small_gicp::align takes two point clouds (std::vectors of Eigen::Vector(3|4)(f|d)) and returns a registration result (estimated transformation and some information on the optimization result). This is the easiest way to use small_gicp but causes an overhead for duplicated preprocessing.

#include <small_gicp/registration/registration_helper.hpp>

std::vector<Eigen::Vector3d> target_points = ...;   // Any of Eigen::Vector(3|4)(f|d) can be used
std::vector<Eigen::Vector3d> source_points = ...;   // 

RegistrationSetting setting;
setting.num_threads = 4;                    // Number of threads to be used
setting.downsampling_resolution = 0.25;     // Downsampling resolution
setting.max_correspondence_distance = 1.0;  // Maximum correspondence distance between points (e.g., triming threshold)

Eigen::Isometry3d init_T_target_source = Eigen::Isometry3d::Identity();
RegistrationResult result = align(target_points, source_points, init_T_target_source, setting);

Eigen::Isometry3d T = result.T_target_source;  // Estimated transformation
size_t num_inliers = result.num_inliers;       // Number of inlier source points
Eigen::Matrix<double, 6, 6> H = result.H;      // Final Hessian matrix (6x6)

There is also a way to perform preprocessing and registration separately. This enables saving time for preprocessing in case registration is performed several times for the same point cloud (e.g., typical odometry estimation based on scan-to-scan matching).

#include <small_gicp/registration/registration_helper.hpp>

std::vector<Eigen::Vector3d> target_points = ...;   // Any of Eigen::Vector(3|4)(f|d) can be used
std::vector<Eigen::Vector3d> source_points = ...;   // 

int num_threads = 4;                    // Number of threads to be used
double downsampling_resolution = 0.25;  // Downsampling resolution
int num_neighbors = 10;                 // Number of neighbor points used for normal and covariance estimation

// std::pair<PointCloud::Ptr, KdTree<PointCloud>::Ptr>
auto [target, target_tree] = preprocess_points(target_points, downsampling_resolution, num_neighbors, num_threads);
auto [source, source_tree] = preprocess_points(source_points, downsampling_resolution, num_neighbors, num_threads);

RegistrationSetting setting;
setting.num_threads = num_threads;
setting.max_correspondence_distance = 1.0;  // Maximum correspondence distance between points (e.g., triming threshold)

Eigen::Isometry3d init_T_target_source = Eigen::Isometry3d::Identity();
RegistrationResult result = align(*target, *source, *target_tree, init_T_target_source, setting);

Eigen::Isometry3d T = result.T_target_source;  // Estimated transformation
size_t num_inliers = result.num_inliers;       // Number of inlier source points
Eigen::Matrix<double, 6, 6> H = result.H;      // Final Hessian matrix (6x6)

#include <small_gicp/pcl/pcl_registration.hpp>

pcl::PointCloud<pcl::PointXYZ>::Ptr raw_target = ...;
pcl::PointCloud<pcl::PointXYZ>::Ptr raw_source = ...;

// small_gicp::voxelgrid_downsampling can directly operate on pcl::PointCloud.
pcl::PointCloud<pcl::PointXYZ>::Ptr target = voxelgrid_sampling_omp(*raw_target, 0.25);
pcl::PointCloud<pcl::PointXYZ>::Ptr source = voxelgrid_sampling_omp(*raw_source, 0.25);

// RegistrationPCL is derived from pcl::Registration and has mostly the same interface as pcl::GeneralizedIterativeClosestPoint.
RegistrationPCL<pcl::PointXYZ, pcl::PointXYZ> reg;
reg.setNumThreads(4);
reg.setCorrespondenceRandomness(20);
reg.setMaxCorrespondenceDistance(1.0);
reg.setVoxelResolution(1.0);
reg.setRegistrationType("VGICP");  // or "GICP" (default = "GICP")

// Set input point clouds.
reg.setInputTarget(target);
reg.setInputSource(source);

// Align point clouds.
auto aligned = pcl::make_shared<pcl::PointCloud<pcl::PointXYZ>>();
reg.align(*aligned);

// Swap source and target and align again.
// This is useful when you want to re-use preprocessed point clouds for successive registrations (e.g., odometry estimation).
reg.swapSourceAndTarget();
reg.align(*aligned);

It is also possible to directly feed pcl::PointCloud to small_gicp::Registration. Because all preprocessed data are exposed in this way, you can easily re-use them to obtain the best efficiency.

#include <small_gicp/pcl/pcl_point.hpp>
#include <small_gicp/pcl/pcl_point_traits.hpp>

pcl::PointCloud<pcl::PointXYZ>::Ptr raw_target = ...;
pcl::PointCloud<pcl::PointXYZ>::Ptr raw_source = ...;

// Downsample points and convert them into pcl::PointCloud<pcl::PointCovariance>.
pcl::PointCloud<pcl::PointCovariance>::Ptr target = voxelgrid_sampling_omp<pcl::PointCloud<pcl::PointXYZ>, pcl::PointCloud<pcl::PointCovariance>>(*raw_target, 0.25);
pcl::PointCloud<pcl::PointCovariance>::Ptr source = voxelgrid_sampling_omp<pcl::PointCloud<pcl::PointXYZ>, pcl::PointCloud<pcl::PointCovariance>>(*raw_source, 0.25);

// Estimate covariances of points.
const int num_threads = 4;
const int num_neighbors = 20;
estimate_covariances_omp(*target, num_neighbors, num_threads);
estimate_covariances_omp(*source, num_neighbors, num_threads);

// Create KdTree for target and source.
auto target_tree = std::make_shared<KdTree<pcl::PointCloud<pcl::PointCovariance>>>(target, KdTreeBuilderOMP(num_threads));
auto source_tree = std::make_shared<KdTree<pcl::PointCloud<pcl::PointCovariance>>>(source, KdTreeBuilderOMP(num_threads));

Registration<GICPFactor, ParallelReductionOMP> registration;
registration.reduction.num_threads = num_threads;
registration.rejector.max_dist_sq = 1.0;

// Align point clouds. Note that the input point clouds are pcl::PointCloud<pcl::PointCovariance>.
auto result = registration.align(*target, *source, *target_tree, Eigen::Isometry3d::Identity());

#include <small_gicp/ann/kdtree_omp.hpp>
#include <small_gicp/points/point_cloud.hpp>
#include <small_gicp/factors/gicp_factor.hpp>
#include <small_gicp/util/normal_estimation_omp.hpp>
#include <small_gicp/registration/reduction_omp.hpp>
#include <small_gicp/registration/registration.hpp>

std::vector<Eigen::Vector3d> target_points = ...;   // Any of Eigen::Vector(3|4)(f|d) can be used
std::vector<Eigen::Vector3d> source_points = ...;   // 

int num_threads = 4;
double downsampling_resolution = 0.25;
int num_neighbors = 10;
double max_correspondence_distance = 1.0;

// Convert to small_gicp::PointCloud
auto target = std::make_shared<PointCloud>(target_points);
auto source = std::make_shared<PointCloud>(source_points);

// Downsampling
target = voxelgrid_sampling_omp(*target, downsampling_resolution, num_threads);
source = voxelgrid_sampling_omp(*source, downsampling_resolution, num_threads);

// Create KdTree
auto target_tree = std::make_shared<KdTree<PointCloud>>(target, KdTreeBuilderOMP(num_threads));
auto source_tree = std::make_shared<KdTree<PointCloud>>(source, KdTreeBuilderOMP(num_threads));

// Estimate point covariances
estimate_covariances_omp(*target, *target_tree, num_neighbors, num_threads);
estimate_covariances_omp(*source, *source_tree, num_neighbors, num_threads);

// GICP + OMP-based parallel reduction
Registration<GICPFactor, ParallelReductionOMP> registration;
registration.reduction.num_threads = num_threads;
registration.rejector.max_dist_sq = max_correspondence_distance * max_correspondence_distance;

// Align point clouds
Eigen::Isometry3d init_T_target_source = Eigen::Isometry3d::Identity();
auto result = registration.align(*target, *source, *target_tree, init_T_target_source);

Eigen::Isometry3d T = result.T_target_source;  // Estimated transformation
size_t num_inliers = result.num_inliers;       // Number of inlier source points
Eigen::Matrix<double, 6, 6> H = result.H;      // Final Hessian matrix (6x6)

See 03_registration_template.cpp for more detailed customization examples.

Example A : Perform registration with numpy arrays

# Align two point clouds using various ICP-like algorithms.
# 
# Parameters
# ----------
# target_points : NDArray[np.float64]
#     Nx3 or Nx4 matrix representing the target point cloud.
# source_points : NDArray[np.float64]
#     Nx3 or Nx4 matrix representing the source point cloud.
# init_T_target_source : np.ndarray[np.float64]
#     4x4 matrix representing the initial transformation from target to source.
# registration_type : str = 'GICP'
#     Type of registration algorithm to use ('ICP', 'PLANE_ICP', 'GICP', 'VGICP').
# voxel_resolution : float = 1.0
#     Resolution of voxels used for correspondence search (used only in VGICP).
# downsampling_resolution : float = 0.25
#     Resolution for downsampling the point clouds.
# max_correspondence_distance : float = 1.0
#     Maximum distance for matching points between point clouds.
# num_threads : int = 1
#     Number of threads to use for parallel processing.
# 
# Returns
# -------
# RegistrationResult
#     Object containing the final transformation matrix and convergence status.
result = small_gicp.align(target_raw_numpy, source_raw_numpy, downsampling_resolution=0.25)

result.T_target_source  # Estimated transformation (4x4 numpy array)
result.converged        # If true, the optimization converged successfully
result.iterations       # Number of iterations the optimization took
result.num_inliers      # Number of inlier points
result.H                # Final Hessian matrix (6x6 matrix)
result.b                # Final information vector (6D vector)
result.e                # Final error (float)

Example B : Perform preprocessing and registration separately

# Preprocess point cloud (downsampling, kdtree construction, and normal/covariance estimation)
#
# Parameters
# ----------
# points : NDArray[np.float64]
#     Nx3 or Nx4 matrix representing the point cloud.
# downsampling_resolution : float = 0.1
#     Resolution for downsampling the point clouds.
# num_neighbors : int = 20
#     Number of neighbor points to usefor point normal/covariance estimation.
# num_threads : int = 1
#     Number of threads to use for parallel processing.
# 
# Returns
# -------
# PointCloud
#     Downsampled point cloud with estimated normals and covariances.
# KdTree
#     KdTree for the downsampled point cloud
target, target_tree = small_gicp.preprocess_points(target_raw_numpy, downsampling_resolution=0.25)
source, source_tree = small_gicp.preprocess_points(source_raw_numpy, downsampling_resolution=0.25)

# `target` and `source` are small_gicp.PointCloud with the following methods
target.size()           # Number of points
target.points()         # Nx4 numpy array   [x, y, z, 1] x N
target.normals()        # Nx4 numpy array   [nx, ny, nz, 0] x N
target.covs()           # Array of 4x4 covariance matrices

#  Align two point clouds using specified ICP-like algorithms, utilizing point cloud and KD-tree inputs.
#
#  Parameters
#  ----------
#  target : PointCloud::ConstPtr
#      Pointer to the target point cloud.
#  source : PointCloud::ConstPtr
#      Pointer to the source point cloud.
#  target_tree : KdTree<PointCloud>::ConstPtr, optional
#      Pointer to the KD-tree of the target for nearest neighbor search. If nullptr, a new tree is built.
#  init_T_target_source : NDArray[np.float64]
#      4x4 matrix representing the initial transformation from target to source.
#  registration_type : str = 'GICP'
#      Type of registration algorithm to use ('ICP', 'PLANE_ICP', 'GICP').
#  max_correspondence_distance : float = 1.0
#      Maximum distance for corresponding point pairs.
#  num_threads : int = 1
#      Number of threads to use for computation.
# 
#  Returns
#  -------
#  RegistrationResult
#      Object containing the final transformation matrix and convergence status.
result = small_gicp.align(target, source, target_tree)

Example C : Perform each of preprocessing steps one-by-one

# Convert numpy arrays (Nx3 or Nx4) to small_gicp.PointCloud
target_raw = small_gicp.PointCloud(target_raw_numpy)
source_raw = small_gicp.PointCloud(source_raw_numpy)

# Downsampling
target = small_gicp.voxelgrid_sampling(target_raw, 0.25)
source = small_gicp.voxelgrid_sampling(source_raw, 0.25)

# KdTree construction
target_tree = small_gicp.KdTree(target)
source_tree = small_gicp.KdTree(source)

# Estimate covariances
small_gicp.estimate_covariances(target, target_tree)
small_gicp.estimate_covariances(source, source_tree)

# Align point clouds
result = small_gicp.align(target, source, target_tree)

Example D: Example with Open3D

target_o3d = open3d.io.read_point_cloud('small_gicp/data/target.ply').paint_uniform_color([0, 1, 0])
source_o3d = open3d.io.read_point_cloud('small_gicp/data/source.ply').paint_uniform_color([0, 0, 1])

target, target_tree = small_gicp.preprocess_points(numpy.asarray(target_o3d.points), downsampling_resolution=0.25)
source, source_tree = small_gicp.preprocess_points(numpy.asarray(source_o3d.points), downsampling_resolution=0.25)
result = small_gicp.align(target, source, target_tree)

source_o3d.transform(result.T_target_source)
open3d.visualization.draw_geometries([target_o3d, source_o3d])