Fast Point Feature Histograms (FPFH) descriptors
The theoretical computational complexity of the Point Feature Histogram (see
Point Feature Histograms (PFH) descriptors) for a given point cloud
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points
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is the number of neighbors for each point
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. For real-time or near real-time applications, the
computation of Point Feature Histograms in dense point neighborhoods can
represent one of the major bottlenecks.
This tutorial describes a simplification of the PFH formulation, called Fast
Point Feature Histograms (FPFH) (see [RusuDissertation] for more information),
that reduces the computational complexity of the algorithm to
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,
while still retaining most of the discriminative power of the PFH.
Theoretical primer
To simplify the histogram feature computation, we proceed as follows:
in a first step, for each query point
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a set of tuples
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between itself and its neighbors are computed
as described in Point Feature Histograms (PFH) descriptors - this will be called the Simplified
Point Feature Histogram (SPFH);
in a second step, for each point its k neighbors are re-determined, and the
neighboring SPFH values are used to weight the final histogram of pq
(called FPFH) as follows:
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where the weight
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represents a distance between the query point
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and a neighbor point
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in some given metric space, thus
scoring the (
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) pair, but could just as well be selected as a
different measure if necessary. To understand the importance of this weighting
scheme, the figure below presents the influence region diagram for a
k-neighborhood set centered at
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.
Thus, for a given query point
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, the algorithm first estimates its
SPFH values by creating pairs between itself and its neighbors (illustrated
using red lines). This is repeated for all the points in the dataset, followed
by a re-weighting of the SPFH values of pq using the SPFH values of its
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neighbors, thus creating the FPFH for
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. The extra FPFH
connections, resultant due to the additional weighting scheme, are shown with
black lines. As the diagram shows, some of the value pairs will be counted
twice (marked with thicker lines in the figure).
Estimating FPFH features
Fast Point Feature Histograms are implemented in PCL as part of the
pcl_features
library.
The default FPFH implementation uses 11 binning subdivisions (e.g., each of the
four feature values will use this many bins from its value interval), and a
decorrelated scheme (see above: the feature histograms are computed separately
and concantenated) which results in a 33-byte array of float values. These are
stored in a pcl::FPFHSignature33 point type.
The following code snippet will estimate a set of FPFH features for all the
points in the input dataset.
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34 | #include <pcl/point_types.h>
#include <pcl/features/fpfh.h>
{
pcl::PointCloud<pcl::PointXYZ>::Ptr cloud (new pcl::PointCloud<pcl::PointXYZ>);
pcl::PointCloud<pcl::Normal>::Ptr normals (new pcl::PointCloud<pcl::Normal> ());
... read, pass in or create a point cloud with normals ...
... (note: you can create a single PointCloud<PointNormal> if you want) ...
// Create the FPFH estimation class, and pass the input dataset+normals to it
pcl::FPFHEstimation<pcl::PointXYZ, pcl::Normal, pcl::FPFHSignature33> fpfh;
fpfh.setInputCloud (cloud);
fpfh.setInputNormals (normals);
// alternatively, if cloud is of tpe PointNormal, do fpfh.setInputNormals (cloud);
// Create an empty kdtree representation, and pass it to the FPFH estimation object.
// Its content will be filled inside the object, based on the given input dataset (as no other search surface is given).
pcl::search::KdTree<PointXYZ>::Ptr tree (new pcl::search::KdTree<PointXYZ>);
fpfh.setSearchMethod (tree);
// Output datasets
pcl::PointCloud<pcl::FPFHSignature33>::Ptr fpfhs (new pcl::PointCloud<pcl::FPFHSignature33> ());
// Use all neighbors in a sphere of radius 5cm
// IMPORTANT: the radius used here has to be larger than the radius used to estimate the surface normals!!!
fpfh.setRadiusSearch (0.05);
// Compute the features
fpfh.compute (*fpfhs);
// fpfhs->points.size () should have the same size as the input cloud->points.size ()*
}
|
The actual compute call from the FPFHEstimation class does nothing internally but:
for each point p in cloud P
1. pass 1:
1. get the nearest neighbors of :math:`p`
2. for each pair of :math:`p, p_k` (where :math:`p_k` is a neighbor of :math:`p`, compute the three angular values
3. bin all the results in an output SPFH histogram
2. pass 2:
1. get the nearest neighbors of :math:`p`
3. use each SPFH of :math:`p` with a weighting scheme to assemble the FPFH of :math:`p`:
Note
For efficiency reasons, the compute method in FPFHEstimation does not check if the normals contains NaN or infinite values.
Passing such values to compute() will result in undefined output.
It is advisable to check the normals, at least during the design of the processing chain or when setting the parameters.
This can be done by inserting the following code before the call to compute():
for (int i = 0; i < normals->points.size(); i++)
{
if (!pcl::isFinite<pcl::Normal>(normals->points[i]))
{
PCL_WARN("normals[%d] is not finite\n", i);
}
}
In production code, preprocessing steps and parameters should be set so that normals are finite or raise an error.