.dot (line_dir);
  float dirdotdir = 1.0f / line_dir.dot (line_dir);
  // Iterate through the 3d points and calculate the distances from them to the sphere
  for (std::size_t i = 0; i < indices_->size (); ++i)
  {
    // Approximate the distance from the point to the cylinder as the difference between
    // dist(point,cylinder_axis) and cylinder radius
    // @note need to revise this.
    Eigen::Vector4f pt ((*input_)[(*indices_)[i]].x, (*input_)[(*indices_)[i]].y, (*input_)[(*indices_)[i]].z, 0.0f);
 
    const double weighted_euclid_dist = (1.0 - normal_distance_weight_) * std::abs (pointToLineDistance (pt, model_coefficients) - model_coefficients[6]);
 
    // Calculate the point's projection on the cylinder axis
    float k = (pt.dot (line_dir) - ptdotdir) * dirdotdir;
    Eigen::Vector4f pt_proj = line_pt + k * line_dir;
    Eigen::Vector4f dir = pt - pt_proj;
    dir.normalize ();
 
    // Calculate the angular distance between the point normal and the (dir=pt_proj->pt) vector
    Eigen::Vector4f n  ((*normals_)[(*indices_)[i]].normal[0], (*normals_)[(*indices_)[i]].normal[1], (*normals_)[(*indices_)[i]].normal[2], 0.0f);
    double d_normal = std::abs (getAngle3D (n, dir));
    d_normal = (std::min) (d_normal, M_PI - d_normal);
 
    distances[i] = std::abs (normal_distance_weight_ * d_normal + weighted_euclid_dist);
  }
}
 
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointT, typename PointNT> void
pcl::SampleConsensusModelCylinder<PointT, PointNT>::selectWithinDistance (
      const Eigen::VectorXf &model_coefficients, const double threshold, Indices &inliers)
{
  // Check if the model is valid given the user constraints
  if (!isModelValid (model_coefficients))
  {
    inliers.clear ();
    return;
  }
 
  inliers.clear ();
  error_sqr_dists_.clear ();
  inliers.reserve (indices_->size ());
  error_sqr_dists_.reserve (indices_->size ());
 
  Eigen::Vector4f line_pt  (model_coefficients[0], model_coefficients[1], model_coefficients[2], 0.0f);
  Eigen::Vector4f line_dir (model_coefficients[3], model_coefficients[4], model_coefficients[5], 0.0f);
  float ptdotdir = line_pt.dot (line_dir);
  float dirdotdir = 1.0f / line_dir.dot (line_dir);
  // Iterate through the 3d points and calculate the distances from them to the sphere
  for (std::size_t i = 0; i < indices_->size (); ++i)
  {
    // Approximate the distance from the point to the cylinder as the difference between
    // dist(point,cylinder_axis) and cylinder radius
    Eigen::Vector4f pt ((*input_)[(*indices_)[i]].x, (*input_)[(*indices_)[i]].y, (*input_)[(*indices_)[i]].z, 0.0f);
    const double weighted_euclid_dist = (1.0 - normal_distance_weight_) * std::abs (pointToLineDistance (pt, model_coefficients) - model_coefficients[6]);
    if (weighted_euclid_dist > threshold) // Early termination: cannot be an inlier
      continue;
 
    // Calculate the point's projection on the cylinder axis
    float k = (pt.dot (line_dir) - ptdotdir) * dirdotdir;
    Eigen::Vector4f pt_proj = line_pt + k * line_dir;
    Eigen::Vector4f dir = pt - pt_proj;
    dir.normalize ();
 
    // Calculate the angular distance between the point normal and the (dir=pt_proj->pt) vector
    Eigen::Vector4f n  ((*normals_)[(*indices_)[i]].normal[0], (*normals_)[(*indices_)[i]].normal[1], (*normals_)[(*indices_)[i]].normal[2], 0.0f);
    double d_normal = std::abs (getAngle3D (n, dir));
    d_normal = (std::min) (d_normal, M_PI - d_normal);
 
    double distance = std::abs (normal_distance_weight_ * d_normal + weighted_euclid_dist);
    if (distance < threshold)
    {
      // Returns the indices of the points whose distances are smaller than the threshold
      inliers.push_back ((*indices_)[i]);
      error_sqr_dists_.push_back (distance);
    }
  }
}
 
