Ejemplo n.º 1
0
template <typename PointInT> void
pcl::NormalEstimation<PointInT, Eigen::MatrixXf>::computeFeatureEigen (pcl::PointCloud<Eigen::MatrixXf> &output)
{
  // Resize the output dataset
  output.points.resize (indices_->size (), 4);

  // Allocate enough space to hold the results
  // \note This resize is irrelevant for a radiusSearch ().
  std::vector<int> nn_indices (k_);
  std::vector<float> nn_dists (k_);

  output.is_dense = true;
  // Save a few cycles by not checking every point for NaN/Inf values if the cloud is set to dense
  if (input_->is_dense)
  {
    // Iterating over the entire index vector
    for (size_t idx = 0; idx < indices_->size (); ++idx)
    {
      if (this->searchForNeighbors ((*indices_)[idx], search_parameter_, nn_indices, nn_dists) == 0)
      {
        output.points (idx, 0) = output.points (idx, 1) = output.points (idx, 2) = output.points (idx, 3) = std::numeric_limits<float>::quiet_NaN ();
        output.is_dense = false;
        continue;
      }

      computePointNormal (*surface_, nn_indices,
                          output.points (idx, 0), output.points (idx, 1), output.points (idx, 2), output.points (idx, 3));

      flipNormalTowardsViewpoint (input_->points[(*indices_)[idx]], vpx_, vpy_, vpz_,
                                  output.points (idx, 0), output.points (idx, 1), output.points (idx, 2));

    }
  }
  else
  {
    // Iterating over the entire index vector
    for (size_t idx = 0; idx < indices_->size (); ++idx)
    {
      if (!isFinite ((*input_)[(*indices_)[idx]]) ||
          this->searchForNeighbors ((*indices_)[idx], search_parameter_, nn_indices, nn_dists) == 0)
      {
        output.points (idx, 0) = output.points (idx, 1) = output.points (idx, 2) = output.points (idx, 3) = std::numeric_limits<float>::quiet_NaN ();
        output.is_dense = false;
        continue;
      }

      computePointNormal (*surface_, nn_indices,
                          output.points (idx, 0), output.points (idx, 1), output.points (idx, 2), output.points (idx, 3));

      flipNormalTowardsViewpoint (input_->points[(*indices_)[idx]], vpx_, vpy_, vpz_,
                                  output.points (idx, 0), output.points (idx, 1), output.points (idx, 2));

    }
  }
}
Ejemplo n.º 2
0
template <typename PointInT, typename PointOutT> void
pcl::NormalEstimation<PointInT, PointOutT>::computeFeature (PointCloudOut &output)
{
  // Allocate enough space to hold the results
  // \note This resize is irrelevant for a radiusSearch ().
  std::vector<int> nn_indices (k_);
  std::vector<float> nn_dists (k_);

  // Iterating over the entire index vector
  for (size_t idx = 0; idx < indices_->size (); ++idx)
  {
    if (!this->searchForNeighbors ((*indices_)[idx], search_parameter_, nn_indices, nn_dists))
    {
      output.points[idx].normal[0] = output.points[idx].normal[1] = output.points[idx].normal[2] = output.points[idx].curvature = std::numeric_limits<float>::quiet_NaN ();
      continue;
    }

    computePointNormal (*surface_, nn_indices,
                        output.points[idx].normal[0], output.points[idx].normal[1], output.points[idx].normal[2], output.points[idx].curvature);

    flipNormalTowardsViewpoint (input_->points[(*indices_)[idx]], vpx_, vpy_, vpz_,
                                output.points[idx].normal[0], output.points[idx].normal[1], output.points[idx].normal[2]);

  }
}
Ejemplo n.º 3
0
template <typename PointInT> void
pcl16::NormalEstimationOMP<PointInT, Eigen::MatrixXf>::computeFeatureEigen (pcl16::PointCloud<Eigen::MatrixXf> &output)
{
  float vpx, vpy, vpz;
  getViewPoint (vpx, vpy, vpz);
  output.is_dense = true;

  // Resize the output dataset
  output.points.resize (indices_->size (), 4);

