How to incrementally register pairs of clouds

This document demonstrates using the Iterative Closest Point algorithm in order to incrementally register a series of point clouds two by two.

The idea is to transform all the clouds in the first cloud’s frame.
This is done by finding the best transform between each consecutive cloud, and accumulating these transforms over the whole set of clouds.
Your data set should consist of clouds that have been roughly pre-aligned in a common frame (e.g. in a robot’s odometry or map frame) and overlap with one another.

The code

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/*
 * Software License Agreement (BSD License)
 *
 *  Copyright (c) 2010, Willow Garage, Inc.
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/* \author Radu Bogdan Rusu
 * adaptation Raphael Favier*/

#include <boost/make_shared.hpp>
#include <pcl/point_types.h>
#include <pcl/point_cloud.h>
#include <pcl/point_representation.h>

#include <pcl/io/pcd_io.h>

#include <pcl/filters/voxel_grid.h>
#include <pcl/filters/filter.h>

#include <pcl/features/normal_3d.h>

#include <pcl/registration/icp.h>
#include <pcl/registration/icp_nl.h>
#include <pcl/registration/transforms.h>

#include <pcl/visualization/pcl_visualizer.h>

using pcl::visualization::PointCloudColorHandlerGenericField;
using pcl::visualization::PointCloudColorHandlerCustom;

//convenient typedefs
typedef pcl::PointXYZ PointT;
typedef pcl::PointCloud<PointT> PointCloud;
typedef pcl::PointNormal PointNormalT;
typedef pcl::PointCloud<PointNormalT> PointCloudWithNormals;

// This is a tutorial so we can afford having global variables 
	//our visualizer
	pcl::visualization::PCLVisualizer *p;
	//its left and right viewports
	int vp_1, vp_2;

//convenient structure to handle our pointclouds
struct PCD
{
  PointCloud::Ptr cloud;
  std::string f_name;

  PCD() : cloud (new PointCloud) {};
};

struct PCDComparator
{
  bool operator () (const PCD& p1, const PCD& p2)
  {
    return (p1.f_name < p2.f_name);
  }
};


// Define a new point representation for < x, y, z, curvature >
class MyPointRepresentation : public pcl::PointRepresentation <PointNormalT>
{
  using pcl::PointRepresentation<PointNormalT>::nr_dimensions_;
public:
  MyPointRepresentation ()
  {
    // Define the number of dimensions
    nr_dimensions_ = 4;
  }

  // Override the copyToFloatArray method to define our feature vector
  virtual void copyToFloatArray (const PointNormalT &p, float * out) const
  {
    // < x, y, z, curvature >
    out[0] = p.x;
    out[1] = p.y;
    out[2] = p.z;
    out[3] = p.curvature;
  }
};


////////////////////////////////////////////////////////////////////////////////
/** \brief Display source and target on the first viewport of the visualizer
 *
 */
void showCloudsLeft(const PointCloud::Ptr cloud_target, const PointCloud::Ptr cloud_source)
{
  p->removePointCloud ("vp1_target");
  p->removePointCloud ("vp1_source");

  PointCloudColorHandlerCustom<PointT> tgt_h (cloud_target, 0, 255, 0);
  PointCloudColorHandlerCustom<PointT> src_h (cloud_source, 255, 0, 0);
  p->addPointCloud (cloud_target, tgt_h, "vp1_target", vp_1);
  p->addPointCloud (cloud_source, src_h, "vp1_source", vp_1);

  PCL_INFO ("Press q to begin the registration.\n");
  p-> spin();
}


////////////////////////////////////////////////////////////////////////////////
/** \brief Display source and target on the second viewport of the visualizer
 *
 */
void showCloudsRight(const PointCloudWithNormals::Ptr cloud_target, const PointCloudWithNormals::Ptr cloud_source)
{
  p->removePointCloud ("source");
  p->removePointCloud ("target");


  PointCloudColorHandlerGenericField<PointNormalT> tgt_color_handler (cloud_target, "curvature");
  if (!tgt_color_handler.isCapable ())
      PCL_WARN ("Cannot create curvature color handler!");

