gicp.hpp

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 * $Id: gicp.hpp 6152 2012-07-04 22:58:53Z rusu $
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#include <boost/unordered_map.hpp>
#include <pcl/registration/exceptions.h>

template <typename PointSource, typename PointTarget> 
template<typename PointT> void
pcl::GeneralizedIterativeClosestPoint<PointSource, PointTarget>::computeCovariances(typename pcl::PointCloud<PointT>::ConstPtr cloud, 
                                                                                    const typename pcl::KdTree<PointT>::Ptr kdtree,
                                                                                    std::vector<Eigen::Matrix3d>& cloud_covariances)
{
  if (k_correspondences_ > int (cloud->size ()))
  {
    PCL_ERROR ("[pcl::GeneralizedIterativeClosestPoint::computeCovariances] Number or points in cloud (%zu) is less than k_correspondences_ (%zu)!\n", cloud->size (), k_correspondences_);
    return;
  }

  Eigen::Vector3d mean;
  std::vector<int> nn_indecies; nn_indecies.reserve (k_correspondences_);
  std::vector<float> nn_dist_sq; nn_dist_sq.reserve (k_correspondences_);

  // We should never get there but who knows
  if(cloud_covariances.size () < cloud->size ())
    cloud_covariances.resize (cloud->size ());

  typename pcl::PointCloud<PointT>::const_iterator points_iterator = cloud->begin ();
  std::vector<Eigen::Matrix3d>::iterator matrices_iterator = cloud_covariances.begin ();
  for(;
      points_iterator != cloud->end ();
      ++points_iterator, ++matrices_iterator)
  {
    const PointT &query_point = *points_iterator;
    Eigen::Matrix3d &cov = *matrices_iterator;
    // Zero out the cov and mean
    cov.setZero ();
    mean.setZero ();

    // Search for the K nearest neighbours
    kdtree->nearestKSearch(query_point, k_correspondences_, nn_indecies, nn_dist_sq);
    
    // Find the covariance matrix
    for(int j = 0; j < k_correspondences_; j++) {
      const PointT &pt = (*cloud)[nn_indecies[j]];
      
      mean[0] += pt.x;
      mean[1] += pt.y;
      mean[2] += pt.z;
      
      cov(0,0) += pt.x*pt.x;
      
      cov(1,0) += pt.y*pt.x;
      cov(1,1) += pt.y*pt.y;
      
      cov(2,0) += pt.z*pt.x;
      cov(2,1) += pt.z*pt.y;
      cov(2,2) += pt.z*pt.z;    
    }
  
    mean /= static_cast<double> (k_correspondences_);
    // Get the actual covariance
    for (int k = 0; k < 3; k++)
      for (int l = 0; l <= k; l++) 
      {
        cov(k,l) /= static_cast<double> (k_correspondences_);
        cov(k,l) -= mean[k]*mean[l];
        cov(l,k) = cov(k,l);
      }
    
    // Compute the SVD (covariance matrix is symmetric so U = V')
    Eigen::JacobiSVD<Eigen::Matrix3d> svd(cov, Eigen::ComputeFullU);
    cov.setZero ();
    Eigen::Matrix3d U = svd.matrixU ();
    // Reconstitute the covariance matrix with modified singular values using the column     // vectors in V.
    for(int k = 0; k < 3; k++) {
      Eigen::Vector3d col = U.col(k);
      double v = 1.; // biggest 2 singular values replaced by 1
      if(k == 2)   // smallest singular value replaced by gicp_epsilon
        v = gicp_epsilon_;
      cov+= v * col * col.transpose(); 
    }
  }
}

template <typename PointSource, typename PointTarget> void
pcl::GeneralizedIterativeClosestPoint<PointSource, PointTarget>::computeRDerivative(const Vector6d &x, const Eigen::Matrix3d &R, Vector6d& g) const
{
  Eigen::Matrix3d dR_dPhi;
  Eigen::Matrix3d dR_dTheta;
  Eigen::Matrix3d dR_dPsi;

  double phi = x[3], theta = x[4], psi = x[5];
  
  double cphi = cos(phi), sphi = sin(phi);
  double ctheta = cos(theta), stheta = sin(theta);
  double cpsi = cos(psi), spsi = sin(psi);
      
  dR_dPhi(0,0) = 0.;
  dR_dPhi(1,0) = 0.;
  dR_dPhi(2,0) = 0.;