  // GCC 4.2.x seems to segfault with "internal compiler error" on MacOS X here
#if defined(_WIN32) || ((__GNUC__ > 4) && (__GNUC_MINOR__ > 2)) 
#pragma omp parallel for schedule (dynamic, threads_)
#endif
  // Iterating over the entire index vector
  for (int idx = 0; idx < static_cast<int> (indices_->size ()); ++idx)
  {
    // Allocate enough space to hold the results
    // \note This resize is irrelevant for a radiusSearch ().
    std::vector<int> nn_indices (k_);
    std::vector<float> nn_dists (k_);

    if (!isFinite ((*input_)[(*indices_)[idx]]) ||
        this->searchForNeighbors ((*indices_)[idx], search_parameter_, nn_indices, nn_dists) == 0)
    {
      output.points (idx, 0) = output.points (idx, 1) = output.points (idx, 2) = output.points (idx, 3) = std::numeric_limits<float>::quiet_NaN ();
      output.is_dense = false;
      continue;
    }

    // 16-bytes aligned placeholder for the XYZ centroid of a surface patch
    Eigen::Vector4f xyz_centroid;
    // Estimate the XYZ centroid
    compute3DCentroid (*surface_, nn_indices, xyz_centroid);

    // Placeholder for the 3x3 covariance matrix at each surface patch
    EIGEN_ALIGN16 Eigen::Matrix3f covariance_matrix;
    // Compute the 3x3 covariance matrix
    computeCovarianceMatrix (*surface_, nn_indices, xyz_centroid, covariance_matrix);

    // Get the plane normal and surface curvature
    solvePlaneParameters (covariance_matrix,
                          output.points (idx, 0), output.points (idx, 1), output.points (idx, 2), output.points (idx, 3));

    flipNormalTowardsViewpoint (input_->points[(*indices_)[idx]], vpx, vpy, vpz,
                                output.points (idx, 0), output.points (idx, 1), output.points (idx, 2));
  }
}
Ejemplo n.º 4
0
template <typename PointInT, typename PointOutT> void
pcl16::NormalEstimationOMP<PointInT, PointOutT>::computeFeature (PointCloudOut &output)
{
  float vpx, vpy, vpz;
  getViewPoint (vpx, vpy, vpz);

  output.is_dense = true;
  // Iterating over the entire index vector
#pragma omp parallel for schedule (dynamic, threads_)
  for (int idx = 0; idx < static_cast<int> (indices_->size ()); ++idx)
  {
    // Allocate enough space to hold the results
    // \note This resize is irrelevant for a radiusSearch ().
    std::vector<int> nn_indices (k_);
    std::vector<float> nn_dists (k_);

    if (!isFinite ((*input_)[(*indices_)[idx]]) ||
        this->searchForNeighbors ((*indices_)[idx], search_parameter_, nn_indices, nn_dists) == 0)
    {
      output.points[idx].normal[0] = output.points[idx].normal[1] = output.points[idx].normal[2] = output.points[idx].curvature = std::numeric_limits<float>::quiet_NaN ();
  
      output.is_dense = false;
      continue;
    }

    // 16-bytes aligned placeholder for the XYZ centroid of a surface patch
    Eigen::Vector4f xyz_centroid;
    // Estimate the XYZ centroid
    compute3DCentroid (*surface_, nn_indices, xyz_centroid);

    // Placeholder for the 3x3 covariance matrix at each surface patch
    EIGEN_ALIGN16 Eigen::Matrix3f covariance_matrix;
    // Compute the 3x3 covariance matrix
    computeCovarianceMatrix (*surface_, nn_indices, xyz_centroid, covariance_matrix);

    // Get the plane normal and surface curvature
    solvePlaneParameters (covariance_matrix,
                          output.points[idx].normal[0], output.points[idx].normal[1], output.points[idx].normal[2], output.points[idx].curvature);

    flipNormalTowardsViewpoint (input_->points[(*indices_)[idx]], vpx, vpy, vpz,
                                output.points[idx].normal[0], output.points[idx].normal[1], output.points[idx].normal[2]);
  }
}
Ejemplo n.º 5
0
template <typename PointInT, typename PointOutT> void
pcl::NormalEstimationOMP<PointInT, PointOutT>::computeFeature (PointCloudOut &output)
{
  // Allocate enough space to hold the results
  // \note This resize is irrelevant for a radiusSearch ().
  std::vector<int> nn_indices (k_);
  std::vector<float> nn_dists (k_);

