In this tutorial we will learn how to use Difference of Normals features, implemented in the pcl::DifferenceOfNormalsEstimation
class, for scale-based segmentation of unorganized point clouds.
This algorithm performs a scale based segmentation of the given input point cloud, finding points that belong within the scale parameters given.
The Difference of Normals (DoN) provides a computationally efficient, multi-scale approach to processing large unorganized 3D point clouds. The idea is very simple in concept, and yet surprisingly effective in the segmentation of scenes with a wide variation of scale. For each point
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in a pointcloud
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, two unit point normals
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are estimated with different radii,
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. The normalized (vector) difference of these point normals defines the operator.
Formally the Difference of Normals operator is defined,
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where
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,
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, and
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is the surface normal estimate at point
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, given the support radius
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. Notice, the response of the operator is a normalized vector field, and is thus orientable (the resulting direction is a key feature), however the operator’s norm often provides an easier quantity to work with, and is always in the range
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.
The primary motivation behind DoN is the observation that surface normals estimated at any given radius reflect the underlying geometry of the surface at the scale of the support radius. Although there are many different methods of estimating the surface normals, normals are always estimated with a support radius (or via a fixed number of neighbours). This support radius determines the scale in the surface structure which the normal represents.
The above diagram illustrates this effect in 1D. Normals,
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, and tangents,
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, estimated with a small support radius
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are affected by small-scale surface structure (and similarly by noise). On the other hand, normals and tangent planes estimated with a large support radius $r_l$ are less affected by small-scale structure, and represent the geometry of larger scale surface structures. In fact a similair set of features is seen in the DoN feature vectors for real-world street curbs in a LiDAR image shown below.
For more comprehensive information, please refer to the article [DON2012].
// Create a search tree, use KDTreee for non-organized data.
pcl::search::Search<PointXYZRGB>::Ptr tree;
if (cloud->isOrganized ())
{
tree.reset (new pcl::search::OrganizedNeighbor<PointXYZRGB> ());
}
else
{
tree.reset (new pcl::search::KdTree<PointXYZRGB> (false));
}
// Set the input pointcloud for the search tree
tree->setInputCloud (cloud);
We will skip the code for loading files and parsing command line arguments, and go straight to the first major PCL calls. For our later calls to calculate normals, we need to create a search tree. For organized data (i.e. a depth image), a much faster search tree is the OrganizedNeighbor search tree. For unorganized data, i.e. LiDAR scans, a KDTree is a good option.
// Compute normals using both small and large scales at each point
pcl::NormalEstimationOMP<PointXYZRGB, PointNormal> ne;
ne.setInputCloud (cloud);
ne.setSearchMethod (tree);
/**
* NOTE: setting viewpoint is very important, so that we can ensure
* normals are all pointed in the same direction!
*/
ne.setViewPoint (std::numeric_limits<float>::max (), std::numeric_limits<float>::max (), std::numeric_limits<float>::max ());
This is perhaps the most important section of code, estimating the normals. This is also the bottleneck computationally, and so we will use the pcl::NormalEstimationOMP
class which makes use of OpenMP to use many threads to calculate the normal using the multiple cores found in most modern processors. We could also use the standard single-threaded class pcl::NormalEstimation
, or even the GPU accelerated class pcl::gpu::NormalEstimation
. Whatever class we use, it is important to set an arbitrary viewpoint to be used across all the normal calculations - this ensures that normals estimated at different scales share a consistent orientation.
// calculate normals with the small scale
cout << "Calculating normals for scale..." << scale1 << endl;
pcl::PointCloud<PointNormal>::Ptr normals_small_scale (new pcl::PointCloud<PointNormal>);
ne.setRadiusSearch (scale1);
ne.compute (*normals_small_scale);
// calculate normals with the large scale
cout << "Calculating normals for scale..." << scale2 << endl;
pcl::PointCloud<PointNormal>::Ptr normals_large_scale (new pcl::PointCloud<PointNormal>);
ne.setRadiusSearch (scale2);
ne.compute (*normals_large_scale);
Next we calculate the normals using our normal estimation class for both the large and small radius. It is important to use the NormalEstimation.setRadiusSearch()
method v.s. the NormalEstimation.setMaximumNeighbours()
method or equivilant. If the normal estimate is restricted to a set number of neighbours, it may not be based on the complete surface of the given radius, and thus is not suitable for the Difference of Normals features.
