icp.cpp

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#include "icp.h"

#include <limits>
#include <cstdlib>
#include <iomanip>
#include <cmath>

#include <pcl/kdtree/kdtree_flann.h>
#include <pcl/common/centroid.h>
#include <pcl/common/time.h>

#include "utils.h"

////////////////////////////////////////////////////////////////////////////////

pcl::ihs::ICP::ICP ()
  : kd_tree_ (new pcl::KdTreeFLANN <PointNormal> ()),

    epsilon_        (10e-6f),
    max_iterations_ (50),
    min_overlap_    (.75f),
    max_fitness_    (.1f),

    factor_ (9.f),
    max_angle_ (45.f)
{
}

////////////////////////////////////////////////////////////////////////////////

void
pcl::ihs::ICP::setEpsilon (const float epsilon)
{
  if (epsilon > 0) epsilon_ = epsilon;
}

float
pcl::ihs::ICP::getEpsilon () const
{
  return (epsilon_);
}

////////////////////////////////////////////////////////////////////////////////

void
pcl::ihs::ICP::setMaxIterations (const unsigned int max_iter)
{
  max_iterations_ = max_iter < 1 ? 1 : max_iter;
}

unsigned int
pcl::ihs::ICP::getMaxIterations () const
{
  return (max_iterations_);
}

////////////////////////////////////////////////////////////////////////////////

void
pcl::ihs::ICP::setMinOverlap (const float overlap)
{
  min_overlap_ = pcl::ihs::clamp (overlap, 0.f, 1.f);
}

float
pcl::ihs::ICP::getMinOverlap () const
{
  return (min_overlap_);
}

////////////////////////////////////////////////////////////////////////////////

void
pcl::ihs::ICP::setMaxFitness (const float fitness)
{
  if (fitness > 0) max_fitness_ = fitness;
}

float
pcl::ihs::ICP::getMaxFitness () const
{
  return (max_fitness_);
}

////////////////////////////////////////////////////////////////////////////////

void
pcl::ihs::ICP::setCorrespondenceRejectionFactor (const float factor)
{
  factor_ = factor < 1.f ? 1.f : factor;
}

float
pcl::ihs::ICP::getCorrespondenceRejectionFactor () const
{
  return (factor_);
}

////////////////////////////////////////////////////////////////////////////////

void
pcl::ihs::ICP::setMaxAngle (const float angle)
{
  max_angle_ = pcl::ihs::clamp (angle, 0.f, 180.f);
}

float
pcl::ihs::ICP::getMaxAngle () const
{
  return (max_angle_);
}

////////////////////////////////////////////////////////////////////////////////

bool
pcl::ihs::ICP::findTransformation (const MeshConstPtr&              mesh_model,
                                   const CloudXYZRGBNormalConstPtr& cloud_data,
                                   const Eigen::Matrix4f&           T_init,
                                   Eigen::Matrix4f&                 T_final)
{
  // Check the input
  // TODO: Double check the minimum number of points necessary for icp
  const size_t n_min = 4;

  if(mesh_model->sizeVertices () < n_min || cloud_data->size () < n_min)
  {
    std::cerr << "ERROR in icp.cpp: Not enough input points!\n";
    return (false);
  }

  // Time measurements
  pcl::StopWatch sw;
  pcl::StopWatch sw_total;
  double t_select     = 0.;
  double t_build      = 0.;
  double t_nn_search  = 0.;
  double t_calc_trafo = 0.;

  // Convergence and registration failure
  float current_fitness  = 0.f;
  float previous_fitness = std::numeric_limits <float>::max ();
  float delta_fitness    = std::numeric_limits <float>::max ();
  float overlap          = std::numeric_limits <float>::quiet_NaN ();

  // Outlier rejection
  float squared_distance_threshold = std::numeric_limits<float>::max();

  // Transformation
  Eigen::Matrix4f T_cur = T_init;