  output.is_dense = true;
  // Save a few cycles by not checking every point for NaN/Inf values if the cloud is set to dense
  if (input_->is_dense)
  {
#ifdef _OPENMP
#pragma omp parallel for shared (output) private (nn_indices, nn_dists) num_threads(threads_)
#endif
    // Iterating over the entire index vector
    for (int idx = 0; idx < static_cast<int> (indices_->size ()); ++idx)
    {
      Eigen::Vector4f n;
      if (this->searchForNeighbors ((*indices_)[idx], search_parameter_, nn_indices, nn_dists) == 0 ||
          !computePointNormal (*surface_, nn_indices, n, output.points[idx].curvature))
      {
        output.points[idx].normal[0] = output.points[idx].normal[1] = output.points[idx].normal[2] = output.points[idx].curvature = std::numeric_limits<float>::quiet_NaN ();

        output.is_dense = false;
        continue;
      }

      output.points[idx].normal_x = n[0];
      output.points[idx].normal_y = n[1];
      output.points[idx].normal_z = n[2];

      flipNormalTowardsViewpoint (input_->points[(*indices_)[idx]], vpx_, vpy_, vpz_,
                                  output.points[idx].normal[0], output.points[idx].normal[1], output.points[idx].normal[2]);

    }
  }
  else
  {
#ifdef _OPENMP
#pragma omp parallel for shared (output) private (nn_indices, nn_dists) num_threads(threads_)
#endif
    // Iterating over the entire index vector
    for (int idx = 0; idx < static_cast<int> (indices_->size ()); ++idx)
    {
      Eigen::Vector4f n;
      if (!isFinite ((*input_)[(*indices_)[idx]]) ||
          this->searchForNeighbors ((*indices_)[idx], search_parameter_, nn_indices, nn_dists) == 0 ||
          !computePointNormal (*surface_, nn_indices, n, output.points[idx].curvature))
      {
        output.points[idx].normal[0] = output.points[idx].normal[1] = output.points[idx].normal[2] = output.points[idx].curvature = std::numeric_limits<float>::quiet_NaN ();

        output.is_dense = false;
        continue;
      }

      output.points[idx].normal_x = n[0];
      output.points[idx].normal_y = n[1];
      output.points[idx].normal_z = n[2];

      flipNormalTowardsViewpoint (input_->points[(*indices_)[idx]], vpx_, vpy_, vpz_,
                                  output.points[idx].normal[0], output.points[idx].normal[1], output.points[idx].normal[2]);

    }
  }
}
Ejemplo n.º 6
0
template <typename PointInT, typename PointOutT> void
pcl::IntegralImageNormalEstimation<PointInT, PointOutT>::computePointNormalMirror (
    const int pos_x, const int pos_y, const unsigned point_index, PointOutT &normal)
{
  float bad_point = std::numeric_limits<float>::quiet_NaN ();

  const int width = input_->width;
  const int height = input_->height;

  // ==============================================================
  if (normal_estimation_method_ == COVARIANCE_MATRIX) 
  {
    if (!init_covariance_matrix_)
      initCovarianceMatrixMethod ();

    const int start_x = pos_x - rect_width_2_;
    const int start_y = pos_y - rect_height_2_;
    const int end_x = start_x + rect_width_;
    const int end_y = start_y + rect_height_;

    unsigned count = 0;
    sumArea<unsigned>(start_x, start_y, end_x, end_y, width, height, boost::bind(&IntegralImage2D<float, 3>::getFiniteElementsCountSE, &integral_image_XYZ_, _1, _2, _3, _4), count);
    
    // no valid points within the rectangular reagion?
    if (count == 0)
    {
      normal.normal_x = normal.normal_y = normal.normal_z = normal.curvature = bad_point;
      return;
    }

    EIGEN_ALIGN16 Eigen::Matrix3f covariance_matrix;
    Eigen::Vector3f center;
    typename IntegralImage2D<float, 3>::SecondOrderType so_elements;
    typename IntegralImage2D<float, 3>::ElementType tmp_center;
    typename IntegralImage2D<float, 3>::SecondOrderType tmp_so_elements;

    center[0] = 0;
    center[1] = 0;
    center[2] = 0;
    tmp_center[0] = 0;
    tmp_center[1] = 0;
    tmp_center[2] = 0;
    so_elements[0] = 0;
    so_elements[1] = 0;
    so_elements[2] = 0;
    so_elements[3] = 0;
    so_elements[4] = 0;
    so_elements[5] = 0;

