多路配准

译注

本篇译自 Open3D 官方教程 Multiway registration（0.19.0）。代码、输出、API 名称保持原文未作改动。

多路配准（multiway registration）是把多块几何体对齐到全局空间的过程。通常，输入是一组几何体（例如点云或 RGBD 图像）$\{\mathbf{P}_{i}\}$，输出是一组刚性变换 $\{\mathbf{T}_{i}\}$，使得变换后的点云 $\{\mathbf{T}_{i}\mathbf{P}_{i}\}$ 在全局空间中对齐。

Open3D 通过位姿图优化（pose graph optimization）来实现多路配准，其后端实现了 [Choi2015] 提出的技术。

输入

教程代码的第一部分从文件中读取三个点云，对它们进行下采样并一起可视化。它们处于未对齐状态。

def load_point_clouds(voxel_size=0.0):
    pcds = []
    demo_icp_pcds = o3d.data.DemoICPPointClouds()
    for path in demo_icp_pcds.paths:
        pcd = o3d.io.read_point_cloud(path)
        pcd_down = pcd.voxel_down_sample(voxel_size=voxel_size)
        pcds.append(pcd_down)
    return pcds

voxel_size = 0.02
pcds_down = load_point_clouds(voxel_size)
o3d.visualization.draw_geometries(pcds_down,
                                  zoom=0.3412,
                                  front=[0.4257, -0.2125, -0.8795],
                                  lookat=[2.6172, 2.0475, 1.532],
                                  up=[-0.0694, -0.9768, 0.2024])

输出：

[Open3D WARNING] GLFW Error: Failed to detect any supported platform
[Open3D WARNING] GLFW initialized for headless rendering.

位姿图

位姿图（pose graph）有两个关键元素：节点（node）和边（edge）。一个节点是一块几何体 $\mathbf{P}_{i}$，关联着一个把 $\mathbf{P}_{i}$ 变换到全局空间的位姿矩阵 $\mathbf{T}_{i}$。集合 $\{\mathbf{T}_{i}\}$ 就是要优化的未知变量。PoseGraph.nodes 是一个 PoseGraphNode 列表。我们把全局空间设为 $\mathbf{P}_{0}$ 所在的空间，因此 $\mathbf{T}_{0}$ 是单位矩阵。其余位姿矩阵通过累加相邻节点之间的变换来初始化。相邻节点通常有较大的重叠，可以用 Point-to-plane ICP 进行配准。

位姿图的边连接两块相互重叠的节点（几何体）。每条边包含一个变换矩阵 $\mathbf{T}_{i,j}$，用于把源几何体 $\mathbf{P}_{i}$ 对齐到目标几何体 $\mathbf{P}_{j}$。本教程使用 Point-to-plane ICP 来估计该变换。在更复杂的情况下，这一两两配准（pairwise registration）问题应通过全局配准来求解。

[Choi2015] 观察到，两两配准容易出错：错误的两两对齐数量甚至可能超过正确对齐的数量。因此，他们将位姿图的边划分为两类。里程计边（odometry edges）连接时间上相近的相邻节点，ICP 这类局部配准算法可以可靠地对齐它们；回环闭合边（loop closure edges）连接任意非相邻的节点，其对应关系由全局配准找到，可靠性较低。在 Open3D 中，这两类边通过 PoseGraphEdge 初始化器中的 uncertain 参数来区分。

除了变换矩阵 $\mathbf{T}_{i}$ 之外，用户还可以为每条边设置信息矩阵 $\mathbf{\Lambda}_{i}$。如果使用函数 get_information_matrix_from_point_clouds 来设置 $\mathbf{\Lambda}_{i}$，则该位姿图边上的损失近似等于两个节点之间对应点集的 RMSE，并带有一个线过程权重。详见 [Choi2015] 的公式 (3) 至 (9) 以及 Redwood 配准基准。

该脚本创建了一个包含 3 个节点和 3 条边的位姿图。在这些边中，有 2 条是里程计边（uncertain = False），1 条是回环闭合边（uncertain = True）。

def pairwise_registration(source, target):
    print("Apply point-to-plane ICP")
    icp_coarse = o3d.pipelines.registration.registration_icp(
        source, target, max_correspondence_distance_coarse, np.identity(4),
        o3d.pipelines.registration.TransformationEstimationPointToPlane())
    icp_fine = o3d.pipelines.registration.registration_icp(
        source, target, max_correspondence_distance_fine,
        icp_coarse.transformation,
        o3d.pipelines.registration.TransformationEstimationPointToPlane())
    transformation_icp = icp_fine.transformation
    information_icp = o3d.pipelines.registration.get_information_matrix_from_point_clouds(
        source, target, max_correspondence_distance_fine,
        icp_fine.transformation)
    return transformation_icp, information_icp


