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Creating a DataPointsFilter
In the following tutorials we will discuss how you can extend the functionality provided in libpointmatcher by taking advantage of its modular design. The following tutorial will detail the development of a a new data filter, which is as of yet not included in libpointmatcher. You may wish to develop customized DataPointFilters, Transformations, OutlierFilters which best fit your project. However, if you believe that your own contributions would benefit a larger user base, please contact us to see how we can integrate them into libpointmatcher.
The Voxel Grid Filter
The filter we wish to implement today is a voxel grid filter. The latter falls into the class of downsampling filters, in that it reduces the number of points in a cloud, as opposed to descriptive filters which add information to the points.
The voxel grid filter downsamples the data by taking a spatial average of the points in the cloud. In the 2D case, one can simply imagine dividing the plane into a regular grid of rectangles. While the term is more suited to 3D spaces, these rectangular areas are known as voxels. The subsampling rate is adjusted by setting the voxel size along each dimension. The set of points which lie within the bounds of a voxel are assigned to that voxel and will be combined into one output point.
There are two options as to how to represent the distribution of points in a voxel by a single point. In the first, we take the centroid or spatial average of the point distribution. In the second, we simply take the geometrical center of the voxel. Clearly, the first option is more accurate since it takes into account the point distribution inside the voxels. However it is more computationally intensive since the centroid must be computed for each voxel. The computational cost increases linearly with the number of points in the cloud and the number of voxels.
In the following figure we show the application of a 2D voxel filter over a 2D point cloud containing uniformly dispersed points. We divide each axis into 5 regions resulting in 25 voxels. The points are downsampled by taking the centroid of the points within each voxel. The centroids are shown in red asterisks. The centers of the voxels are shown in green squares.
Figure 1: A 2D Voxel Grid with red stars representing the voxel centroids  : 
Implementation as a DataPointsFilter
Overview
We will now implement the voxel grid within the framework of libpointmatcher. Our implementation of the voxel grid filter will support 2D and 3D data and will be parametrized to support different voxel sizes and both downsampling methods mentioned above.
Parameter  Description  Default value  Allowable range 

vSizeX  Size of the voxel along the xaxis  1.0  inf to inf 
vSizeY  Size of the voxel along the yaxis  1.0  inf to inf 
vSizeZ  Size of the voxel along the zaxis  1.0  inf to inf 
useCentroid  If 1, downsample by using the centroid of each voxel. If 0, use the voxel center  1  1 or 0 
averageExistingDescriptors  If 1, descriptors are downsampled by taking their average in the voxel. If 0, we use the descriptors from the first point found in the voxel  1  1 or 0 
Declaration
The implementations of data point filters are declared in pointmatcher/DataPointsFiltersImpl.h. In this file, we declare a new templated struct called VoxelGridDataPointsFiler
. This class is derived from the general class DataPointsFilter
so as to inherit pure virtual methods and functionality that are common to all data point filters.
Note: Libpointmatcher is a templated library and supports data of either float or double types. This allows users the flexibility of selecting between two levels of precision depending on the requirements of their application. As a result, classes which are added to libpointmatcher should be templated so as to support both types.
template <typename T>
struct VoxelGridDataPointsFilter : public PointMatcher<T>::DataPointsFilter
In order to register the voxel grid filter as a parameterizable module in libpointmatcher we must define the two following static functions:
inline static const std::string description()
{
return "Construct Voxel grid of point cloud. Downsample by taking centroid or center of grid cells./n";
}
This function should return a string containing a short description of what the filter does. The description will be printing when listing available modules in libpointmatcher.
inline static const ParametersDoc availableParameters()
{
return boost::assign::list_of<ParameterDoc>
( "vSizeX", "Dimension of each voxel cell in x direction", "1.0", "inf", "inf", &P::Comp<T> )
( "vSizeY", "Dimension of each voxel cell in y direction", "1.0", "inf", "inf", &P::Comp<T> )
( "vSizeZ", "Dimension of each voxel cell in z direction", "1.0", "inf", "inf", &P::Comp<T> )
( "useCentroid", "If 1 (true), downsample by using centroid of voxel cell. If false (0), use center of voxel cell.", "1", "0", "1", P::Comp<bool> )
( "averageExistingDescriptors", "whether the filter average the descriptor values in a voxel or use a single value", "1", "0", "1", &P::Comp<T> )
;
}
This function should return the list of parameters or settings used by this filter. The parameters are stored in a struct called ParameterDoc
. A parameter is defined by providing:
 A string with the name of the parameter in camelcase
 A string containing the description of the parameter
 A string containing the default value of this parameter
 If the bounds are checked, a string containing the minimum value of this parameter
 If the bounds are checked, a string containing the maximum value of this parameter
 If the parameter contains a nonstandard type, the pointer to a comparison function for the parameter values
One can use the boost convenience function boost::assign::list_of
to define a parameter in one line of c++. We define a constructor taking as argument a list of parameters. These parameters are stored in the voxel grid filter member variables.