    sumArea<typename IntegralImage2D<float, 3>::ElementType>(start_x, start_y, end_x, end_y, width, height, boost::bind(&IntegralImage2D<float, 3>::getFirstOrderSumSE, &integral_image_XYZ_, _1, _2, _3, _4), tmp_center);
    sumArea<typename IntegralImage2D<float, 3>::SecondOrderType>(start_x, start_y, end_x, end_y, width, height, boost::bind(&IntegralImage2D<float, 3>::getSecondOrderSumSE, &integral_image_XYZ_, _1, _2, _3, _4), so_elements);

    center[0] = float (tmp_center[0]);
    center[1] = float (tmp_center[1]);
    center[2] = float (tmp_center[2]);

    covariance_matrix.coeffRef (0) = static_cast<float> (so_elements [0]);
    covariance_matrix.coeffRef (1) = covariance_matrix.coeffRef (3) = static_cast<float> (so_elements [1]);
    covariance_matrix.coeffRef (2) = covariance_matrix.coeffRef (6) = static_cast<float> (so_elements [2]);
    covariance_matrix.coeffRef (4) = static_cast<float> (so_elements [3]);
    covariance_matrix.coeffRef (5) = covariance_matrix.coeffRef (7) = static_cast<float> (so_elements [4]);
    covariance_matrix.coeffRef (8) = static_cast<float> (so_elements [5]);
    covariance_matrix -= (center * center.transpose ()) / static_cast<float> (count);
    float eigen_value;
    Eigen::Vector3f eigen_vector;
    pcl::eigen33 (covariance_matrix, eigen_value, eigen_vector);
    flipNormalTowardsViewpoint (input_->points[point_index], vpx_, vpy_, vpz_, eigen_vector[0], eigen_vector[1], eigen_vector[2]);
    normal.getNormalVector3fMap () = eigen_vector;

    // Compute the curvature surface change
    if (eigen_value > 0.0)
      normal.curvature = fabsf (eigen_value / (covariance_matrix.coeff (0) + covariance_matrix.coeff (4) + covariance_matrix.coeff (8)));
    else
      normal.curvature = 0;

    return;
  }
  // =======================================================
  else if (normal_estimation_method_ == AVERAGE_3D_GRADIENT) 
  {
    if (!init_average_3d_gradient_)
      initAverage3DGradientMethod ();

    const int start_x = pos_x - rect_width_2_;
    const int start_y = pos_y - rect_height_2_;
    const int end_x = start_x + rect_width_;
    const int end_y = start_y + rect_height_;

    unsigned count_x = 0;
    unsigned count_y = 0;

    sumArea<unsigned>(start_x, start_y, end_x, end_y, width, height, boost::bind(&IntegralImage2D<float, 3>::getFiniteElementsCountSE, &integral_image_DX_, _1, _2, _3, _4), count_x);
    sumArea<unsigned>(start_x, start_y, end_x, end_y, width, height, boost::bind(&IntegralImage2D<float, 3>::getFiniteElementsCountSE, &integral_image_DY_, _1, _2, _3, _4), count_y);


    if (count_x == 0 || count_y == 0)
    {
      normal.normal_x = normal.normal_y = normal.normal_z = normal.curvature = bad_point;
      return;
    }
    Eigen::Vector3d gradient_x (0, 0, 0);
    Eigen::Vector3d gradient_y (0, 0, 0);

    sumArea<typename IntegralImage2D<float, 3>::ElementType>(start_x, start_y, end_x, end_y, width, height, boost::bind(&IntegralImage2D<float, 3>::getFirstOrderSumSE, &integral_image_DX_, _1, _2, _3, _4), gradient_x);
    sumArea<typename IntegralImage2D<float, 3>::ElementType>(start_x, start_y, end_x, end_y, width, height, boost::bind(&IntegralImage2D<float, 3>::getFirstOrderSumSE, &integral_image_DY_, _1, _2, _3, _4), gradient_y);