  // Point selection
  sw.reset ();
  const CloudNormalConstPtr cloud_model_selected = this->selectModelPoints (mesh_model, T_init.inverse ());
  const CloudNormalConstPtr cloud_data_selected  = this->selectDataPoints (cloud_data);
  t_select = sw.getTime ();

  const size_t n_model = cloud_model_selected->size ();
  const size_t n_data  = cloud_data_selected->size ();
  if(n_model < n_min) {std::cerr << "ERROR in icp.cpp: Not enough model points after selection!\n"; return (false);}
  if(n_data < n_min)  {std::cerr << "ERROR in icp.cpp: Not enough data points after selection!\n"; return (false);}

  // Build a kd-tree
  sw.reset ();
  kd_tree_->setInputCloud (cloud_model_selected);
  t_build = sw.getTime ();

  std::vector <int>   index (1);
  std::vector <float> squared_distance (1);

  // Clouds with one to one correspondences
  CloudNormal cloud_model_corr;
  CloudNormal cloud_data_corr;

  cloud_model_corr.reserve (n_data);
  cloud_data_corr.reserve (n_data);

  // ICP main loop
  unsigned int iter = 1;
  PointNormal pt_d;
  const float dot_min = std::cos (max_angle_ * 17.45329252e-3); // deg to rad
  while (true)
  {
    // Accumulated error
    float squared_distance_sum = 0.f;

    // NN search
    cloud_model_corr.clear ();
    cloud_data_corr.clear ();
    sw.reset ();
    for (CloudNormal::const_iterator it_d = cloud_data_selected->begin (); it_d!=cloud_data_selected->end (); ++it_d)
    {
      // Transform the data point
      pt_d = *it_d;
      pt_d.getVector4fMap ()       = T_cur * pt_d.getVector4fMap ();
      pt_d.getNormalVector4fMap () = T_cur * pt_d.getNormalVector4fMap ();

      // Find the correspondence to the model points
      if (!kd_tree_->nearestKSearch (pt_d, 1, index, squared_distance))
      {
        std::cerr << "ERROR in icp.cpp: nearestKSearch failed!\n";
        return (false);
      }

      // Check the distance threshold
      if (squared_distance [0] < squared_distance_threshold)
      {
        if (index [0] >= cloud_model_selected->size ())
        {
          std::cerr << "ERROR in icp.cpp: Segfault!\n";
          std::cerr << "  Trying to access index " << index [0] << " >= " << cloud_model_selected->size () << std::endl;
          exit (EXIT_FAILURE);
        }

        const PointNormal& pt_m = cloud_model_selected->operator [] (index [0]);

        // Check the normals threshold
        if (pt_m.getNormalVector4fMap ().dot (pt_d.getNormalVector4fMap ()) > dot_min)
        {
          squared_distance_sum += squared_distance [0];

          cloud_model_corr.push_back (pt_m);
          cloud_data_corr.push_back (pt_d);
        }
      }
    }

    t_nn_search += sw.getTime ();

    const size_t n_corr = cloud_data_corr.size ();
    if (n_corr < n_min)
    {
      std::cerr << "ERROR in icp.cpp: Not enough correspondences: " << n_corr << " < " << n_min << std::endl;
      return (false);
    }

    // NOTE: The fitness is calculated with the transformation from the previous iteration (I don't re-calculate it after the transformation estimation). This means that the actual fitness will be one iteration "better" than the calculated fitness suggests. This should be no problem because the difference is small at the state of convergence.
    previous_fitness           = current_fitness;
    current_fitness            = squared_distance_sum / static_cast <float> (n_corr);
    delta_fitness              = std::abs (previous_fitness - current_fitness);
    squared_distance_threshold = factor_ * current_fitness;
    overlap                    = static_cast <float> (n_corr) / static_cast <float> (n_data);

    //    std::cerr << "Iter: " << std::left << std::setw(3) << iter
    //              << " | Overlap: " << std::setprecision(2) << std::setw(4) << overlap
    //              << " | current fitness: " << std::setprecision(5) << std::setw(10) << current_fitness
    //              << " | delta fitness: " << std::setprecision(5) << std::setw(10) << delta_fitness << std::endl;