VoxelGridDataPointsFilter(const Parameters& params);
const T vSizeX;
const T vSizeY;
const T vSizeZ;
const bool useCentroid;
const bool averageExistingDescriptors;
For convenience, we declare a Voxel
struct which will contain the following two pieces of information about a voxel:
struct Voxel {
unsigned int numPoints;
unsigned int firstPoint;
Voxel() : numPoints(0), firstPoint(0) {}
};
numPoints
: The total number of points contained in a voxelfirstPoint
: The index of the first point contained in a voxel (corresponding column of the DataPoints object)
DataPointsFilter
contains two pure virtual functions which we must define in order to complete the implementation of our filter.
virtual DataPoints filter(const DataPoints& input);
virtual void inPlaceFilter(DataPoints& cloud);
The filter
function performs the filter operation on the input point cloud and returns the downsampled point cloud. This function in fact calls the inPlaceFilter
function which performs the filtering operation by directly modifying the input point cloud. The use of an "in place filter" may be preferable if we do not need to keep an intact copy of the input as we do not need to create a new point cloud to hold the output and the memory footprint is thus lower. This can make a difference when operating on large point clouds with many voxels.
Implementation of the Filter
The steps performed by the filter are all contained in the inPlaceFilter
function. Because the voxel grid filter does not subsample points from the input but rather creates new points, we use the following strategy for performing in place filtering.

Voxel Assignment
We pass through the input point cloud and assign each point to a voxel while recording the number of points contained in each voxel. We record the index of the first point that is assigned to a given voxel. This point will be modified to contain the downsampled point representing the voxel. 
Voxel Point Computation
Centroid Downsampling
a) Make a second pass through the input cloud and compute the sum of point positions in each given voxel. This sum is stored in the place of the first point of a voxel. If the descriptors are to be averaged, we store their sum in the place of the first point's descriptors.
b) The first points containing the summed points are normalized by the number of points in the voxel. Similarly, the descriptors are normalized by the number of points. If a voxel does not contain any points, it is discarded.
Center Downsampling
a) If we wish to keep an average of the descriptors, we need to make an extra pass through the data to sum up the descriptors. The first points are replaced by the center of the voxels and the descriptors are normalized. 
Point Cloud Truncation
The downsampled points to be kept are sorted by index, and are moved to the beginning of the point cloud. The latter is then truncated to only contain the downsampled points.
Initiation
const int numPoints(cloud.features.cols());
const int featDim(cloud.features.rows());
const int descDim(cloud.descriptors.rows());
assert (featDim == 3  featDim == 4);
int insertDim(0);
if (averageExistingDescriptors)
{
for(unsigned int i = 0; i < cloud.descriptorLabels.size(); i++)
insertDim += cloud.descriptorLabels[i].span;
if (insertDim != descDim)
throw InvalidField("VoxelGridDataPointsFilter: Error, descriptor labels do not match descriptor data");
}
In the initiation phase we obtain the number of points, the feature and descriptor dimensions from the input point cloud. We check also check that the descriptor fields are valid.
