Point Cloud

This tutorial demonstrates basic usage of a point cloud.

Visualize point cloud

The first part of the tutorial reads a point cloud and visualizes it.

print("Load a ply point cloud, print it, and render it")
pcd = o3d.io.read_point_cloud("../../TestData/fragment.ply")
print(pcd)
print(np.asarray(pcd.points))
o3d.visualization.draw_geometries([pcd], zoom=0.3412,
                                  front=[0.4257, -0.2125, -0.8795],
                                  lookat=[2.6172, 2.0475, 1.532],
                                  up=[-0.0694, -0.9768, 0.2024])

Load a ply point cloud, print it, and render it
geometry::PointCloud with 196133 points.
[[0.65234375 0.84686458 2.37890625]
 [0.65234375 0.83984375 2.38430572]
 [0.66737998 0.83984375 2.37890625]
 ...
 [2.00839925 2.39453125 1.88671875]
 [2.00390625 2.39488506 1.88671875]
 [2.00390625 2.39453125 1.88793314]]

read_point_cloud reads a point cloud from a file. It tries to decode the file based on the extension name. The supported extension names are: pcd, ply, xyz, xyzrgb, xyzn, pts.

draw_geometries visualizes the point cloud. Use mouse/trackpad to see the geometry from different view point.

It looks like a dense surface, but it is actually a point cloud rendered as surfels. The GUI supports various keyboard functions. One of them, the - key reduces the size of the points (surfels).

Note:

Press h key to print out a complete list of keyboard instructions for the GUI. For more information of the visualization GUI, refer to Visualization and Customized visualization.

Note:

On OS X, the GUI window may not receive keyboard event. In this case, try to launch Python with pythonw instead of python.

Voxel downsampling

Voxel downsampling uses a regular voxel grid to create a uniformly downsampled point cloud from an input point cloud. It is often used as a pre-processing step for many point cloud processing tasks. The algorithm operates in two steps:

1. Points are bucketed into voxels.

2. Each occupied voxel generates exact one point by averaging all points inside.

print("Downsample the point cloud with a voxel of 0.05")
downpcd = pcd.voxel_down_sample(voxel_size=0.05)
o3d.visualization.draw_geometries([downpcd], zoom=0.3412,
                                  front=[0.4257, -0.2125, -0.8795],
                                  lookat=[2.6172, 2.0475, 1.532],
                                  up=[-0.0694, -0.9768, 0.2024])

Downsample the point cloud with a voxel of 0.05

Vertex normal estimation

Another basic operation for point cloud is point normal estimation. Press n to see point normal. Key - and key + can be used to control the length of the normal.

print("Recompute the normal of the downsampled point cloud")
downpcd.estimate_normals(search_param=o3d.geometry.KDTreeSearchParamHybrid(radius=0.1, max_nn=30))
o3d.visualization.draw_geometries([downpcd], zoom=0.3412,
                                  front=[0.4257, -0.2125, -0.8795],
                                  lookat=[2.6172, 2.0475, 1.532],
                                  up=[-0.0694, -0.9768, 0.2024],
                                  point_show_normal=True)

Recompute the normal of the downsampled point cloud

estimate_normals computes normal for every point. The function finds adjacent points and calculate the principal axis of the adjacent points using covariance analysis.

The function takes an instance of KDTreeSearchParamHybrid class as an argument. The two key arguments radius = 0.1 and max_nn = 30 specifies search radius and maximum nearest neighbor. It has 10cm of search radius, and only considers up to 30 neighbors to save computation time.

Note:

The covariance analysis algorithm produces two opposite directions as normal candidates. Without knowing the global structure of the geometry, both can be correct. This is known as the normal orientation problem. Open3D tries to orient the normal to align with the original normal if it exists. Otherwise, Open3D does a random guess. Further orientation functions such as orient_normals_to_align_with_direction and orient_normals_towards_camera_location need to be called if the orientation is a concern.