  PointCloudColorHandlerGenericField<PointNormalT> src_color_handler (cloud_source, "curvature");
  if (!src_color_handler.isCapable ())
      PCL_WARN ("Cannot create curvature color handler!");


  p->addPointCloud (cloud_target, tgt_color_handler, "target", vp_2);
  p->addPointCloud (cloud_source, src_color_handler, "source", vp_2);

  p->spinOnce();
}

////////////////////////////////////////////////////////////////////////////////
/** \brief Load a set of PCD files that we want to register together
  * \param argc the number of arguments (pass from main ())
  * \param argv the actual command line arguments (pass from main ())
  * \param models the resultant vector of point cloud datasets
  */
void loadData (int argc, char **argv, std::vector<PCD, Eigen::aligned_allocator<PCD> > &models)
{
  std::string extension (".pcd");
  // Suppose the first argument is the actual test model
  for (int i = 1; i < argc; i++)
  {
    std::string fname = std::string (argv[i]);
    // Needs to be at least 5: .plot
    if (fname.size () <= extension.size ())
      continue;

    std::transform (fname.begin (), fname.end (), fname.begin (), (int(*)(int))tolower);

    //check that the argument is a pcd file
    if (fname.compare (fname.size () - extension.size (), extension.size (), extension) == 0)
    {
      // Load the cloud and saves it into the global list of models
      PCD m;
      m.f_name = argv[i];
      pcl::io::loadPCDFile (argv[i], *m.cloud);
      //remove NAN points from the cloud
      std::vector<int> indices;
      pcl::removeNaNFromPointCloud(*m.cloud,*m.cloud, indices);

      models.push_back (m);
    }
  }
}


////////////////////////////////////////////////////////////////////////////////
/** \brief Align a pair of PointCloud datasets and return the result
  * \param cloud_src the source PointCloud
  * \param cloud_tgt the target PointCloud
  * \param output the resultant aligned source PointCloud
  * \param final_transform the resultant transform between source and target
  */
void pairAlign (const PointCloud::Ptr cloud_src, const PointCloud::Ptr cloud_tgt, PointCloud::Ptr output, Eigen::Matrix4f &final_transform, bool downsample = false)
{
  //
  // Downsample for consistency and speed
  // \note enable this for large datasets
  PointCloud::Ptr src (new PointCloud);
  PointCloud::Ptr tgt (new PointCloud);
  pcl::VoxelGrid<PointT> grid;
  if (downsample)
  {
    grid.setLeafSize (0.05, 0.05, 0.05);
    grid.setInputCloud (cloud_src);
    grid.filter (*src);

    grid.setInputCloud (cloud_tgt);
    grid.filter (*tgt);
  }
  else
  {
    src = cloud_src;
    tgt = cloud_tgt;
  }


  // Compute surface normals and curvature
  PointCloudWithNormals::Ptr points_with_normals_src (new PointCloudWithNormals);
  PointCloudWithNormals::Ptr points_with_normals_tgt (new PointCloudWithNormals);

  pcl::NormalEstimation<PointT, PointNormalT> norm_est;
  pcl::search::KdTree<pcl::PointXYZ>::Ptr tree (new pcl::search::KdTree<pcl::PointXYZ> ());
  norm_est.setSearchMethod (tree);
  norm_est.setKSearch (30);
  
  norm_est.setInputCloud (src);
  norm_est.compute (*points_with_normals_src);
  pcl::copyPointCloud (*src, *points_with_normals_src);

  norm_est.setInputCloud (tgt);
  norm_est.compute (*points_with_normals_tgt);
  pcl::copyPointCloud (*tgt, *points_with_normals_tgt);

  //
  // Instantiate our custom point representation (defined above) ...
  MyPointRepresentation point_representation;
  // ... and weight the 'curvature' dimension so that it is balanced against x, y, and z
  float alpha[4] = {1.0, 1.0, 1.0, 1.0};
  point_representation.setRescaleValues (alpha);

  //
  // Align
  pcl::IterativeClosestPointNonLinear<PointNormalT, PointNormalT> reg;
  reg.setTransformationEpsilon (1e-6);
  // Set the maximum distance between two correspondences (src<->tgt) to 10cm
  // Note: adjust this based on the size of your datasets
  reg.setMaxCorrespondenceDistance (0.1);  
  // Set the point representation
  reg.setPointRepresentation (boost::make_shared<const MyPointRepresentation> (point_representation));

  reg.setInputSource (points_with_normals_src);
  reg.setInputTarget (points_with_normals_tgt);