1. Voxel Assignment
// Calculate number of divisions along each axis
Vector minValues = cloud.features.rowwise().minCoeff();
Vector maxValues = cloud.features.rowwise().maxCoeff();
T minBoundX = minValues.x() / vSizeX;
T maxBoundX = maxValues.x() / vSizeX;
T minBoundY = minValues.y() / vSizeY;
T maxBoundY = maxValues.y() / vSizeY;
T minBoundZ = 0;
T maxBoundZ = 0;
if (featDim == 4)
{
minBoundZ = minValues.z() / vSizeZ;
maxBoundZ = maxValues.z() / vSizeZ;
}
// number of divisions is total size / voxel size voxels of equal length + 1
// with remaining space
unsigned int numDivX = 1 + maxBoundX  minBoundX;
unsigned int numDivY = 1 + maxBoundY  minBoundY;;
unsigned int numDivZ = 0;
// If a 3D point cloud
if (featDim == 4 )
numDivZ = 1 + maxBoundZ  minBoundZ;
unsigned int numVox = numDivX * numDivY;
if ( featDim == 4)
numVox *= numDivZ;
// Assume point cloud is randomly ordered
// compute a linear index of the following type
// i, j, k are the component indices
// nx, ny number of divisions in x and y components
// idx = i + j * nx + k * nx * ny
std::vector<unsigned int> indices(numPoints);
// vector to hold the first point in a voxel
// this point will be ovewritten in the input cloud with
// the output value
std::vector<Voxel>* voxels;
// try allocating vector. If too big return error
try {
voxels = new std::vector<Voxel>(numVox);
} catch (std::bad_alloc&) {
throw InvalidParameter((boost::format("VoxelGridDataPointsFilter: Memory allocation error with %1% voxels. Try increasing the voxel dimensions.") % numVox).str());
}
for (int p = 0; p < numPoints; p++ )
{
unsigned int i = floor(cloud.features(0,p)/vSizeX  minBoundX);
unsigned int j = floor(cloud.features(1,p)/vSizeY minBoundY);
unsigned int k = 0;
unsigned int idx;
if ( featDim == 4 )
{
k = floor(cloud.features(2,p)/vSizeZ  minBoundZ);
idx = i + j * numDivX + k * numDivX * numDivY;
}
else
{
idx = i + j * numDivX;
}
unsigned int pointsInVox = (*voxels)[idx].numPoints + 1;
if (pointsInVox == 1)
{
(*voxels)[idx].firstPoint = p;
}
(*voxels)[idx].numPoints = pointsInVox;
indices[p] = idx;
}
The bounding area of the point cloud is calculated by finding the minimum and maximum positions in the feature dimensions. The number of divisions along each direction which form a voxel are calculated by dividing the bounding box size by the voxel size. Note that unless the bounding box size is an exact multiple of the voxel size, the voxels cannot all be the same size. We simply use N1 voxels of equal size and the remaining space is used by the last voxel.
Each voxel is identified by a unique linear index. If i,j,k represent the voxel indices in the x,y,z dimensions respectively, the formula to encode the linear index is the following: idx = i + j * numDivX + k * numDivX * numDivY. Each point in the cloud is given a voxel index. The number of points and the first point in a given voxel is recorded in a vector of Voxel
objects.
2. Voxel Point Computation
Using the Centroid
// store which points contain voxel position
std::vector<unsigned int> pointsToKeep;
// Store voxel centroid in output
if (useCentroid)
{
// Iterate through the indices and sum values to compute centroid
for (int p = 0; p < numPoints ; p++)
{
unsigned int idx = indices[p];
unsigned int firstPoint = (*voxels)[idx].firstPoint;
// If this is the first point in the voxel, leave as is
// if not sum up this point for centroid calculation
if (firstPoint != p)
{
// Sum up features and descriptors (if we are also averaging descriptors)
for (int f = 0; f < (featDim  1); f++ )
{
cloud.features(f,firstPoint) += cloud.features(f,p);
}
if (averageExistingDescriptors)
{
for (int d = 0; d < descDim; d++)
{
cloud.descriptors(d,firstPoint) += cloud.descriptors(d,p);
}
}
}
}
// Now iterating through the voxels
// Normalize sums to get centroid (average)
// Some voxels may be empty and are discarded
for( int idx = 0; idx < numVox; idx++)
{
unsigned int numPoints = (*voxels)[idx].numPoints;
unsigned int firstPoint = (*voxels)[idx].firstPoint;
if(numPoints > 0)
{
for ( int f = 0; f < (featDim  1); f++ )
cloud.features(f,firstPoint) /= numPoints;
if (averageExistingDescriptors) {
for ( int d = 0; d < descDim; d++ )
cloud.descriptors(d,firstPoint) /= numPoints;
}
pointsToKeep.push_back(firstPoint);
}
}
}
We make a second pass through the data and take the sum of the features in the place of each voxel's first point. If needed, the descriptors are also summed up. We then iterate through the voxels and normalize non empty voxels. Their first points are recorded to be ignored by the truncation operation applied at the end of filtering.