  dR_dPhi(0,1) = sphi*spsi + cphi*cpsi*stheta;
  dR_dPhi(1,1) = -cpsi*sphi + cphi*spsi*stheta;
  dR_dPhi(2,1) = cphi*ctheta;

  dR_dPhi(0,2) = cphi*spsi - cpsi*sphi*stheta;
  dR_dPhi(1,2) = -cphi*cpsi - sphi*spsi*stheta;
  dR_dPhi(2,2) = -ctheta*sphi;

  dR_dTheta(0,0) = -cpsi*stheta;
  dR_dTheta(1,0) = -spsi*stheta;
  dR_dTheta(2,0) = -ctheta;

  dR_dTheta(0,1) = cpsi*ctheta*sphi;
  dR_dTheta(1,1) = ctheta*sphi*spsi;
  dR_dTheta(2,1) = -sphi*stheta;

  dR_dTheta(0,2) = cphi*cpsi*ctheta;
  dR_dTheta(1,2) = cphi*ctheta*spsi;
  dR_dTheta(2,2) = -cphi*stheta;

  dR_dPsi(0,0) = -ctheta*spsi;
  dR_dPsi(1,0) = cpsi*ctheta;
  dR_dPsi(2,0) = 0.;

  dR_dPsi(0,1) = -cphi*cpsi - sphi*spsi*stheta;
  dR_dPsi(1,1) = -cphi*spsi + cpsi*sphi*stheta;
  dR_dPsi(2,1) = 0.;

  dR_dPsi(0,2) = cpsi*sphi - cphi*spsi*stheta;
  dR_dPsi(1,2) = sphi*spsi + cphi*cpsi*stheta;
  dR_dPsi(2,2) = 0.;
      
  g[3] = matricesInnerProd(dR_dPhi, R);
  g[4] = matricesInnerProd(dR_dTheta, R);
  g[5] = matricesInnerProd(dR_dPsi, R);
}

template <typename PointSource, typename PointTarget> void
pcl::GeneralizedIterativeClosestPoint<PointSource, PointTarget>::estimateRigidTransformationBFGS (const PointCloudSource &cloud_src, 
                                                                                                  const std::vector<int> &indices_src, 
                                                                                                  const PointCloudTarget &cloud_tgt, 
                                                                                                  const std::vector<int> &indices_tgt, 
                                                                                                  Eigen::Matrix4f &transformation_matrix)
{
  if (indices_src.size () < 4)     // need at least 4 samples
  {
    PCL_THROW_EXCEPTION (NotEnoughPointsException, 
                         "[pcl::GeneralizedIterativeClosestPoint::estimateRigidTransformationBFGS] Need at least 4 points to estimate a transform! Source and target have " << indices_src.size () << " points!");
    return;
  }
  // Set the initial solution
  Vector6d x = Vector6d::Zero ();
  x[0] = transformation_matrix (0,3);
  x[1] = transformation_matrix (1,3);
  x[2] = transformation_matrix (2,3);
  x[3] = atan2 (transformation_matrix (2,1), transformation_matrix (2,2));
  x[4] = asin (-transformation_matrix (2,0));
  x[5] = atan2 (transformation_matrix (1,0), transformation_matrix (0,0));

  // Set temporary pointers
  tmp_src_ = &cloud_src;
  tmp_tgt_ = &cloud_tgt;
  tmp_idx_src_ = &indices_src;
  tmp_idx_tgt_ = &indices_tgt;

  // Optimize using forward-difference approximation LM
  const double gradient_tol = 1e-2;
  OptimizationFunctorWithIndices functor(this);
  BFGS<OptimizationFunctorWithIndices> bfgs (functor);
  bfgs.parameters.sigma = 0.01;
  bfgs.parameters.rho = 0.01;
  bfgs.parameters.tau1 = 9;
  bfgs.parameters.tau2 = 0.05;
  bfgs.parameters.tau3 = 0.5;
  bfgs.parameters.order = 3;