    // Minimize the point to plane distance
    sw.reset ();
    Eigen::Matrix4f T_delta = Eigen::Matrix4f::Identity ();
    if (!this->minimizePointPlane (cloud_data_corr, cloud_model_corr, T_delta))
    {
      std::cerr << "ERROR in icp.cpp: minimizePointPlane failed!\n";
      return (false);
    }
    t_calc_trafo += sw.getTime ();

    T_cur = T_delta * T_cur;

    // Convergence
    if (delta_fitness < epsilon_) break;
    ++iter;
    if (iter > max_iterations_)   break;

  } // End ICP main loop

  // Some output
  std::cerr << "Registration:\n"

            << "  - num model     / num data       : "
            << std::setw (8) << std::right << n_model << " / "
            << std::setw (8) << std::left  << n_data << "\n"

            << std::scientific << std::setprecision (1)

            << "  - delta fitness / epsilon        : "
            << std::setw (8) << std::right << delta_fitness << " / "
            << std::setw (8) << std::left  << epsilon_
            << (delta_fitness < epsilon_ ? " <-- :-)\n" : "\n")

            << "  - fitness       / max fitness    : "
            << std::setw (8) << std::right << current_fitness << " / "
            << std::setw (8) << std::left  << max_fitness_
            << (current_fitness > max_fitness_ ? " <-- :-(\n" : "\n")

            << std::fixed << std::setprecision (2)

            << "  - iter          / max iter       : "
            << std::setw (8) << std::right << iter << " / "
            << std::setw (8) << std::left  << max_iterations_
            << (iter > max_iterations_ ? " <-- :-(\n" : "\n")

            << "  - overlap       / min overlap    : "
            << std::setw (8) << std::right << overlap << " / "
            << std::setw (8) << std::left  << min_overlap_
            << (overlap < min_overlap_ ? " <-- :-(\n" : "\n")

            << std::fixed << std::setprecision (0)

            << "  - time select                    : "
            << std::setw (8) << std::right << t_select << " ms\n"

            << "  - time build kd-tree             : "
            << std::setw (8) << std::right << t_build << " ms\n"

            << "  - time nn-search / trafo / reject: "
            << std::setw (8) << std::right << t_nn_search << " ms\n"

            << "  - time minimize                  : "
            << std::setw (8) << std::right << t_calc_trafo << " ms\n"

            << "  - total time                     : "
            << std::setw (8) << std::right << sw_total.getTime () << " ms\n";

  if (iter > max_iterations_ || overlap <  min_overlap_ || current_fitness > max_fitness_)
  {
    return (false);
  }
  else if (delta_fitness <= epsilon_)
  {
    T_final = T_cur;
    return (true);
  }
  else
  {
    std::cerr << "ERROR in icp.cpp: Congratulations! you found a bug.\n";
    exit (EXIT_FAILURE);
  }
}

////////////////////////////////////////////////////////////////////////////////

pcl::ihs::ICP::CloudNormalConstPtr
pcl::ihs::ICP::selectModelPoints (const MeshConstPtr&    mesh_model,
                                  const Eigen::Matrix4f& T_inv) const
{
  const CloudNormalPtr cloud_model_out (new CloudNormal ());
  cloud_model_out->reserve (mesh_model->sizeVertices ());

  const Mesh::VertexDataCloud& cloud = mesh_model->getVertexDataCloud ();

  for (Mesh::VertexDataCloud::const_iterator it=cloud.begin (); it!=cloud.end (); ++it)
  {
    // Don't consider points that are facing away from the camera.
    if ((T_inv.lazyProduct (it->getNormalVector4fMap ())).z () < 0.f)
    {
      PointNormal pt;
      pt.getVector4fMap ()       = it->getVector4fMap ();
      pt.getNormalVector4fMap () = it->getNormalVector4fMap ();