Access estimated vertex normal

Estimated normal vectors can be retrieved by normals variable of downpcd.

print("Print a normal vector of the 0th point")
print(downpcd.normals[0])

Print a normal vector of the 0th point
[-0.21838377 -0.94240442 -0.25334252]

To check out other variables, please use help(downpcd). Normal vectors can be transformed as a numpy array using np.asarray.

print("Print the normal vectors of the first 10 points")
print(np.asarray(downpcd.normals)[:10, :])

Print the normal vectors of the first 10 points
[[-0.21838377 -0.94240442 -0.25334252]
 [-0.39147152 -0.43746664 -0.8095511 ]
 [-0.00694405 -0.99478075 -0.10179902]
 [-0.00399871 -0.99965423 -0.02598917]
 [-0.93768261 -0.07378998  0.3395679 ]
 [-0.43476205 -0.62438493 -0.64894177]
 [-0.09739809 -0.9928602  -0.06886388]
 [-0.11728718 -0.95516445 -0.27185399]
 [-0.01038945 -0.99968858 -0.02268921]
 [-0.00816546 -0.99965616 -0.02491762]]

Check Working with NumPy for more examples regarding numpy array.

Crop point cloud

print("Load a polygon volume and use it to crop the original point cloud")
vol = o3d.visualization.read_selection_polygon_volume("../../TestData/Crop/cropped.json")
chair = vol.crop_point_cloud(pcd)
o3d.visualization.draw_geometries([chair], zoom=0.7,
                                  front=[0.5439, -0.2333, -0.8060],
                                  lookat=[2.4615, 2.1331, 1.338],
                                  up=[-0.1781, -0.9708, 0.1608])

Load a polygon volume and use it to crop the original point cloud

read_selection_polygon_volume reads a json file that specifies polygon selection area. vol.crop_point_cloud(pcd) filters out points. Only the chair remains.

Paint point cloud

print("Paint chair")
chair.paint_uniform_color([1, 0.706, 0])
o3d.visualization.draw_geometries([chair], zoom=0.7,
                                  front=[0.5439, -0.2333, -0.8060],
                                  lookat=[2.4615, 2.1331, 1.338],
                                  up=[-0.1781, -0.9708, 0.1608])

Paint chair

paint_uniform_color paints all the points to a uniform color. The color is in RGB space, [0, 1] range.

Bounding Volumes

The PointCloud geometry type has bounding volumes as all other geometry types in Open3D. Currently, Open3D implements an AxisAlignedBoundingBox and an OrientedBoundingBox that can also be used to crop the geometry.

aabb = chair.get_axis_aligned_bounding_box()
aabb.color = (1,0,0)
obb = chair.get_oriented_bounding_box()
obb.color = (0,1,0)
o3d.visualization.draw_geometries([chair, aabb, obb], zoom=0.7,
                                  front=[0.5439, -0.2333, -0.8060],
                                  lookat=[2.4615, 2.1331, 1.338],
                                  up=[-0.1781, -0.9708, 0.1608])

Convex hull

The convex hull of a point cloud is the smallest convex set that contains all points. Open3D contains the method compute_convex_hull that computes the convex hull for example of a point cloud. The implementation is based on Qhull

In the example code below we first sample a point cloud from a mesh and compute the convex hull that is returned as triangle mesh. Then, we visualize the convex hull as a red LineSet.

pcl = o3dtut.get_bunny_mesh().sample_points_poisson_disk(number_of_points=2000)
hull, _ = pcl.compute_convex_hull()
hull_ls = o3d.geometry.LineSet.create_from_triangle_mesh(hull)
hull_ls.paint_uniform_color((1, 0, 0))
o3d.visualization.draw_geometries([pcl, hull_ls])

downloading bunny mesh
extract bunny mesh

DBSCAN clustering

Given a point clound for example from a depth sensor we want to group local point clouds together. For this purpose, we can use clustering algorithms. Open3D implements DBSCAN [Ester1996] that is a density based clustering algorithm. The algorithm is implemented in cluster_dbscan and requires two parameters. eps defines the distance to neighbours in a cluster and min_points defines the minimun number of points required to form a cluster. The function returns labels, where the label -1 indicates noise.