Using Centers
// Although we don't sum over the features, we may still need to sum the descriptors
if (averageExistingDescriptors)
{
// Iterate through the indices and sum values to compute centroid
for (int p = 0; p < numPoints ; p++)
{
unsigned int idx = indices[p];
unsigned int firstPoint = (*voxels)[idx].firstPoint;
// If this is the first point in the voxel, leave as is
// if not sum up this point for centroid calculation
if (firstPoint != p)
{
for (int d = 0; d < descDim; d++ )
{
cloud.descriptors(d,firstPoint) += cloud.descriptors(d,p);
}
}
}
}
for (int idx = 0; idx < numVox; idx++)
{
unsigned int numPoints = (*voxels)[idx].numPoints;
unsigned int firstPoint = (*voxels)[idx].firstPoint;
if (numPoints > 0)
{
// get back voxel indices in grid format
// If we are in the last division, the voxel is smaller in size
// We adjust the center as from the end of the last voxel to the bounding area
unsigned int i = 0;
unsigned int j = 0;
unsigned int k = 0;
if (featDim == 4)
{
k = idx / (numDivX * numDivY);
if (k == numDivZ)
cloud.features(3,firstPoint) = maxValues.z()  (k1) * vSizeZ/2;
else
cloud.features(3,firstPoint) = k * vSizeZ + vSizeZ/2;
}
j = (idx  k * numDivX * numDivY) / numDivX;
if (j == numDivY)
cloud.features(2,firstPoint) = maxValues.y()  (j1) * vSizeY/2;
else
cloud.features(2,firstPoint) = j * vSizeY + vSizeY / 2;
i = idx  k * numDivX * numDivY  j * numDivX;
if (i == numDivX)
cloud.features(1,firstPoint) = maxValues.x()  (i1) * vSizeX/2;
else
cloud.features(1,firstPoint) = i * vSizeX + vSizeX / 2;
// Descriptors : normalize if we are averaging or keep as is
if (averageExistingDescriptors) {
for ( int d = 0; d < descDim; d++ )
cloud.descriptors(d,firstPoint) /= numPoints;
}
pointsToKeep.push_back(firstPoint);
}
}
// deallocate voxels vector
delete voxels;
If we are averaging descriptors, we perform a summing step as in the previous case. We then iterate through the voxels and replace the first point from each nonempty voxel with the voxel center. If descriptors are averaged, these are normalized as well. We also record the points to keep during the truncation process.
3. Point Cloud Truncation
// Move the points to be kept to the start
// Bring the data we keep to the front of the arrays then
// wipe the leftover unused space.
std::sort(pointsToKeep.begin(), pointsToKeep.end());
int numPtsOut = pointsToKeep.size();
for (int i = 0; i < numPtsOut; i++){
int k = pointsToKeep[i];
assert(i <= k);
cloud.features.col(i) = cloud.features.col(k);
if (cloud.descriptors.rows() != 0)
cloud.descriptors.col(i) = cloud.descriptors.col(k);
}
cloud.features.conservativeResize(Eigen::NoChange, numPtsOut);
cloud.descriptors.conservativeResize(Eigen::NoChange, numPtsOut);
We first sort the points voxel points by index and place them in order, at the beginning of the point cloud. The unwanted points are removed from the point cloud by using Eigen's conservativeResize
function.
Registering the Filter as a Libpointmatcher Module
Now that we have completed the implementation of our voxel filter, we can add it to libpointmatcher as a usable DataPointsFilter. We do so by adding the following macro function in pointmatcher/Registry.cpp
ADD_TO_REGISTRAR(DataPointsFilter, VoxelGridDataPointsFilter, typename DataPointsFiltersImpl<T>::VoxelGridDataPointsFilter)
Now recompile the library and check that the new transformation is listed as an available module by running pcmip l  grep C 10 VoxelGridDataPointsFilter
.
Where To Go From Here
If you are not comfortable with the material covered in this tutorial, we suggest that you attempt to redesign a very simple filter such as the MaxDistDataPointsFilter
. You can find its implementation in pointmatcher/DataPointsFiltersImpl.h and pointmatcher/DataPointsFiltersImpl.cpp with which to compare your solution.
For more information on extending libpointmatcher the next tutorial covers the design of a transformation class and is similar in nature to this tutorial.
Nevertheless, you can skip directly to this tutorial to learn how to write unit tests to validate that your modules are working correctly. The module that is tested in that lesson is the voxel grid filter that was just designed here and is thus natural next step to take.