      // NOTE: Not the transformed points!!
      cloud_model_out->push_back (pt);
    }
  }

  return (cloud_model_out);
}

////////////////////////////////////////////////////////////////////////////////

pcl::ihs::ICP::CloudNormalConstPtr
pcl::ihs::ICP::selectDataPoints (const CloudXYZRGBNormalConstPtr& cloud_data) const
{
  const CloudNormalPtr cloud_data_out (new CloudNormal ());
  cloud_data_out->reserve (cloud_data->size ());

  CloudXYZRGBNormal::const_iterator it_in = cloud_data->begin ();
  for (; it_in!=cloud_data->end (); ++it_in)
  {
    if (!boost::math::isnan (it_in->x))
    {
      PointNormal pt;
      pt.getVector4fMap ()       = it_in->getVector4fMap ();
      pt.getNormalVector4fMap () = it_in->getNormalVector4fMap ();

      cloud_data_out->push_back (pt);
    }
  }

  return (cloud_data_out);
}

////////////////////////////////////////////////////////////////////////////////

bool
pcl::ihs::ICP::minimizePointPlane (const CloudNormal& cloud_source,
                                   const CloudNormal& cloud_target,
                                   Eigen::Matrix4f&   T) const
{
  // Check the input
  // n < n_min already checked in the icp main loop
  const size_t n = cloud_source.size ();
  if (cloud_target.size () != n)
  {
    std::cerr << "ERROR in icp.cpp: Input must have the same size!\n";
    return (false);
  }

  // For numerical stability
  // - Low: Linear Least-Squares Optimization for Point-to-Plane ICP Surface Registration (2004), in the discussion: "To improve the numerical stability of the computation, it is important to use a unit of distance that is comparable in magnitude with the rotation angles. The simplest way is to rescale and move the two input surfaces so that they are bounded within a unit sphere or cube centered at the origin."
  // - Gelfand et al.: Geometrically Stable Sampling for the ICP Algorithm (2003), in sec 3.1: "As is common with PCA methods, we will shift the center of mass of the points	to the origin." ... "Therefore, af- ter shifting the center of mass, we will scale the point set so that the average distance of points	from the origin is 1."
  // - Hartley, Zisserman: - Multiple View Geometry (2004), page 109: They normalize to sqrt(2)
  // TODO: Check the resulting C matrix for the conditioning.

  // Subtract the centroid and calculate the scaling factor
  Eigen::Vector4f c_s (0.f, 0.f, 0.f, 1.f);
  Eigen::Vector4f c_t (0.f, 0.f, 0.f, 1.f);
  pcl::compute3DCentroid (cloud_source, c_s); c_s.w () = 1.f;
  pcl::compute3DCentroid (cloud_target, c_t); c_t.w () = 1.f;

  // The normals are only needed for the target
  typedef std::vector <Eigen::Vector4f, Eigen::aligned_allocator <Eigen::Vector4f> > Vec4Xf;
  Vec4Xf xyz_s, xyz_t, nor_t;
  xyz_s.reserve (n);
  xyz_t.reserve (n);
  nor_t.reserve (n);

  CloudNormal::const_iterator it_s = cloud_source.begin ();
  CloudNormal::const_iterator it_t = cloud_target.begin ();

  float accum = 0.f;
  Eigen::Vector4f pt_s, pt_t;
  for (; it_s!=cloud_source.end (); ++it_s, ++it_t)
  {
    // Subtract the centroid
    pt_s = it_s->getVector4fMap () - c_s;
    pt_t = it_t->getVector4fMap () - c_t;

    xyz_s.push_back (pt_s);
    xyz_t.push_back (pt_t);
    nor_t.push_back (it_t->getNormalVector4fMap ());

    // Calculate the radius (L2 norm) of the bounding sphere through both shapes and accumulate the average
    // TODO: Change to squared norm and adapt the rest accordingly
    accum += pt_s.head <3> ().norm () + pt_t.head <3> ().norm ();
  }

  // Inverse factor (do a multiplication instead of division later)
  const float factor         = 2.f * static_cast <float> (n) / accum;
  const float factor_squared = factor*factor;