pcd = o3d.io.read_point_cloud("../../TestData/fragment.ply")

with o3d.utility.VerbosityContextManager(o3d.utility.VerbosityLevel.Debug) as cm:
    labels = np.array(pcd.cluster_dbscan(eps=0.02, min_points=10, print_progress=True))

max_label = labels.max()
print(f"point cloud has {max_label + 1} clusters")
colors = plt.get_cmap("tab20")(labels / (max_label if max_label > 0 else 1))
colors[labels < 0] = 0
pcd.colors = o3d.utility.Vector3dVector(colors[:, :3])
o3d.visualization.draw_geometries([pcd], zoom=0.455,
                                  front=[-0.4999, -0.1659, -0.8499],
                                  lookat=[2.1813, 2.0619, 2.0999],
                                  up=[0.1204, -0.9852, 0.1215])

point cloud has 10 clusters

Note:

This algorithm precomputes all neighbours in the epsilon radius for all points. This can require a lot of memory if epsilon is choosen too large.

Plane segmentation

Open3D contains also support to segment geometric primitives from point clouds using RANSAC. To find the plane with the largest support in the point cloud, we can use segement_plane. The method has three arguments. distance_threshold defines the maximum distance a point can have to an estimated plane to be considered an inlier, ransac_n defines the number of points that are randomly sampled to estimate a plane, and num_iterations defines how often a random plane is sampled and verified. The function than returns the plane as \((a,b,c,d)\) such that for each point \((x,y,z)\) on the plane we have \(ax + by + cz + d = 0\). The function further retuns a list of indices of the inlier points.

pcd = o3d.io.read_point_cloud("../../TestData/fragment.pcd")
plane_model, inliers = pcd.segment_plane(distance_threshold=0.01,
                                         ransac_n=3,
                                         num_iterations=1000)
[a, b, c, d] = plane_model
print(f"Plane equation: {a:.2f}x + {b:.2f}y + {c:.2f}z + {d:.2f} = 0")

inlier_cloud = pcd.select_by_index(inliers)
inlier_cloud.paint_uniform_color([1.0, 0, 0])
outlier_cloud = pcd.select_by_index(inliers, invert=True)
o3d.visualization.draw_geometries([inlier_cloud, outlier_cloud], zoom=0.8,
                                  front=[-0.4999, -0.1659, -0.8499],
                                  lookat=[2.1813, 2.0619, 2.0999],
                                  up=[0.1204, -0.9852, 0.1215])

Plane equation: -0.06x + -0.10y + 0.99z + -1.06 = 0

Hidden point removal

Imagine you want to render a point cloud from a given view point, but points from the background leak into the foreground because they are not occluded by other points. For this purpose we can apply a hidden point removal algorithm. In Open3D the method by [Katz2007] is implemented that approximates the visibility of a point cloud from a given view without surface reconstruction or normal estimation.

print("Convert mesh to a point cloud and estimate dimensions")
pcd = o3dtut.get_armadillo_mesh().sample_points_poisson_disk(5000)
diameter = np.linalg.norm(np.asarray(pcd.get_max_bound()) - np.asarray(pcd.get_min_bound()))
o3d.visualization.draw_geometries([pcd])

Convert mesh to a point cloud and estimate dimensions
downloading armadillo mesh
extract armadillo mesh

print("Define parameters used for hidden_point_removal")
camera = [0, 0, diameter]
radius = diameter * 100

print("Get all points that are visible from given view point")
_, pt_map = pcd.hidden_point_removal(camera, radius)

print("Visualize result")
pcd = pcd.select_by_index(pt_map)
o3d.visualization.draw_geometries([pcd])

Define parameters used for hidden_point_removal
Get all points that are visible from given view point
Visualize result