  //
  // Run the same optimization in a loop and visualize the results
  Eigen::Matrix4f Ti = Eigen::Matrix4f::Identity (), prev, targetToSource;
  PointCloudWithNormals::Ptr reg_result = points_with_normals_src;
  reg.setMaximumIterations (2);
  for (int i = 0; i < 30; ++i)
  {
    PCL_INFO ("Iteration Nr. %d.\n", i);

    // save cloud for visualization purpose
    points_with_normals_src = reg_result;

    // Estimate
    reg.setInputSource (points_with_normals_src);
    reg.align (*reg_result);

		//accumulate transformation between each Iteration
    Ti = reg.getFinalTransformation () * Ti;

		//if the difference between this transformation and the previous one
		//is smaller than the threshold, refine the process by reducing
		//the maximal correspondence distance
    if (fabs ((reg.getLastIncrementalTransformation () - prev).sum ()) < reg.getTransformationEpsilon ())
      reg.setMaxCorrespondenceDistance (reg.getMaxCorrespondenceDistance () - 0.001);
    
    prev = reg.getLastIncrementalTransformation ();

    // visualize current state
    showCloudsRight(points_with_normals_tgt, points_with_normals_src);
  }

	//
  // Get the transformation from target to source
  targetToSource = Ti.inverse();

  //
  // Transform target back in source frame
  pcl::transformPointCloud (*cloud_tgt, *output, targetToSource);

  p->removePointCloud ("source");
  p->removePointCloud ("target");

  PointCloudColorHandlerCustom<PointT> cloud_tgt_h (output, 0, 255, 0);
  PointCloudColorHandlerCustom<PointT> cloud_src_h (cloud_src, 255, 0, 0);
  p->addPointCloud (output, cloud_tgt_h, "target", vp_2);
  p->addPointCloud (cloud_src, cloud_src_h, "source", vp_2);

	PCL_INFO ("Press q to continue the registration.\n");
  p->spin ();

  p->removePointCloud ("source"); 
  p->removePointCloud ("target");

  //add the source to the transformed target
  *output += *cloud_src;
  
  final_transform = targetToSource;
 }


/* ---[ */
int main (int argc, char** argv)
{
  // Load data
  std::vector<PCD, Eigen::aligned_allocator<PCD> > data;
  loadData (argc, argv, data);

  // Check user input
  if (data.empty ())
  {
    PCL_ERROR ("Syntax is: %s <source.pcd> <target.pcd> [*]", argv[0]);
    PCL_ERROR ("[*] - multiple files can be added. The registration results of (i, i+1) will be registered against (i+2), etc");
    return (-1);
  }
  PCL_INFO ("Loaded %d datasets.", (int)data.size ());
  
  // Create a PCLVisualizer object
  p = new pcl::visualization::PCLVisualizer (argc, argv, "Pairwise Incremental Registration example");
  p->createViewPort (0.0, 0, 0.5, 1.0, vp_1);
  p->createViewPort (0.5, 0, 1.0, 1.0, vp_2);

	PointCloud::Ptr result (new PointCloud), source, target;
  Eigen::Matrix4f GlobalTransform = Eigen::Matrix4f::Identity (), pairTransform;
  
  for (size_t i = 1; i < data.size (); ++i)
  {
    source = data[i-1].cloud;
    target = data[i].cloud;

    // Add visualization data
    showCloudsLeft(source, target);

    PointCloud::Ptr temp (new PointCloud);
    PCL_INFO ("Aligning %s (%d) with %s (%d).\n", data[i-1].f_name.c_str (), source->points.size (), data[i].f_name.c_str (), target->points.size ());
    pairAlign (source, target, temp, pairTransform, true);

    //transform current pair into the global transform
    pcl::transformPointCloud (*temp, *result, GlobalTransform);

    //update the global transform
    GlobalTransform = GlobalTransform * pairTransform;

		//save aligned pair, transformed into the first cloud's frame
    std::stringstream ss;
    ss << i << ".pcd";
    pcl::io::savePCDFile (ss.str (), *result, true);

  }
}
/* ]--- */

The explanation

Let’s breakdown this code piece by piece.
We will first make a quick run through the declarations. Then, we will study the registering functions.

Declarations

These are the header files that contain the definitions for all of the classes which we will use.