  // Covariance matrix C
  Eigen::Matrix <float, 6, 6> C;

  // Right hand side vector b
  Eigen::Matrix <float, 6, 1> b;

  // For Eigen vectorization: use 4x4 submatrixes instead of 3x3 submatrixes
  // -> top left 3x3 matrix will form the final C
  // Same for b
  Eigen::Matrix4f C_tl    = Eigen::Matrix4f::Zero(); // top left corner
  Eigen::Matrix4f C_tr_bl = Eigen::Matrix4f::Zero(); // top right / bottom left
  Eigen::Matrix4f C_br    = Eigen::Matrix4f::Zero(); // bottom right

  Eigen::Vector4f b_t     = Eigen::Vector4f::Zero(); // top
  Eigen::Vector4f b_b     = Eigen::Vector4f::Zero(); // bottom

  Vec4Xf::const_iterator it_xyz_s = xyz_s.begin ();
  Vec4Xf::const_iterator it_xyz_t = xyz_t.begin ();
  Vec4Xf::const_iterator it_nor_t = nor_t.begin ();

  Eigen::Vector4f cross;
  float dot;
  for (; it_xyz_s!=xyz_s.end (); ++it_xyz_s, ++it_xyz_t, ++it_nor_t)
  {
    cross    = it_xyz_s->cross3 (*it_nor_t);

    C_tl    += cross     * cross.    transpose ();
    C_tr_bl += cross     * it_nor_t->transpose ();
    C_br    += *it_nor_t * it_nor_t->transpose ();

    dot      = (*it_xyz_t-*it_xyz_s).dot (*it_nor_t);

    b_t     += cross     * dot;
    b_b     += *it_nor_t * dot;
  }

  // Scale with the factor and copy the 3x3 submatrixes into C and b
  C_tl    *= factor_squared;
  C_tr_bl *= factor;

  C << C_tl.  topLeftCorner <3, 3> ()            , C_tr_bl.topLeftCorner <3, 3> (),
      C_tr_bl.topLeftCorner <3, 3> ().transpose(), C_br.   topLeftCorner <3, 3> ();

  b << b_t.head <3> () * factor_squared,
      b_b. head <3> () * factor;

  // Solve C * x = b with a Cholesky factorization with pivoting
  // x = [alpha; beta; gamma; trans_x; trans_y; trans_z]
  Eigen::Matrix <float, 6, 1> x = C.selfadjointView <Eigen::Lower> ().ldlt ().solve (b);

  // The calculated transformation in the scaled coordinate system
  const float
      sa = std::sin (x (0)),
      ca = std::cos (x (0)),
      sb = std::sin (x (1)),
      cb = std::cos (x (1)),
      sg = std::sin (x (2)),
      cg = std::cos (x (2)),
      tx = x (3),
      ty = x (4),
      tz = x (5);

  Eigen::Matrix4f TT;
  TT << cg*cb, -sg*ca+cg*sb*sa,  sg*sa+cg*sb*ca, tx,
      sg*cb  ,  cg*ca+sg*sb*sa, -cg*sa+sg*sb*ca, ty,
      -sb    ,  cb*sa         ,  cb*ca         , tz,
      0.f    ,  0.f           ,  0.f           , 1.f;

  // Transformation matrixes into the local coordinate systems of model/data
  Eigen::Matrix4f T_s, T_t;

  T_s << factor, 0.f   , 0.f   , -c_s.x () * factor,
      0.f      , factor, 0.f   , -c_s.y () * factor,
      0.f      , 0.f   , factor, -c_s.z () * factor,
      0.f      , 0.f   , 0.f   ,  1.f;

  T_t << factor, 0.f   , 0.f   , -c_t.x () * factor,
      0.f      , factor, 0.f   , -c_t.y () * factor,
      0.f      , 0.f   , factor, -c_t.z () * factor,
      0.f      , 0.f   , 0.f   ,  1.f;

  // Output transformation T
  T = T_t.inverse () * TT * T_s;

  return (true);
}

////////////////////////////////////////////////////////////////////////////////