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointT, typename PointNT> std::size_t
pcl::SampleConsensusModelCylinder<PointT, PointNT>::countWithinDistance (
      const Eigen::VectorXf &model_coefficients, const double threshold) const
{
  // Check if the model is valid given the user constraints
  if (!isModelValid (model_coefficients))
    return (0);
 
  std::size_t nr_p = 0;
 
  Eigen::Vector4f line_pt  (model_coefficients[0], model_coefficients[1], model_coefficients[2], 0);
  Eigen::Vector4f line_dir (model_coefficients[3], model_coefficients[4], model_coefficients[5], 0);
  float ptdotdir = line_pt.dot (line_dir);
  float dirdotdir = 1.0f / line_dir.dot (line_dir);
  // Iterate through the 3d points and calculate the distances from them to the sphere
  for (std::size_t i = 0; i < indices_->size (); ++i)
  {
    // Approximate the distance from the point to the cylinder as the difference between
    // dist(point,cylinder_axis) and cylinder radius
    Eigen::Vector4f pt ((*input_)[(*indices_)[i]].x, (*input_)[(*indices_)[i]].y, (*input_)[(*indices_)[i]].z, 0.0f);
    const double weighted_euclid_dist = (1.0 - normal_distance_weight_) * std::abs (pointToLineDistance (pt, model_coefficients) - model_coefficients[6]);
    if (weighted_euclid_dist > threshold) // Early termination: cannot be an inlier
      continue;
 
    // Calculate the point's projection on the cylinder axis
    float k = (pt.dot (line_dir) - ptdotdir) * dirdotdir;
    Eigen::Vector4f pt_proj = line_pt + k * line_dir;
    Eigen::Vector4f dir = pt - pt_proj;
    dir.normalize ();
 
    // Calculate the angular distance between the point normal and the (dir=pt_proj->pt) vector
    Eigen::Vector4f n  ((*normals_)[(*indices_)[i]].normal[0], (*normals_)[(*indices_)[i]].normal[1], (*normals_)[(*indices_)[i]].normal[2], 0.0f);
    double d_normal = std::abs (getAngle3D (n, dir));
    d_normal = (std::min) (d_normal, M_PI - d_normal);
 
    if (std::abs (normal_distance_weight_ * d_normal + weighted_euclid_dist) < threshold)
      nr_p++;
  }
  return (nr_p);
}
 
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointT, typename PointNT> void
pcl::SampleConsensusModelCylinder<PointT, PointNT>::optimizeModelCoefficients (
      const Indices &inliers, const Eigen::VectorXf &model_coefficients, Eigen::VectorXf &optimized_coefficients) const
{
  optimized_coefficients = model_coefficients;
 
  // Needs a set of valid model coefficients
  if (!isModelValid (model_coefficients))
  {
    PCL_ERROR ("[pcl::SampleConsensusModelCylinder::optimizeModelCoefficients] Given model is invalid!\n");
    return;
  }
 
  // Need more than the minimum sample size to make a difference
  if (inliers.size () <= sample_size_)
  {
    PCL_ERROR ("[pcl::SampleConsensusModelCylinder:optimizeModelCoefficients] Not enough inliers found to optimize model coefficients (%lu)! Returning the same coefficients.\n", inliers.size ());
    return;
  }
 
  OptimizationFunctor functor (this, inliers);
  Eigen::NumericalDiff<OptimizationFunctor > num_diff (functor);
  Eigen::LevenbergMarquardt<Eigen::NumericalDiff<OptimizationFunctor>, float> lm (num_diff);
  int info = lm.minimize (optimized_coefficients);
  
  // Compute the L2 norm of the residuals
  PCL_DEBUG ("[pcl::SampleConsensusModelCylinder::optimizeModelCoefficients] LM solver finished with exit code %i, having a residual norm of %g. \nInitial solution: %g %g %g %g %g %g %g \nFinal solution: %g %g %g %g %g %g %g\n",
             info, lm.fvec.norm (), model_coefficients[0], model_coefficients[1], model_coefficients[2], model_coefficients[3],
             model_coefficients[4], model_coefficients[5], model_coefficients[6], optimized_coefficients[0], optimized_coefficients[1], optimized_coefficients[2], optimized_coefficients[3], optimized_coefficients[4], optimized_coefficients[5], optimized_coefficients[6]);
    