#include <boost/make_shared.hpp>
#include <pcl/point_types.h>
#include <pcl/point_cloud.h>
#include <pcl/point_representation.h>

#include <pcl/io/pcd_io.h>

#include <pcl/filters/voxel_grid.h>
#include <pcl/filters/filter.h>

#include <pcl/features/normal_3d.h>

#include <pcl/registration/icp.h>
#include <pcl/registration/icp_nl.h>
#include <pcl/registration/transforms.h>

#include <pcl/visualization/pcl_visualizer.h>

Creates global variables for visualization purpose

// This is a tutorial so we can afford having global variables 
	//our visualizer
	pcl::visualization::PCLVisualizer *p;
	//its left and right viewports
	int vp_1, vp_2;

Declare a convenient structure that allow us to handle clouds as couple [points - filename]

struct PCD
{
  PointCloud::Ptr cloud;
  std::string f_name;

  PCD() : cloud (new PointCloud) {};
};

Define a new point representation (see Adding your own custom PointT type for more on the subject)

// Define a new point representation for < x, y, z, curvature >
class MyPointRepresentation : public pcl::PointRepresentation <PointNormalT>
{
  using pcl::PointRepresentation<PointNormalT>::nr_dimensions_;
public:
  MyPointRepresentation ()
  {
    // Define the number of dimensions
    nr_dimensions_ = 4;
  }

  // Override the copyToFloatArray method to define our feature vector
  virtual void copyToFloatArray (const PointNormalT &p, float * out) const
  {
    // < x, y, z, curvature >
    out[0] = p.x;
    out[1] = p.y;
    out[2] = p.z;
    out[3] = p.curvature;
  }
};

Registering functions

Let’s see how are our functions organized.

The main function checks the user input, loads the data in a vector and starts the pair-registration process..
After a transform is found for a pair, the pair is transformed into the first cloud’s frame, and the global transformation is updated.
int main (int argc, char** argv)
{
  // Load data
  std::vector<PCD, Eigen::aligned_allocator<PCD> > data;
  loadData (argc, argv, data);

  // Check user input
  if (data.empty ())
  {
    PCL_ERROR ("Syntax is: %s <source.pcd> <target.pcd> [*]", argv[0]);
    PCL_ERROR ("[*] - multiple files can be added. The registration results of (i, i+1) will be registered against (i+2), etc");
    return (-1);
  }
  PCL_INFO ("Loaded %d datasets.", (int)data.size ());
  
  // Create a PCLVisualizer object
  p = new pcl::visualization::PCLVisualizer (argc, argv, "Pairwise Incremental Registration example");
  p->createViewPort (0.0, 0, 0.5, 1.0, vp_1);
  p->createViewPort (0.5, 0, 1.0, 1.0, vp_2);

	PointCloud::Ptr result (new PointCloud), source, target;
  Eigen::Matrix4f GlobalTransform = Eigen::Matrix4f::Identity (), pairTransform;
  
  for (size_t i = 1; i < data.size (); ++i)
  {
    source = data[i-1].cloud;
    target = data[i].cloud;

    // Add visualization data
    showCloudsLeft(source, target);

    PointCloud::Ptr temp (new PointCloud);
    PCL_INFO ("Aligning %s (%d) with %s (%d).\n", data[i-1].f_name.c_str (), source->points.size (), data[i].f_name.c_str (), target->points.size ());
    pairAlign (source, target, temp, pairTransform, true);

    //transform current pair into the global transform
    pcl::transformPointCloud (*temp, *result, GlobalTransform);

    //update the global transform
    GlobalTransform = GlobalTransform * pairTransform;

		//save aligned pair, transformed into the first cloud's frame
    std::stringstream ss;
    ss << i << ".pcd";
    pcl::io::savePCDFile (ss.str (), *result, true);

  }
}
/* ]--- */
Loading data is pretty straightforward. We iterate other the program’s arguments.
For each argument, we check if it links to a pcd file. If so, we create a PCD object that is added to the vector of clouds.
void loadData (int argc, char **argv, std::vector<PCD, Eigen::aligned_allocator<PCD> > &models)
{
  std::string extension (".pcd");
  // Suppose the first argument is the actual test model
  for (int i = 1; i < argc; i++)
  {
    std::string fname = std::string (argv[i]);
    // Needs to be at least 5: .plot
    if (fname.size () <= extension.size ())
      continue;

    std::transform (fname.begin (), fname.end (), fname.begin (), (int(*)(int))tolower);