  int inner_iterations_ = 0;
  int result = bfgs.minimizeInit (x);
  do
  {
    inner_iterations_++;
    result = bfgs.minimizeOneStep (x);
    if(result)
    {
      break;
    }
    result = bfgs.testGradient(gradient_tol);
  } while(result == BFGSSpace::Running && inner_iterations_ < max_inner_iterations_);
  if(result == BFGSSpace::NoProgress || result == BFGSSpace::Success || inner_iterations_ == max_inner_iterations_)
  {
    PCL_DEBUG ("[pcl::registration::TransformationEstimationBFGS::estimateRigidTransformation]");
    PCL_DEBUG ("BFGS solver finished with exit code %i \n", result);
    transformation_matrix.setIdentity();
    applyState(transformation_matrix, x);
  }
  else
    PCL_THROW_EXCEPTION(SolverDidntConvergeException, 
                        "[pcl::" << getClassName () << "::TransformationEstimationBFGS::estimateRigidTransformation] BFGS solver didn't converge!");
}

template <typename PointSource, typename PointTarget> inline double
pcl::GeneralizedIterativeClosestPoint<PointSource, PointTarget>::OptimizationFunctorWithIndices::operator() (const Vector6d& x)
{
  Eigen::Matrix4f transformation_matrix = gicp_->base_transformation_;
  gicp_->applyState(transformation_matrix, x);
  double f = 0;
  int m = static_cast<int> (gicp_->tmp_idx_src_->size ());
  for (int i = 0; i < m; ++i)
  {
    // The last coordinate, p_src[3] is guaranteed to be set to 1.0 in registration.hpp
    Vector4fMapConst p_src = gicp_->tmp_src_->points[(*gicp_->tmp_idx_src_)[i]].getVector4fMap ();
    // The last coordinate, p_tgt[3] is guaranteed to be set to 1.0 in registration.hpp
    Vector4fMapConst p_tgt = gicp_->tmp_tgt_->points[(*gicp_->tmp_idx_tgt_)[i]].getVector4fMap ();
    Eigen::Vector4f pp (transformation_matrix * p_src);
    // Estimate the distance (cost function)
    // The last coordiante is still guaranteed to be set to 1.0
    Eigen::Vector3d res(pp[0] - p_tgt[0], pp[1] - p_tgt[1], pp[2] - p_tgt[2]);
    Eigen::Vector3d temp (gicp_->mahalanobis((*gicp_->tmp_idx_src_)[i]) * res);
    //increment= res'*temp/num_matches = temp'*M*temp/num_matches (we postpone 1/num_matches after the loop closes)
    f+= double(res.transpose() * temp);
  }
  return f/m;
}

template <typename PointSource, typename PointTarget> inline void
pcl::GeneralizedIterativeClosestPoint<PointSource, PointTarget>::OptimizationFunctorWithIndices::df (const Vector6d& x, Vector6d& g)
{
  Eigen::Matrix4f transformation_matrix = gicp_->base_transformation_;
  gicp_->applyState(transformation_matrix, x);
  //Zero out g
  g.setZero ();
  //Eigen::Vector3d g_t = g.head<3> ();
  Eigen::Matrix3d R = Eigen::Matrix3d::Zero ();
  int m = static_cast<int> (gicp_->tmp_idx_src_->size ());
  for (int i = 0; i < m; ++i)
  {
    // The last coordinate, p_src[3] is guaranteed to be set to 1.0 in registration.hpp
    Vector4fMapConst p_src = gicp_->tmp_src_->points[(*gicp_->tmp_idx_src_)[i]].getVector4fMap ();
    // The last coordinate, p_tgt[3] is guaranteed to be set to 1.0 in registration.hpp
    Vector4fMapConst p_tgt = gicp_->tmp_tgt_->points[(*gicp_->tmp_idx_tgt_)[i]].getVector4fMap ();

    Eigen::Vector4f pp (transformation_matrix * p_src);
    // The last coordiante is still guaranteed to be set to 1.0
    Eigen::Vector3d res (pp[0] - p_tgt[0], pp[1] - p_tgt[1], pp[2] - p_tgt[2]);
    // temp = M*res
    Eigen::Vector3d temp (gicp_->mahalanobis ((*gicp_->tmp_idx_src_)[i]) * res);
    // Increment translation gradient
    // g.head<3> ()+= 2*M*res/num_matches (we postpone 2/num_matches after the loop closes)
    g.head<3> ()+= temp;
    // Increment rotation gradient
    pp = gicp_->base_transformation_ * p_src;
    Eigen::Vector3d p_src3 (pp[0], pp[1], pp[2]);
    R+= p_src3 * temp.transpose();
  }
  g.head<3> ()*= 2.0/m;
  R*= 2.0/m;
  gicp_->computeRDerivative(x, R, g);
}