    Eigen::Vector3d normal_vector = gradient_y.cross (gradient_x);
    double normal_length = normal_vector.squaredNorm ();
    if (normal_length == 0.0f)
    {
      normal.getNormalVector3fMap ().setConstant (bad_point);
      normal.curvature = bad_point;
      return;
    }

    normal_vector /= sqrt (normal_length);

    float nx = static_cast<float> (normal_vector [0]);
    float ny = static_cast<float> (normal_vector [1]);
    float nz = static_cast<float> (normal_vector [2]);

    flipNormalTowardsViewpoint (input_->points[point_index], vpx_, vpy_, vpz_, nx, ny, nz);

    normal.normal_x = nx;
    normal.normal_y = ny;
    normal.normal_z = nz;
    normal.curvature = bad_point;
    return;
  }
  // ======================================================
  else if (normal_estimation_method_ == AVERAGE_DEPTH_CHANGE) 
  {
    if (!init_depth_change_)
      initAverageDepthChangeMethod ();

    int point_index_L_x = pos_x - rect_width_4_ - 1;
    int point_index_L_y = pos_y;
    int point_index_R_x = pos_x + rect_width_4_ + 1;
    int point_index_R_y = pos_y;
    int point_index_U_x = pos_x - 1;
    int point_index_U_y = pos_y - rect_height_4_;
    int point_index_D_x = pos_x + 1;
    int point_index_D_y = pos_y + rect_height_4_;

    if (point_index_L_x < 0)
      point_index_L_x = -point_index_L_x;
    if (point_index_U_x < 0)
      point_index_U_x = -point_index_U_x;
    if (point_index_U_y < 0)
      point_index_U_y = -point_index_U_y;

    if (point_index_R_x >= width)
      point_index_R_x = width-(point_index_R_x-(width-1));
    if (point_index_D_x >= width)
      point_index_D_x = width-(point_index_D_x-(width-1));
    if (point_index_D_y >= height)
      point_index_D_y = height-(point_index_D_y-(height-1));

    const int start_x_L = pos_x - rect_width_2_;
    const int start_y_L = pos_y - rect_height_4_;
    const int end_x_L = start_x_L + rect_width_2_;
    const int end_y_L = start_y_L + rect_height_2_;

    const int start_x_R = pos_x + 1;
    const int start_y_R = pos_y - rect_height_4_;
    const int end_x_R = start_x_R + rect_width_2_;
    const int end_y_R = start_y_R + rect_height_2_;

    const int start_x_U = pos_x - rect_width_4_;
    const int start_y_U = pos_y - rect_height_2_;
    const int end_x_U = start_x_U + rect_width_2_;
    const int end_y_U = start_y_U + rect_height_2_;

    const int start_x_D = pos_x - rect_width_4_;
    const int start_y_D = pos_y + 1;
    const int end_x_D = start_x_D + rect_width_2_;
    const int end_y_D = start_y_D + rect_height_2_;

    unsigned count_L_z = 0;
    unsigned count_R_z = 0;
    unsigned count_U_z = 0;
    unsigned count_D_z = 0;

    sumArea<unsigned>(start_x_L, start_y_L, end_x_L, end_y_L, width, height, boost::bind(&IntegralImage2D<float, 1>::getFiniteElementsCountSE, &integral_image_depth_, _1, _2, _3, _4), count_L_z);
    sumArea<unsigned>(start_x_R, start_y_R, end_x_R, end_y_R, width, height, boost::bind(&IntegralImage2D<float, 1>::getFiniteElementsCountSE, &integral_image_depth_, _1, _2, _3, _4), count_R_z);
    sumArea<unsigned>(start_x_U, start_y_U, end_x_U, end_y_U, width, height, boost::bind(&IntegralImage2D<float, 1>::getFiniteElementsCountSE, &integral_image_depth_, _1, _2, _3, _4), count_U_z);
    sumArea<unsigned>(start_x_D, start_y_D, end_x_D, end_y_D, width, height, boost::bind(&IntegralImage2D<float, 1>::getFiniteElementsCountSE, &integral_image_depth_, _1, _2, _3, _4), count_D_z);

    if (count_L_z == 0 || count_R_z == 0 || count_U_z == 0 || count_D_z == 0)
    {
      normal.normal_x = normal.normal_y = normal.normal_z = normal.curvature = bad_point;
      return;
    }

    float mean_L_z = 0;
    float mean_R_z = 0;
    float mean_U_z = 0;
    float mean_D_z = 0;