  Eigen::Vector3f line_dir (optimized_coefficients[3], optimized_coefficients[4], optimized_coefficients[5]);
  line_dir.normalize ();
  optimized_coefficients[3] = line_dir[0];
  optimized_coefficients[4] = line_dir[1];
  optimized_coefficients[5] = line_dir[2];
}
 
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointT, typename PointNT> void
pcl::SampleConsensusModelCylinder<PointT, PointNT>::projectPoints (
      const Indices &inliers, const Eigen::VectorXf &model_coefficients, PointCloud &projected_points, bool copy_data_fields) const
{
  // Needs a valid set of model coefficients
  if (!isModelValid (model_coefficients))
  {
    PCL_ERROR ("[pcl::SampleConsensusModelCylinder::projectPoints] Given model is invalid!\n");
    return;
  }
 
  projected_points.header = input_->header;
  projected_points.is_dense = input_->is_dense;
 
  Eigen::Vector4f line_pt  (model_coefficients[0], model_coefficients[1], model_coefficients[2], 0.0f);
  Eigen::Vector4f line_dir (model_coefficients[3], model_coefficients[4], model_coefficients[5], 0.0f);
  float ptdotdir = line_pt.dot (line_dir);
  float dirdotdir = 1.0f / line_dir.dot (line_dir);
 
  // Copy all the data fields from the input cloud to the projected one?
  if (copy_data_fields)
  {
    // Allocate enough space and copy the basics
    projected_points.resize (input_->size ());
    projected_points.width    = input_->width;
    projected_points.height   = input_->height;
 
    using FieldList = typename pcl::traits::fieldList<PointT>::type;
    // Iterate over each point
    for (std::size_t i = 0; i < projected_points.size (); ++i)
      // Iterate over each dimension
      pcl::for_each_type <FieldList> (NdConcatenateFunctor <PointT, PointT> ((*input_)[i], projected_points[i]));
 
    // Iterate through the 3d points and calculate the distances from them to the cylinder
    for (const auto &inlier : inliers)
    {
      Eigen::Vector4f p ((*input_)[inlier].x,
                         (*input_)[inlier].y,
                         (*input_)[inlier].z,
                         1);
 
      float k = (p.dot (line_dir) - ptdotdir) * dirdotdir;
 
      pcl::Vector4fMap pp = projected_points[inlier].getVector4fMap ();
      pp.matrix () = line_pt + k * line_dir;
 
      Eigen::Vector4f dir = p - pp;
      dir[3] = 0.0f;
      dir.normalize ();
 
      // Calculate the projection of the point onto the cylinder
      pp += dir * model_coefficients[6];
    }
  }
  else
  {
    // Allocate enough space and copy the basics
    projected_points.resize (inliers.size ());
    projected_points.width    = inliers.size ();
    projected_points.height   = 1;
 
    using FieldList = typename pcl::traits::fieldList<PointT>::type;
    // Iterate over each point
    for (std::size_t i = 0; i < inliers.size (); ++i)
      // Iterate over each dimension
      pcl::for_each_type <FieldList> (NdConcatenateFunctor <PointT, PointT> ((*input_)[inliers[i]], projected_points[i]));
 
    // Iterate through the 3d points and calculate the distances from them to the cylinder
    for (std::size_t i = 0; i < inliers.size (); ++i)
    {
      pcl::Vector4fMap pp = projected_points[i].getVector4fMap ();
      pcl::Vector4fMapConst p = (*input_)[inliers[i]].getVector4fMap ();
 
      float k = (p.dot (line_dir) - ptdotdir) * dirdotdir;
      // Calculate the projection of the point on the line
      pp.matrix () = line_pt + k * line_dir;
 
      Eigen::Vector4f dir = p - pp;
      dir[3] = 0.0f;
      dir.normalize ();
 
      // Calculate the projection of the point onto the cylinder
      pp += dir * model_coefficients[6];
    }
  }
}
 