template <typename PointSource, typename PointTarget> inline void
pcl::GeneralizedIterativeClosestPoint<PointSource, PointTarget>::OptimizationFunctorWithIndices::fdf (const Vector6d& x, double& f, Vector6d& g)
{
  Eigen::Matrix4f transformation_matrix = gicp_->base_transformation_;
  gicp_->applyState(transformation_matrix, x);
  f = 0;
  g.setZero ();
  Eigen::Matrix3d R = Eigen::Matrix3d::Zero ();
  const int m = static_cast<const int> (gicp_->tmp_idx_src_->size ());
  for (int i = 0; i < m; ++i)
  {
    // The last coordinate, p_src[3] is guaranteed to be set to 1.0 in registration.hpp
    Vector4fMapConst p_src = gicp_->tmp_src_->points[(*gicp_->tmp_idx_src_)[i]].getVector4fMap ();
    // The last coordinate, p_tgt[3] is guaranteed to be set to 1.0 in registration.hpp
    Vector4fMapConst p_tgt = gicp_->tmp_tgt_->points[(*gicp_->tmp_idx_tgt_)[i]].getVector4fMap ();
    Eigen::Vector4f pp (transformation_matrix * p_src);
    // The last coordiante is still guaranteed to be set to 1.0
    Eigen::Vector3d res (pp[0] - p_tgt[0], pp[1] - p_tgt[1], pp[2] - p_tgt[2]);
    // temp = M*res
    Eigen::Vector3d temp (gicp_->mahalanobis((*gicp_->tmp_idx_src_)[i]) * res);
    // Increment total error
    f+= double(res.transpose() * temp);
    // Increment translation gradient
    // g.head<3> ()+= 2*M*res/num_matches (we postpone 2/num_matches after the loop closes)
    g.head<3> ()+= temp;
    pp = gicp_->base_transformation_ * p_src;
    Eigen::Vector3d p_src3 (pp[0], pp[1], pp[2]);
    // Increment rotation gradient
    R+= p_src3 * temp.transpose();    
  }
  f/= double(m);
  g.head<3> ()*= double(2.0/m);
  R*= 2.0/m;
  gicp_->computeRDerivative(x, R, g);
}

template <typename PointSource, typename PointTarget> inline void
pcl::GeneralizedIterativeClosestPoint<PointSource, PointTarget>::computeTransformation (PointCloudSource &output, const Eigen::Matrix4f& guess)
{
  using namespace std;
  // Difference between consecutive transforms
  double delta = 0;
  // Get the size of the target
  const size_t N = indices_->size ();
  // Set the mahalanobis matrices to identity
  mahalanobis_.resize (N, Eigen::Matrix3d::Identity ());
  // Compute target cloud covariance matrices
  computeCovariances<PointTarget> (target_, tree_, target_covariances_);
  // Compute input cloud covariance matrices
  computeCovariances<PointSource> (input_, input_tree_, input_covariances_);

  base_transformation_ = guess;
  nr_iterations_ = 0;
  converged_ = false;
  double dist_threshold = corr_dist_threshold_ * corr_dist_threshold_;
  std::vector<int> nn_indices (1);
  std::vector<float> nn_dists (1);

  while(!converged_)
  {
    size_t cnt = 0;
    std::vector<int> source_indices (indices_->size ());
    std::vector<int> target_indices (indices_->size ());

    // guess corresponds to base_t and transformation_ to t
    Eigen::Matrix4d transform_R = Eigen::Matrix4d::Zero ();
    for(size_t i = 0; i < 4; i++)
      for(size_t j = 0; j < 4; j++)
        for(size_t k = 0; k < 4; k++)
          transform_R(i,j)+= double(transformation_(i,k)) * double(guess(k,j));

    Eigen::Matrix3d R = transform_R.topLeftCorner<3,3> ();

    for (size_t i = 0; i < N; i++)
    {
      PointSource query = output[i];
      query.getVector4fMap () = guess * query.getVector4fMap ();
      query.getVector4fMap () = transformation_ * query.getVector4fMap ();

      if (!searchForNeighbors (query, nn_indices, nn_dists))
      {
        PCL_ERROR ("[pcl::%s::computeTransformation] Unable to find a nearest neighbor in the target dataset for point %d in the source!\n", getClassName ().c_str (), (*indices_)[i]);
        return;
      }
      
