Beispiel #1
0
template <typename PointInT, typename PointOutT> void
pcl::IntegralImageNormalEstimation<PointInT, PointOutT>::initData ()
{
  if (border_policy_ != BORDER_POLICY_IGNORE &&
      border_policy_ != BORDER_POLICY_MIRROR)
    PCL_THROW_EXCEPTION (InitFailedException,
                         "[pcl::IntegralImageNormalEstimation::initData] unknown border policy.");

  if (normal_estimation_method_ != COVARIANCE_MATRIX &&
      normal_estimation_method_ != AVERAGE_3D_GRADIENT &&
      normal_estimation_method_ != AVERAGE_DEPTH_CHANGE &&
      normal_estimation_method_ != SIMPLE_3D_GRADIENT)
    PCL_THROW_EXCEPTION (InitFailedException,
                         "[pcl::IntegralImageNormalEstimation::initData] unknown normal estimation method.");

  // compute derivatives
  if (diff_x_ != NULL) delete[] diff_x_;
  if (diff_y_ != NULL) delete[] diff_y_;
  if (depth_data_ != NULL) delete[] depth_data_;
  if (distance_map_ != NULL) delete[] distance_map_;
  diff_x_ = NULL;
  diff_y_ = NULL;
  depth_data_ = NULL;
  distance_map_ = NULL;

  if (normal_estimation_method_ == COVARIANCE_MATRIX)
    initCovarianceMatrixMethod ();
  else if (normal_estimation_method_ == AVERAGE_3D_GRADIENT)
    initAverage3DGradientMethod ();
  else if (normal_estimation_method_ == AVERAGE_DEPTH_CHANGE)
    initAverageDepthChangeMethod ();
  else if (normal_estimation_method_ == SIMPLE_3D_GRADIENT)
    initSimple3DGradientMethod ();
}
template <typename PointInT, typename PointOutT> void
pcl::IntegralImageNormalEstimation<PointInT, PointOutT>::initData ()
{
  // compute derivatives
  if (diff_x_ != NULL) delete diff_x_;
  if (diff_y_ != NULL) delete diff_y_;
  if (depth_data_ != NULL) delete depth_data_;
  if (distance_map_ != NULL) delete distance_map_;
  diff_x_ = NULL;
  diff_y_ = NULL;
  depth_data_ = NULL;
  distance_map_ = NULL;

  if (normal_estimation_method_ == COVARIANCE_MATRIX)
    initCovarianceMatrixMethod ();
  else if (normal_estimation_method_ == AVERAGE_3D_GRADIENT)
    initAverage3DGradientMethod ();
  else if (normal_estimation_method_ == AVERAGE_DEPTH_CHANGE)
    initAverageDepthChangeMethod ();
  else if (normal_estimation_method_ == SIMPLE_3D_GRADIENT)
    initSimple3DGradientMethod ();
}
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 = std::numeric_limits<float>::quiet_NaN ();
      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_).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);
    //pcl::flipNormalTowardsViewpoint (input_->points[point_index], vpx_, vpy_, vpz_, eigen_vector);
    pcl::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 = std::numeric_limits<float>::quiet_NaN ();
      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.getNormalVector4fMap ().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]);

    //pcl::flipNormalTowardsViewpoint (input_->points[point_index], vpx_, vpy_, vpz_, normal_vector);
    pcl::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 ();

//    unsigned count = integral_image_depth_.getFiniteElementsCount (pos_x - rect_width_2_, pos_y - rect_height_2_, rect_width_, rect_height_);
//    if (count == 0)
//    {
//      normal.normal_x = normal.normal_y = normal.normal_z = normal.curvature = std::numeric_limits<float>::quiet_NaN ();
//      return;
//    }
//    const float mean_L_z = integral_image_depth_.getFirstOrderSum (pos_x - rect_width_2_ - 1, pos_y - rect_height_2_    , rect_width_ - 1, rect_height_ - 1) / ((rect_width_-1)*(rect_height_-1));
//    const float mean_R_z = integral_image_depth_.getFirstOrderSum (pos_x - rect_width_2_ + 1, pos_y - rect_height_2_    , rect_width_ - 1, rect_height_ - 1) / ((rect_width_-1)*(rect_height_-1));
//    const float mean_U_z = integral_image_depth_.getFirstOrderSum (pos_x - rect_width_2_    , pos_y - rect_height_2_ - 1, rect_width_ - 1, rect_height_ - 1) / ((rect_width_-1)*(rect_height_-1));
//    const float mean_D_z = integral_image_depth_.getFirstOrderSum (pos_x - rect_width_2_    , pos_y - rect_height_2_ + 1, rect_width_ - 1, rect_height_ - 1) / ((rect_width_-1)*(rect_height_-1));

    // 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 = std::numeric_limits<float>::quiet_NaN ();
      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.getNormalVector4fMap ().setConstant (bad_point);
      normal.curvature = bad_point;
      return;
    }

    pcl::flipNormalTowardsViewpoint (input_->points[point_index], vpx_, vpy_, vpz_, normal_x, normal_y, normal_z);
    
    const float scale = 1.0f / sqrt (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.getNormalVector4fMap ().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]);

    //pcl::flipNormalTowardsViewpoint (input_->points[point_index], vpx_, vpy_, vpz_, normal_vector);
    pcl::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.getNormalVector4fMap ().setConstant (bad_point);
  normal.curvature = bad_point;
  return;
}
Beispiel #4
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;
}