    sumArea<float>(start_x_L, start_y_L, end_x_L, end_y_L, width, height, boost::bind(&IntegralImage2D<float, 1>::getFirstOrderSumSE, &integral_image_depth_, _1, _2, _3, _4), mean_L_z);
    sumArea<float>(start_x_R, start_y_R, end_x_R, end_y_R, width, height, boost::bind(&IntegralImage2D<float, 1>::getFirstOrderSumSE, &integral_image_depth_, _1, _2, _3, _4), mean_R_z);
    sumArea<float>(start_x_U, start_y_U, end_x_U, end_y_U, width, height, boost::bind(&IntegralImage2D<float, 1>::getFirstOrderSumSE, &integral_image_depth_, _1, _2, _3, _4), mean_U_z);
    sumArea<float>(start_x_D, start_y_D, end_x_D, end_y_D, width, height, boost::bind(&IntegralImage2D<float, 1>::getFirstOrderSumSE, &integral_image_depth_, _1, _2, _3, _4), mean_D_z);

    mean_L_z /= float (count_L_z);
    mean_R_z /= float (count_R_z);
    mean_U_z /= float (count_U_z);
    mean_D_z /= float (count_D_z);


    PointInT pointL = input_->points[point_index_L_y*width + point_index_L_x];
    PointInT pointR = input_->points[point_index_R_y*width + point_index_R_x];
    PointInT pointU = input_->points[point_index_U_y*width + point_index_U_x];
    PointInT pointD = input_->points[point_index_D_y*width + point_index_D_x];

    const float mean_x_z = mean_R_z - mean_L_z;
    const float mean_y_z = mean_D_z - mean_U_z;

    const float mean_x_x = pointR.x - pointL.x;
    const float mean_x_y = pointR.y - pointL.y;
    const float mean_y_x = pointD.x - pointU.x;
    const float mean_y_y = pointD.y - pointU.y;

    float normal_x = mean_x_y * mean_y_z - mean_x_z * mean_y_y;
    float normal_y = mean_x_z * mean_y_x - mean_x_x * mean_y_z;
    float normal_z = mean_x_x * mean_y_y - mean_x_y * mean_y_x;

    const float normal_length = (normal_x * normal_x + normal_y * normal_y + normal_z * normal_z);

    if (normal_length == 0.0f)
    {
      normal.getNormalVector3fMap ().setConstant (bad_point);
      normal.curvature = bad_point;
      return;
    }

    flipNormalTowardsViewpoint (input_->points[point_index], vpx_, vpy_, vpz_, normal_x, normal_y, normal_z);
    
    const float scale = 1.0f / sqrtf (normal_length);

    normal.normal_x = normal_x * scale;
    normal.normal_y = normal_y * scale;
    normal.normal_z = normal_z * scale;
    normal.curvature = bad_point;

    return;
  }
  // ========================================================
  else if (normal_estimation_method_ == SIMPLE_3D_GRADIENT) 
  {
    PCL_THROW_EXCEPTION (PCLException, "BORDER_POLICY_MIRROR not supported for normal estimation method SIMPLE_3D_GRADIENT");
  }

  normal.getNormalVector3fMap ().setConstant (bad_point);
  normal.curvature = bad_point;
  return;
}
Ejemplo n.º 7
0
template <typename PointInT, typename PointOutT> void
pcl::IntegralImageNormalEstimation<PointInT, PointOutT>::computePointNormal (
    const int pos_x, const int pos_y, const unsigned point_index, PointOutT &normal)
{
  float bad_point = std::numeric_limits<float>::quiet_NaN ();

  if (normal_estimation_method_ == COVARIANCE_MATRIX)
  {
    if (!init_covariance_matrix_)
      initCovarianceMatrixMethod ();

    unsigned count = integral_image_XYZ_.getFiniteElementsCount (pos_x - (rect_width_2_), pos_y - (rect_height_2_), rect_width_, rect_height_);

    // no valid points within the rectangular reagion?
    if (count == 0)
    {
      normal.normal_x = normal.normal_y = normal.normal_z = normal.curvature = bad_point;
      return;
    }