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointT, typename PointNT> bool
pcl::SampleConsensusModelCylinder<PointT, PointNT>::doSamplesVerifyModel (
      const std::set<index_t> &indices, const Eigen::VectorXf &model_coefficients, const double threshold) const
{
  // Needs a valid model coefficients
  if (!isModelValid (model_coefficients))
  {
    PCL_ERROR ("[pcl::SampleConsensusModelCylinder::doSamplesVerifyModel] Given model is invalid!\n");
    return (false);
  }
 
  for (const auto &index : indices)
  {
    // Approximate the distance from the point to the cylinder as the difference between
    // dist(point,cylinder_axis) and cylinder radius
    // @note need to revise this.
    Eigen::Vector4f pt ((*input_)[index].x, (*input_)[index].y, (*input_)[index].z, 0.0f);
    if (std::abs (pointToLineDistance (pt, model_coefficients) - model_coefficients[6]) > threshold)
      return (false);
  }
 
  return (true);
}
 
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointT, typename PointNT> double
pcl::SampleConsensusModelCylinder<PointT, PointNT>::pointToLineDistance (
      const Eigen::Vector4f &pt, const Eigen::VectorXf &model_coefficients) const
{
  Eigen::Vector4f line_pt  (model_coefficients[0], model_coefficients[1], model_coefficients[2], 0.0f);
  Eigen::Vector4f line_dir (model_coefficients[3], model_coefficients[4], model_coefficients[5], 0.0f);
  return sqrt(pcl::sqrPointToLineDistance (pt, line_pt, line_dir));
}
 
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointT, typename PointNT> void
pcl::SampleConsensusModelCylinder<PointT, PointNT>::projectPointToCylinder (
      const Eigen::Vector4f &pt, const Eigen::VectorXf &model_coefficients, Eigen::Vector4f &pt_proj) const
{
  Eigen::Vector4f line_pt  (model_coefficients[0], model_coefficients[1], model_coefficients[2], 0.0f);
  Eigen::Vector4f line_dir (model_coefficients[3], model_coefficients[4], model_coefficients[5], 0.0f);
 
  float k = (pt.dot (line_dir) - line_pt.dot (line_dir)) * line_dir.dot (line_dir);
  pt_proj = line_pt + k * line_dir;
 
  Eigen::Vector4f dir = pt - pt_proj;
  dir.normalize ();
 
  // Calculate the projection of the point onto the cylinder
  pt_proj += dir * model_coefficients[6];
}
 
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointT, typename PointNT> bool 
pcl::SampleConsensusModelCylinder<PointT, PointNT>::isModelValid (const Eigen::VectorXf &model_coefficients) const
{
  if (!SampleConsensusModel<PointT>::isModelValid (model_coefficients))
    return (false);
 
  // Check against template, if given
  if (eps_angle_ > 0.0)
  {
    // Obtain the cylinder direction
    const Eigen::Vector3f coeff(model_coefficients[3], model_coefficients[4], model_coefficients[5]);
 
    double angle_diff = std::abs (getAngle3D (axis_, coeff));
    angle_diff = (std::min) (angle_diff, M_PI - angle_diff);
    // Check whether the current cylinder model satisfies our angle threshold criterion with respect to the given axis
    if (angle_diff > eps_angle_)
    {
      PCL_DEBUG ("[pcl::SampleConsensusModelCylinder::isModelValid] Angle between cylinder direction and given axis is too large.\n");
      return (false);
    }
  }
 
  if (radius_min_ != -std::numeric_limits<double>::max() && model_coefficients[6] < radius_min_)
  {
    PCL_DEBUG ("[pcl::SampleConsensusModelCylinder::isModelValid] Radius is too small: should be larger than %g, but is %g.\n",
               radius_min_, model_coefficients[6]);
    return (false);
  }
  if (radius_max_ != std::numeric_limits<double>::max() && model_coefficients[6] > radius_max_)
  {
    PCL_DEBUG ("[pcl::SampleConsensusModelCylinder::isModelValid] Radius is too big: should be smaller than %g, but is %g.\n",
               radius_max_, model_coefficients[6]);
    return (false);
  }
 
  return (true);
}
 
#define PCL_INSTANTIATE_SampleConsensusModelCylinder(PointT, PointNT) template class PCL_EXPORTS pcl::SampleConsensusModelCylinder<PointT, PointNT>;
 
#endif    // PCL_SAMPLE_CONSENSUS_IMPL_SAC_MODEL_CYLINDER_H_