[PCL]2 点云法向量计算NormalEstimation

从GitHub的代码版本库下载源代码https://github.com/PointCloudLibrary/pcl，用CMake生成VS项目，查看PCL的源码位于pcl_features项目下

1.Feature类：

template <typename PointInT, typename PointOutT>   class Feature : public PCLBase<PointInT>

注意 Feature是一个泛型类，有一个compute方法。

 template <typename PointInT, typename PointOutT> void pcl::Feature<PointInT, PointOutT>::compute (PointCloudOut &output)
 {
   if (!initCompute ())
   {
     output.width = output.height = ;
     output.points.clear ();
     return;
   }
   // Copy the header
   output.header = input_->header;
   // Resize the output dataset
   if (output.points.size () != indices_->size ())
     output.points.resize (indices_->size ());
   // Check if the output will be computed for all points or only a subset
   // If the input width or height are not set, set output width as size
   if (indices_->size () != input_->points.size () || input_->width * input_->height == )
   {
     output.width = static_cast<uint32_t> (indices_->size ());
     output.height = ;
   }
   else
   {
     output.width = input_->width;
     output.height = input_->height;
   }
   output.is_dense = input_->is_dense;
   // Perform the actual feature computation
   computeFeature (output);
   deinitCompute ();
 }

2.注意computeFeature (output);方法 ，可以知道这是一个私有的虚方法。

 private:

      /** \brief Abstract feature estimation method.

        * \param[out] output the resultant features    */

      virtual void    computeFeature (PointCloudOut &output) = 0;

3.查看Feature的继承关系可以知道

template <typename PointInT, typename PointOutT>   class NormalEstimation: public Feature<PointInT, PointOutT>

NormalEstimation类是Feature模板类的子类，因此执行的是NormalEstimation类的computeFeature方法。查看computeFeature方法：

 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_);
   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 = ; idx < indices_->size (); ++idx)
     {
       if (this ->searchForNeighbors ((*indices_)[idx], search_parameter_, nn_indices, nn_dists) ==  ||
           !computePointNormal (*surface_, nn_indices, output.points[idx].normal[], output.points[idx].normal[], output.points[idx].normal[], output.points[idx].curvature))
       {
         output.points[idx].normal[] = output.points[idx].normal[] = output.points[idx].normal[] = output.points[idx].curvature = std::numeric_limits<float >::quiet_NaN ();
         output.is_dense = false;
         continue;
       }

       flipNormalTowardsViewpoint (input_->points[(*indices_)[idx]], vpx_, vpy_, vpz_, output.points[idx].normal[], output.points[idx].normal[], output.points[idx].normal[]);
     }
   }
   else
   {
     // Iterating over the entire index vector
     for (size_t idx = ; idx < indices_->size (); ++idx)
     {
       if (!isFinite ((*input_)[(*indices_)[idx]]) ||
           this->searchForNeighbors ((*indices_)[idx], search_parameter_, nn_indices, nn_dists) ==  ||
           !computePointNormal (*surface_, nn_indices, output.points[idx].normal[], output.points[idx].normal[], output.points[idx].normal[], output.points[idx].curvature))
       {
         output.points[idx].normal[] = output.points[idx].normal[] = output.points[idx].normal[] = output.points[idx].curvature = std::numeric_limits<float >::quiet_NaN ();

         output.is_dense = false;
         continue;
       }
       flipNormalTowardsViewpoint (input_->points[(*indices_)[idx]], vpx_, vpy_, vpz_,  output.points[idx].normal[], output.points[idx].normal[], output.points[idx].normal[]);
     }
   }
 }

4.因此分析NormalEstimation的算法流程如下：

 　  （1）进行点云的初始化initCompute

　　（2）初始化计算结果输出对象output

　　（3）计算点云法向量，具体由子类的computeFeature方法实现。先搜索近邻searchForNeighbors ，然后计算computePointNormal