      // Check if the distance to the nearest neighbor is smaller than the user imposed threshold
      if (nn_dists[0] < dist_threshold)
      {
        Eigen::Matrix3d &C1 = input_covariances_[i];
        Eigen::Matrix3d &C2 = target_covariances_[nn_indices[0]];
        Eigen::Matrix3d &M = mahalanobis_[i];
        // M = R*C1
        M = R * C1;
        // temp = M*R' + C2 = R*C1*R' + C2
        Eigen::Matrix3d temp = M * R.transpose();        
        temp+= C2;
        // M = temp^-1
        M = temp.inverse ();
        source_indices[cnt] = static_cast<int> (i);
        target_indices[cnt] = nn_indices[0];
        cnt++;
      }
    }
    // Resize to the actual number of valid correspondences
    source_indices.resize(cnt); target_indices.resize(cnt);
    /* optimize transformation using the current assignment and Mahalanobis metrics*/
    previous_transformation_ = transformation_;
    //optimization right here
    try
    {
      rigid_transformation_estimation_(output, source_indices, *target_, target_indices, transformation_);
      /* compute the delta from this iteration */
      delta = 0.;
      for(int k = 0; k < 4; k++) {
        for(int l = 0; l < 4; l++) {
          double ratio = 1;
          if(k < 3 && l < 3) // rotation part of the transform
            ratio = 1./rotation_epsilon_;
          else
            ratio = 1./transformation_epsilon_;
          double c_delta = ratio*fabs(previous_transformation_(k,l) - transformation_(k,l));
          if(c_delta > delta)
            delta = c_delta;
        }
      }
    } 
    catch (PCLException &e)
    {
      PCL_DEBUG ("[pcl::%s::computeTransformation] Optimization issue %s\n", getClassName ().c_str (), e.what ());
      break;
    }
    nr_iterations_++;
    // Check for convergence
    if (nr_iterations_ >= max_iterations_ || delta < 1)
    {
      converged_ = true;
      previous_transformation_ = transformation_;
      PCL_DEBUG ("[pcl::%s::computeTransformation] Convergence reached. Number of iterations: %d out of %d. Transformation difference: %f\n",
                 getClassName ().c_str (), nr_iterations_, max_iterations_, (transformation_ - previous_transformation_).array ().abs ().sum ());
    } 
    else
      PCL_DEBUG ("[pcl::%s::computeTransformation] Convergence failed\n", getClassName ().c_str ());
  }
  //for some reason the static equivalent methode raises an error
  // final_transformation_.block<3,3> (0,0) = (transformation_.block<3,3> (0,0)) * (guess.block<3,3> (0,0));
  // final_transformation_.block <3, 1> (0, 3) = transformation_.block <3, 1> (0, 3) + guess.rightCols<1>.block <3, 1> (0, 3);
  final_transformation_.topLeftCorner (3,3) = previous_transformation_.topLeftCorner (3,3) * guess.topLeftCorner (3,3);
  final_transformation_(0,3) = previous_transformation_(0,3) + guess(0,3);
  final_transformation_(1,3) = previous_transformation_(1,3) + guess(1,3);
  final_transformation_(2,3) = previous_transformation_(2,3) + guess(2,3);
}

template <typename PointSource, typename PointTarget> void
pcl::GeneralizedIterativeClosestPoint<PointSource, PointTarget>::applyState(Eigen::Matrix4f &t, const Vector6d& x) const
{
  // !!! CAUTION Stanford GICP uses the Z Y X euler angles convention
  Eigen::Matrix3f R;
  R = Eigen::AngleAxisf (static_cast<float> (x[5]), Eigen::Vector3f::UnitZ ())
    * Eigen::AngleAxisf (static_cast<float> (x[4]), Eigen::Vector3f::UnitY ())
    * Eigen::AngleAxisf (static_cast<float> (x[3]), Eigen::Vector3f::UnitX ());
  t.topLeftCorner<3,3> () = R * t.topLeftCorner<3,3> ();
  Eigen::Vector4f T (static_cast<float> (x[0]), static_cast<float> (x[1]), static_cast<float> (x[2]), 0.0f);
  t.col (3) += T;
}