    EIGEN_ALIGN16 Eigen::Matrix3f covariance_matrix;
    Eigen::Vector3f center;
    typename IntegralImage2D<float, 3>::SecondOrderType so_elements;
    center = integral_image_XYZ_.getFirstOrderSum(pos_x - rect_width_2_, pos_y - rect_height_2_, rect_width_, rect_height_).template cast<float> ();
    so_elements = integral_image_XYZ_.getSecondOrderSum(pos_x - rect_width_2_, pos_y - rect_height_2_, rect_width_, rect_height_);

    covariance_matrix.coeffRef (0) = static_cast<float> (so_elements [0]);
    covariance_matrix.coeffRef (1) = covariance_matrix.coeffRef (3) = static_cast<float> (so_elements [1]);
    covariance_matrix.coeffRef (2) = covariance_matrix.coeffRef (6) = static_cast<float> (so_elements [2]);
    covariance_matrix.coeffRef (4) = static_cast<float> (so_elements [3]);
    covariance_matrix.coeffRef (5) = covariance_matrix.coeffRef (7) = static_cast<float> (so_elements [4]);
    covariance_matrix.coeffRef (8) = static_cast<float> (so_elements [5]);
    covariance_matrix -= (center * center.transpose ()) / static_cast<float> (count);
    float eigen_value;
    Eigen::Vector3f eigen_vector;
    pcl::eigen33 (covariance_matrix, eigen_value, eigen_vector);
    flipNormalTowardsViewpoint (input_->points[point_index], vpx_, vpy_, vpz_, eigen_vector[0], eigen_vector[1], eigen_vector[2]);
    normal.getNormalVector3fMap () = eigen_vector;

    // Compute the curvature surface change
    if (eigen_value > 0.0)
      normal.curvature = fabsf (eigen_value / (covariance_matrix.coeff (0) + covariance_matrix.coeff (4) + covariance_matrix.coeff (8)));
    else
      normal.curvature = 0;

    return;
  }
  else if (normal_estimation_method_ == AVERAGE_3D_GRADIENT)
  {
    if (!init_average_3d_gradient_)
      initAverage3DGradientMethod ();

    unsigned count_x = integral_image_DX_.getFiniteElementsCount (pos_x - rect_width_2_, pos_y - rect_height_2_, rect_width_, rect_height_);
    unsigned count_y = integral_image_DY_.getFiniteElementsCount (pos_x - rect_width_2_, pos_y - rect_height_2_, rect_width_, rect_height_);
    if (count_x == 0 || count_y == 0)
    {
      normal.normal_x = normal.normal_y = normal.normal_z = normal.curvature = bad_point;
      return;
    }
    Eigen::Vector3d gradient_x = integral_image_DX_.getFirstOrderSum (pos_x - rect_width_2_, pos_y - rect_height_2_, rect_width_, rect_height_);
    Eigen::Vector3d gradient_y = integral_image_DY_.getFirstOrderSum (pos_x - rect_width_2_, pos_y - rect_height_2_, rect_width_, rect_height_);

    Eigen::Vector3d normal_vector = gradient_y.cross (gradient_x);
    double normal_length = normal_vector.squaredNorm ();
    if (normal_length == 0.0f)
    {
      normal.getNormalVector3fMap ().setConstant (bad_point);
      normal.curvature = bad_point;
      return;
    }

    normal_vector /= sqrt (normal_length);

    float nx = static_cast<float> (normal_vector [0]);
    float ny = static_cast<float> (normal_vector [1]);
    float nz = static_cast<float> (normal_vector [2]);

    flipNormalTowardsViewpoint (input_->points[point_index], vpx_, vpy_, vpz_, nx, ny, nz);

    normal.normal_x = nx;
    normal.normal_y = ny;
    normal.normal_z = nz;
    normal.curvature = bad_point;
    return;
  }
  else if (normal_estimation_method_ == AVERAGE_DEPTH_CHANGE)
  {
    if (!init_depth_change_)
      initAverageDepthChangeMethod ();

    // width and height are at least 3 x 3
    unsigned count_L_z = integral_image_depth_.getFiniteElementsCount (pos_x - rect_width_2_, pos_y - rect_height_4_, rect_width_2_, rect_height_2_);
    unsigned count_R_z = integral_image_depth_.getFiniteElementsCount (pos_x + 1            , pos_y - rect_height_4_, rect_width_2_, rect_height_2_);
    unsigned count_U_z = integral_image_depth_.getFiniteElementsCount (pos_x - rect_width_4_, pos_y - rect_height_2_, rect_width_2_, rect_height_2_);
    unsigned count_D_z = integral_image_depth_.getFiniteElementsCount (pos_x - rect_width_4_, pos_y + 1             , rect_width_2_, rect_height_2_);

    if (count_L_z == 0 || count_R_z == 0 || count_U_z == 0 || count_D_z == 0)
    {
      normal.normal_x = normal.normal_y = normal.normal_z = normal.curvature = bad_point;
      return;
    }

    float mean_L_z = static_cast<float> (integral_image_depth_.getFirstOrderSum (pos_x - rect_width_2_, pos_y - rect_height_4_, rect_width_2_, rect_height_2_) / count_L_z);
    float mean_R_z = static_cast<float> (integral_image_depth_.getFirstOrderSum (pos_x + 1            , pos_y - rect_height_4_, rect_width_2_, rect_height_2_) / count_R_z);
    float mean_U_z = static_cast<float> (integral_image_depth_.getFirstOrderSum (pos_x - rect_width_4_, pos_y - rect_height_2_, rect_width_2_, rect_height_2_) / count_U_z);
    float mean_D_z = static_cast<float> (integral_image_depth_.getFirstOrderSum (pos_x - rect_width_4_, pos_y + 1             , rect_width_2_, rect_height_2_) / count_D_z);

    PointInT pointL = input_->points[point_index - rect_width_4_ - 1];
    PointInT pointR = input_->points[point_index + rect_width_4_ + 1];
    PointInT pointU = input_->points[point_index - rect_height_4_ * input_->width - 1];
    PointInT pointD = input_->points[point_index + rect_height_4_ * input_->width + 1];

    const float mean_x_z = mean_R_z - mean_L_z;
    const float mean_y_z = mean_D_z - mean_U_z;

    const float mean_x_x = pointR.x - pointL.x;
    const float mean_x_y = pointR.y - pointL.y;
    const float mean_y_x = pointD.x - pointU.x;
    const float mean_y_y = pointD.y - pointU.y;

    float normal_x = mean_x_y * mean_y_z - mean_x_z * mean_y_y;
    float normal_y = mean_x_z * mean_y_x - mean_x_x * mean_y_z;
    float normal_z = mean_x_x * mean_y_y - mean_x_y * mean_y_x;

    const float normal_length = (normal_x * normal_x + normal_y * normal_y + normal_z * normal_z);

    if (normal_length == 0.0f)
    {
      normal.getNormalVector3fMap ().setConstant (bad_point);
      normal.curvature = bad_point;
      return;
    }

    flipNormalTowardsViewpoint (input_->points[point_index], vpx_, vpy_, vpz_, normal_x, normal_y, normal_z);
    
    const float scale = 1.0f / sqrtf (normal_length);

    normal.normal_x = normal_x * scale;
    normal.normal_y = normal_y * scale;
    normal.normal_z = normal_z * scale;
    normal.curvature = bad_point;

    return;
  }
  else if (normal_estimation_method_ == SIMPLE_3D_GRADIENT)
  {
    if (!init_simple_3d_gradient_)
      initSimple3DGradientMethod ();

    // this method does not work if lots of NaNs are in the neighborhood of the point
    Eigen::Vector3d gradient_x = integral_image_XYZ_.getFirstOrderSum (pos_x + rect_width_2_, pos_y - rect_height_2_, 1, rect_height_) -
                                 integral_image_XYZ_.getFirstOrderSum (pos_x - rect_width_2_, pos_y - rect_height_2_, 1, rect_height_);

    Eigen::Vector3d gradient_y = integral_image_XYZ_.getFirstOrderSum (pos_x - rect_width_2_, pos_y + rect_height_2_, rect_width_, 1) -
                                 integral_image_XYZ_.getFirstOrderSum (pos_x - rect_width_2_, pos_y - rect_height_2_, rect_width_, 1);
    Eigen::Vector3d normal_vector = gradient_y.cross (gradient_x);
    double normal_length = normal_vector.squaredNorm ();
    if (normal_length == 0.0f)
    {
      normal.getNormalVector3fMap ().setConstant (bad_point);
      normal.curvature = bad_point;
      return;
    }

    normal_vector /= sqrt (normal_length);

    float nx = static_cast<float> (normal_vector [0]);
    float ny = static_cast<float> (normal_vector [1]);
    float nz = static_cast<float> (normal_vector [2]);

    flipNormalTowardsViewpoint (input_->points[point_index], vpx_, vpy_, vpz_, nx, ny, nz);
    
    normal.normal_x = nx;
    normal.normal_y = ny;
    normal.normal_z = nz;
    normal.curvature = bad_point;
    return;
  }

  normal.getNormalVector3fMap ().setConstant (bad_point);
  normal.curvature = bad_point;
  return;
}