Note
For large supporting radii in dense point clouds, calculating the normal would be a very computationally intensive task potentially utilizing thousands of points in the calculation, when hundreds are more than enough for an accurate estimate. A simple method to speed up the calculation is to uniformly subsample the pointcloud when doing a large radius search, see the full example code in the PCL distribution at examples/features/example_difference_of_normals.cpp
for more details.
// Create output cloud for DoN results
PointCloud<PointNormal>::Ptr doncloud (new pcl::PointCloud<PointNormal>);
copyPointCloud<PointXYZRGB, PointNormal>(*cloud, *doncloud);
We can now perform the actual Difference of Normals feature calculation using our normal estimates. The Difference of Normals result is a vector field, so we initialize the point cloud to store the results in as a pcl::PointNormal
point cloud, and copy the points from our input pointcloud over to it, so we have what may be regarded as an uninitialized vector field for our point cloud.
// Create DoN operator
pcl::DifferenceOfNormalsEstimation<PointXYZRGB, PointNormal, PointNormal> don;
don.setInputCloud (cloud);
don.setNormalScaleLarge (normals_large_scale);
don.setNormalScaleSmall (normals_small_scale);
if (!don.initCompute ())
{
std::cerr << "Error: Could not intialize DoN feature operator" << std::endl;
exit (EXIT_FAILURE);
}
// Compute DoN
don.computeFeature (*doncloud);
We instantiate a new pcl::DifferenceOfNormalsEstimation
class to take care of calculating the Difference of Normals vector field.
The pcl::DifferenceOfNormalsEstimation
class has 3 template parameters, the first corresponds to the input point cloud type, in this case pcl::PointXYZRGB
, the second corresponds to the type of the normals estimated for the point cloud, in this case pcl::PointNormal
, and the third corresponds to the vector field output type, in this case also pcl::PointNormal
. Next we set the input point cloud and give both of the normals estimated for the point cloud, and check that the requirements for computing the features are satisfied using the pcl::DifferenceOfNormalsEstimation::initCompute()
method. Finally we compute the features by calling the pcl::DifferenceOfNormalsEstimation::computeFeature()
method.
Note
The pcl::DifferenceOfNormalsEstimation
class expects the given point cloud and normal point clouds indices to match, i.e. the first point in the input point cloud’s normals should also be the first point in the two normal point clouds.
While we now have a Difference of Normals vector field, we still have the complete point set. To begin the segmentation process, we must actually discriminate points based on their Difference of Normals vector result. There are a number of common quantities you may want to try filtering by:
Quantity |
PointNormal Field |
Description |
Usage Scenario |
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DoN vector |
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DoN
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norm |
Filtering points by scale membership, large magnitude
indicates point has a strong response at then given
scale parameters |
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, |
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facades with large
large
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, |
float normal[2] |
DoN vector z component |
In this example we will do a simple magnitude threshold, looking for objects of a scale regardless of their orientation in the scene. To do so, we must create a conditional filter:
// Build the condition for filtering
pcl::ConditionOr<PointNormal>::Ptr range_cond (
new pcl::ConditionOr<PointNormal> ()
);
range_cond->addComparison (pcl::FieldComparison<PointNormal>::ConstPtr (
new pcl::FieldComparison<PointNormal> ("curvature", pcl::ComparisonOps::GT, threshold))
);
// Build the filter
pcl::ConditionalRemoval<PointNormal> condrem (range_cond);
condrem.setInputCloud (doncloud);
pcl::PointCloud<PointNormal>::Ptr doncloud_filtered (new pcl::PointCloud<PointNormal>);
// Apply filter
condrem.filter (*doncloud_filtered);
After we apply the filter we are left with a reduced pointcloud consisting of the points with a strong response with the given scale parameters.
cout << "Clustering using EuclideanClusterExtraction with tolerance <= " << segradius << "..." << endl;
pcl::search::KdTree<PointNormal>::Ptr segtree (new pcl::search::KdTree<PointNormal>);
segtree->setInputCloud (doncloud);
std::vector<pcl::PointIndices> cluster_indices;
pcl::EuclideanClusterExtraction<PointNormal> ec;
ec.setClusterTolerance (segradius);
ec.setMinClusterSize (50);
ec.setMaxClusterSize (100000);
ec.setSearchMethod (segtree);
ec.setInputCloud (doncloud);
ec.extract (cluster_indices);
Finally, we are usually left with a number of objects or regions with good isolation, allowing us to use a simple clustering algorithm to segment the results. In this example we used Euclidean Clustering with a threshold equal to the small radius parameter.
After the segmentation the cloud viewer window will be opened and you will see something similar to those images: