projection_matrix.hpp

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#ifndef __PCL_ORGANIZED_PROJECTION_MATRIX_HPP__
#define __PCL_ORGANIZED_PROJECTION_MATRIX_HPP__

#include <pcl/cloud_iterator.h>

namespace pcl
{
  namespace common
  {
    namespace internal
    {
      template <typename MatrixT> void
      makeSymmetric (MatrixT& matrix, bool use_upper_triangular = true)
      {
        if (use_upper_triangular && (MatrixT::Flags & Eigen::RowMajorBit))
        {
          matrix.coeffRef (4) = matrix.coeff (1);
          matrix.coeffRef (8) = matrix.coeff (2);
          matrix.coeffRef (9) = matrix.coeff (6);
          matrix.coeffRef (12) = matrix.coeff (3);
          matrix.coeffRef (13) = matrix.coeff (7);
          matrix.coeffRef (14) = matrix.coeff (11);
        }
        else
        {
          matrix.coeffRef (1) = matrix.coeff (4);
          matrix.coeffRef (2) = matrix.coeff (8);
          matrix.coeffRef (6) = matrix.coeff (9);
          matrix.coeffRef (3) = matrix.coeff (12);
          matrix.coeffRef (7) = matrix.coeff (13);
          matrix.coeffRef (11) = matrix.coeff (14);
        }
      }
    }
  }
}

template <typename PointT> double 
pcl::estimateProjectionMatrix (
    typename pcl::PointCloud<PointT>::ConstPtr cloud, 
    Eigen::Matrix<float, 3, 4, Eigen::RowMajor>& projection_matrix, 
    const std::vector<int>& indices)
{
  // internally we calculate with double but store the result into float matrices.
  typedef double Scalar;
  projection_matrix.setZero ();
  if (cloud->height == 1 || cloud->width == 1)
  {
    PCL_ERROR ("[pcl::estimateProjectionMatrix] Input dataset is not organized!\n");
    return (-1.0);
  }
  
  Eigen::Matrix<Scalar, 4, 4, Eigen::RowMajor> A = Eigen::Matrix<Scalar, 4, 4, Eigen::RowMajor>::Zero ();
  Eigen::Matrix<Scalar, 4, 4, Eigen::RowMajor> B = Eigen::Matrix<Scalar, 4, 4, Eigen::RowMajor>::Zero ();
  Eigen::Matrix<Scalar, 4, 4, Eigen::RowMajor> C = Eigen::Matrix<Scalar, 4, 4, Eigen::RowMajor>::Zero ();
  Eigen::Matrix<Scalar, 4, 4, Eigen::RowMajor> D = Eigen::Matrix<Scalar, 4, 4, Eigen::RowMajor>::Zero ();

  pcl::ConstCloudIterator <PointT> pointIt (*cloud, indices);
  
  while (pointIt)
  {
    unsigned yIdx = pointIt.getCurrentPointIndex () / cloud->width;
    unsigned xIdx = pointIt.getCurrentPointIndex () % cloud->width;
    
    const PointT& point = *pointIt;
    if (pcl_isfinite (point.x))
    {
      Scalar xx = point.x * point.x;
      Scalar xy = point.x * point.y;
      Scalar xz = point.x * point.z;
      Scalar yy = point.y * point.y;
      Scalar yz = point.y * point.z;
      Scalar zz = point.z * point.z;
      Scalar xx_yy = xIdx * xIdx + yIdx * yIdx;

      A.coeffRef (0) += xx;
      A.coeffRef (1) += xy;
      A.coeffRef (2) += xz;
      A.coeffRef (3) += point.x;

      A.coeffRef (5) += yy;
      A.coeffRef (6) += yz;
      A.coeffRef (7) += point.y;

      A.coeffRef (10) += zz;
      A.coeffRef (11) += point.z;
      A.coeffRef (15) += 1.0;

      B.coeffRef (0) -= xx * xIdx;
      B.coeffRef (1) -= xy * xIdx;
      B.coeffRef (2) -= xz * xIdx;
      B.coeffRef (3) -= point.x * static_cast<double>(xIdx);

      B.coeffRef (5) -= yy * xIdx;
      B.coeffRef (6) -= yz * xIdx;
      B.coeffRef (7) -= point.y * static_cast<double>(xIdx);

