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
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：