    //check that the argument is a pcd file
    if (fname.compare (fname.size () - extension.size (), extension.size (), extension) == 0)
    {
      // Load the cloud and saves it into the global list of models
      PCD m;
      m.f_name = argv[i];
      pcl::io::loadPCDFile (argv[i], *m.cloud);
      //remove NAN points from the cloud
      std::vector<int> indices;
      pcl::removeNaNFromPointCloud(*m.cloud,*m.cloud, indices);

      models.push_back (m);
    }
  }
}

We now arrive to the actual pair registration.

void pairAlign (const PointCloud::Ptr cloud_src, const PointCloud::Ptr cloud_tgt, PointCloud::Ptr output, Eigen::Matrix4f &final_transform, bool downsample = false)
First, we optionally down sample our clouds. This is useful in the case of large datasets. Curvature are then computed (for visualization purpose).
We then create the ICP object, set its parameters and link it to the two clouds we wish to align. Remember to adapt these to your own datasets.
// Align
pcl::IterativeClosestPointNonLinear<PointNormalT, PointNormalT> reg;
reg.setTransformationEpsilon (1e-6);
// Set the maximum distance between two correspondences (src<->tgt) to 10cm
// Note: adjust this based on the size of your datasets
reg.setMaxCorrespondenceDistance (0.1);
// Set the point representation
reg.setPointRepresentation (boost::make_shared<const MyPointRepresentation> (point_representation));

reg.setInputCloud (points_with_normals_src);
reg.setInputTarget (points_with_normals_tgt);
As this is a tutorial, we wish to display the intermediate of the registration process.
To this end, the ICP is limited to 2 registration iterations:
reg.setMaximumIterations (2);

And is manually iterated (30 times in our case):

for (int i = 0; i < 30; ++i)
{
        [...]
        points_with_normals_src = reg_result;
        // Estimate
        reg.setInputCloud (points_with_normals_src);
        reg.align (*reg_result);
        [...]
}

During each iteration, we keep track of and accumulate the transformations returned by the ICP:

Eigen::Matrix4f Ti = Eigen::Matrix4f::Identity (), prev, targetToSource;
[...]
for (int i = 0; i < 30; ++i)
{
       [...]
       Ti = reg.getFinalTransformation () * Ti;
       [...]
}
If the difference between the transform found at iteration N and the one found at iteration N-1 is smaller than the transform threshold passed to ICP,
we refine the matching process by choosing closer correspondences between the source and the target:
for (int i = 0; i < 30; ++i)
{
 [...]
 if (fabs ((reg.getLastIncrementalTransformation () - prev).sum ()) < reg.getTransformationEpsilon ())
   reg.setMaxCorrespondenceDistance (reg.getMaxCorrespondenceDistance () - 0.001);

 prev = reg.getLastIncrementalTransformation ();
 [...]
}
Once the best transformation has been found, we invert it (to get the transformation from target to source) and apply it to the target cloud.
The transformed target is then added to the source and returned to the main function with the transformation.
//
// Get the transformation from target to source
targetToSource = Ti.inverse();

//
// Transform target back in source frame
pcl::transformPointCloud (*cloud_tgt, *output, targetToSource);
[...]
*output += *cloud_tgt;
final_transform = targetToSource;

Compiling and running the program

Create a file named pairwise_incremental_registration.cpp and paste the full code in it.

Create CMakeLists.txt file and add the following line in it:

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cmake_minimum_required(VERSION 2.6 FATAL_ERROR)

project(tuto-pairwise)

find_package(PCL 1.4 REQUIRED)

include_directories(${PCL_INCLUDE_DIRS})
link_directories(${PCL_LIBRARY_DIRS})
add_definitions(${PCL_DEFINITIONS})

add_executable (pairwise_incremental_registration pairwise_incremental_registration.cpp)
target_link_libraries (pairwise_incremental_registration ${PCL_LIBRARIES})

Copy the files from github.com/PointCloudLibrary/data/tree/master/tutorials/pairwise in your working folder.

After you have made the executable (cmake ., make), you can run it. Simply do:

$ ./pairwise_incremental_registration capture000[1-5].pcd

You will see something similar to:

_images/1.png _images/2.png _images/3.png

Visualize the final results by running:

$ pcl_viewer 1.pcd 2.pcd 3.pcd 4.pcd
_images/4.png _images/5.png

NOTE: if you only see a black screen in your viewer, try adjusting the camera position with your mouse. This may happen with the sample PCD files of this tutorial.