　　　　采用的方法是PCA主成分分析法。

　　　　参考文献：《Semantic 3D Object Maps for Everyday Manipulation in Human Living Environments》 P45-49

　　　　　　　　　　http://www.pclcn.org/study/shownews.php?lang=cn&id=105

　　　　点云的法向量主要是通过点所在区域的局部拟合的表面进行计算。平面通过一个点和法向量进行表示。对于每一个点Pi,对应的协方差矩阵C

　　　　

　　　　关于主成份分析的基本原理和算法流程参考：http://blog.csdn.net/lming_08/article/details/21335313

　　（4）flipNormalTowardsViewpoint 法向量定向，采用方法是：使法向量的方向朝向viewpoint。

5.NormalEstimation模板类的重载方法computeFeature分析，computePointNormal分析。

  inline bool computePointNormal (const pcl::PointCloud<PointInT> &cloud, const std::vector<int> &indices,
                           float &nx, float &ny, float &nz, float &curvature)
       {
         if (indices.size () <  ||
             computeMeanAndCovarianceMatrix (cloud, indices, covariance_matrix_, xyz_centroid_) == )
         {
           nx = ny = nz = curvature = std::numeric_limits<float>::quiet_NaN ();
           return false;
         }

         // Get the plane normal and surface curvature
         solvePlaneParameters (covariance_matrix_, nx, ny, nz, curvature);
         return true;
       }

computeMeanAndCovarianceMatrix主要是PCA过程中计算平均值和协方差矩阵，在类centroid.hpp中。
而solvePlaneParameters方法则是为了求解特征值和特征向量。代码见feature.hpp。具体实现时采用了pcl::eigen33方法。

 inline void pcl::solvePlaneParameters (const Eigen::Matrix3f &covariance_matrix,
                            float &nx, float &ny, float &nz, float &curvature)
 {
   // Avoid getting hung on Eigen's optimizers
 //  for (int i = 0; i < 9; ++i)
 //    if (!pcl_isfinite (covariance_matrix.coeff (i)))
 //    {
 //      //PCL_WARN ("[pcl::solvePlaneParameteres] Covariance matrix has NaN/Inf values!\n");
 //      nx = ny = nz = curvature = std::numeric_limits<float>::quiet_NaN ();
 //      return;
 //    }
   // Extract the smallest eigenvalue and its eigenvector
   EIGEN_ALIGN16 Eigen::Vector3f::Scalar eigen_value;
   EIGEN_ALIGN16 Eigen::Vector3f eigen_vector;
   pcl::eigen33 (covariance_matrix, eigen_value, eigen_vector);

   nx = eigen_vector [];
   ny = eigen_vector [];
   nz = eigen_vector [];

   // Compute the curvature surface change
   float eig_sum = covariance_matrix.coeff () + covariance_matrix.coeff () + covariance_matrix.coeff ();
   if (eig_sum != )
     curvature = fabsf (eigen_value / eig_sum);
   else
     curvature = ;
 }

6.法向量定向

见normal_3d.h文件中，有多个覆写方法。摘其一：

  /** \brief Flip (in place) the estimated normal of a point towards a given viewpoint
     * \param point a given point
     * \param vp_x the X coordinate of the viewpoint
     * \param vp_y the X coordinate of the viewpoint
     * \param vp_z the X coordinate of the viewpoint
     * \param nx the resultant X component of the plane normal
     * \param ny the resultant Y component of the plane normal
     * \param nz the resultant Z component of the plane normal
     * \ingroup features
     */
   template <typename PointT> inline void
   flipNormalTowardsViewpoint (const PointT &point, float vp_x, float vp_y, float vp_z,
                               float &nx, float &ny, float &nz)
   {
     // See if we need to flip any plane normals
     vp_x -= point.x;
     vp_y -= point.y;
     vp_z -= point.z;

     // Dot product between the (viewpoint - point) and the plane normal
     float cos_theta = (vp_x * nx + vp_y * ny + vp_z * nz);

     // Flip the plane normal
     if (cos_theta < )
     {
       nx *= -;
       ny *= -;
       nz *= -;
     }
   }

运行的实例结果：