      B.coeffRef (10) -= zz * xIdx;
      B.coeffRef (11) -= point.z * static_cast<double>(xIdx);

      B.coeffRef (15) -= xIdx;

      C.coeffRef (0) -= xx * yIdx;
      C.coeffRef (1) -= xy * yIdx;
      C.coeffRef (2) -= xz * yIdx;
      C.coeffRef (3) -= point.x * static_cast<double>(yIdx);

      C.coeffRef (5) -= yy * yIdx;
      C.coeffRef (6) -= yz * yIdx;
      C.coeffRef (7) -= point.y * static_cast<double>(yIdx);

      C.coeffRef (10) -= zz * yIdx;
      C.coeffRef (11) -= point.z * static_cast<double>(yIdx);

      C.coeffRef (15) -= yIdx;

      D.coeffRef (0) += xx * xx_yy;
      D.coeffRef (1) += xy * xx_yy;
      D.coeffRef (2) += xz * xx_yy;
      D.coeffRef (3) += point.x * xx_yy;

      D.coeffRef (5) += yy * xx_yy;
      D.coeffRef (6) += yz * xx_yy;
      D.coeffRef (7) += point.y * xx_yy;

      D.coeffRef (10) += zz * xx_yy;
      D.coeffRef (11) += point.z * xx_yy;

      D.coeffRef (15) += xx_yy;
    }
    
    ++pointIt;
  } // while  
  
  pcl::common::internal::makeSymmetric (A);
  pcl::common::internal::makeSymmetric (B);
  pcl::common::internal::makeSymmetric (C);
  pcl::common::internal::makeSymmetric (D);

  Eigen::Matrix<Scalar, 12, 12, Eigen::RowMajor> X = Eigen::Matrix<Scalar, 12, 12, Eigen::RowMajor>::Zero ();
  X.topLeftCorner<4,4> ().matrix () = A;
  X.block<4,4> (0, 8).matrix () = B;
  X.block<4,4> (8, 0).matrix () = B;
  X.block<4,4> (4, 4).matrix () = A;
  X.block<4,4> (4, 8).matrix () = C;
  X.block<4,4> (8, 4).matrix () = C;
  X.block<4,4> (8, 8).matrix () = D;

  Eigen::SelfAdjointEigenSolver<Eigen::Matrix<Scalar, 12, 12, Eigen::RowMajor> > ei_symm (X);
  Eigen::Matrix<Scalar, 12, 12, Eigen::RowMajor> eigen_vectors = ei_symm.eigenvectors ();

  // check whether the residual MSE is low. If its high, the cloud was not captured from a projective device.
  Eigen::Matrix<Scalar, 1, 1> residual_sqr = eigen_vectors.col (0).transpose () * X *  eigen_vectors.col (0);
  
  double residual = residual_sqr.coeff (0);

  projection_matrix.coeffRef (0) = static_cast <float> (eigen_vectors.coeff (0));
  projection_matrix.coeffRef (1) = static_cast <float> (eigen_vectors.coeff (12));
  projection_matrix.coeffRef (2) = static_cast <float> (eigen_vectors.coeff (24));
  projection_matrix.coeffRef (3) = static_cast <float> (eigen_vectors.coeff (36));
  projection_matrix.coeffRef (4) = static_cast <float> (eigen_vectors.coeff (48));
  projection_matrix.coeffRef (5) = static_cast <float> (eigen_vectors.coeff (60));
  projection_matrix.coeffRef (6) = static_cast <float> (eigen_vectors.coeff (72));
  projection_matrix.coeffRef (7) = static_cast <float> (eigen_vectors.coeff (84));
  projection_matrix.coeffRef (8) = static_cast <float> (eigen_vectors.coeff (96));
  projection_matrix.coeffRef (9) = static_cast <float> (eigen_vectors.coeff (108));
  projection_matrix.coeffRef (10) = static_cast <float> (eigen_vectors.coeff (120));
  projection_matrix.coeffRef (11) = static_cast <float> (eigen_vectors.coeff (132));

  if (projection_matrix.coeff (0) < 0)
    projection_matrix *= -1.0;

  return (residual);
}

#endif