def full_registration(pcds, max_correspondence_distance_coarse,
                      max_correspondence_distance_fine):
    pose_graph = o3d.pipelines.registration.PoseGraph()
    odometry = np.identity(4)
    pose_graph.nodes.append(o3d.pipelines.registration.PoseGraphNode(odometry))
    n_pcds = len(pcds)
    for source_id in range(n_pcds):
        for target_id in range(source_id + 1, n_pcds):
            transformation_icp, information_icp = pairwise_registration(
                pcds[source_id], pcds[target_id])
            print("Build o3d.pipelines.registration.PoseGraph")
            if target_id == source_id + 1:  # odometry case
                odometry = np.dot(transformation_icp, odometry)
                pose_graph.nodes.append(
                    o3d.pipelines.registration.PoseGraphNode(
                        np.linalg.inv(odometry)))
                pose_graph.edges.append(
                    o3d.pipelines.registration.PoseGraphEdge(source_id,
                                                             target_id,
                                                             transformation_icp,
                                                             information_icp,
                                                             uncertain=False))
            else:  # loop closure case
                pose_graph.edges.append(
                    o3d.pipelines.registration.PoseGraphEdge(source_id,
                                                             target_id,
                                                             transformation_icp,
                                                             information_icp,
                                                             uncertain=True))
    return pose_graph

print("Full registration ...")
max_correspondence_distance_coarse = voxel_size * 15
max_correspondence_distance_fine = voxel_size * 1.5
with o3d.utility.VerbosityContextManager(
        o3d.utility.VerbosityLevel.Debug) as cm:
    pose_graph = full_registration(pcds_down,
                                   max_correspondence_distance_coarse,
                                   max_correspondence_distance_fine)

输出：

Full registration ...
Apply point-to-plane ICP
[Open3D DEBUG] ICP Iteration #0: Fitness 0.6258, RMSE 0.1566
[Open3D DEBUG] Residual : 1.85e-02 (# of elements : 17029)
[Open3D DEBUG] ICP Iteration #1: Fitness 0.6873, RMSE 0.1427
[Open3D DEBUG] Residual : 1.34e-02 (# of elements : 18703)
[Open3D DEBUG] ICP Iteration #2: Fitness 0.7258, RMSE 0.1364
[Open3D DEBUG] Residual : 1.11e-02 (# of elements : 19751)
[Open3D DEBUG] ICP Iteration #3: Fitness 0.7514, RMSE 0.1330
[Open3D DEBUG] Residual : 1.02e-02 (# of elements : 20446)
[Open3D DEBUG] ICP Iteration #4: Fitness 0.7743, RMSE 0.1296
[Open3D DEBUG] Residual : 9.36e-03 (# of elements : 21070)
[Open3D DEBUG] ICP Iteration #5: Fitness 0.7881, RMSE 0.1214
[Open3D DEBUG] Residual : 7.82e-03 (# of elements : 21444)
[Open3D DEBUG] ICP Iteration #6: Fitness 0.7959, RMSE 0.1142
[Open3D DEBUG] Residual : 6.81e-03 (# of elements : 21657)
[Open3D DEBUG] ICP Iteration #7: Fitness 0.8024, RMSE 0.1127
[Open3D DEBUG] Residual : 6.56e-03 (# of elements : 21833)
[Open3D DEBUG] ICP Iteration #8: Fitness 0.8026, RMSE 0.1108
[Open3D DEBUG] Residual : 6.34e-03 (# of elements : 21840)
[Open3D DEBUG] ICP Iteration #9: Fitness 0.7959, RMSE 0.1050
[Open3D DEBUG] Residual : 5.79e-03 (# of elements : 21658)
[Open3D DEBUG] ICP Iteration #10: Fitness 0.7816, RMSE 0.0914
[Open3D DEBUG] Residual : 4.30e-03 (# of elements : 21268)
[Open3D DEBUG] ICP Iteration #11: Fitness 0.7676, RMSE 0.0758
[Open3D DEBUG] Residual : 2.52e-03 (# of elements : 20887)
[Open3D DEBUG] ICP Iteration #12: Fitness 0.7573, RMSE 0.0682
[Open3D DEBUG] Residual : 1.73e-03 (# of elements : 20606)
[Open3D DEBUG] ICP Iteration #13: Fitness 0.7525, RMSE 0.0656
[Open3D DEBUG] Residual : 1.48e-03 (# of elements : 20475)
[Open3D DEBUG] ICP Iteration #14: Fitness 0.7500, RMSE 0.0645
[Open3D DEBUG] Residual : 1.40e-03 (# of elements : 20407)
[Open3D DEBUG] ICP Iteration #15: Fitness 0.7489, RMSE 0.0639
[Open3D DEBUG] Residual : 1.36e-03 (# of elements : 20377)
[Open3D DEBUG] ICP Iteration #16: Fitness 0.7482, RMSE 0.0635
[Open3D DEBUG] Residual : 1.32e-03 (# of elements : 20358)
[Open3D DEBUG] ICP Iteration #17: Fitness 0.7477, RMSE 0.0632
[Open3D DEBUG] Residual : 1.31e-03 (# of elements : 20347)
[Open3D DEBUG] ICP Iteration #18: Fitness 0.7476, RMSE 0.0631
[Open3D DEBUG] Residual : 1.30e-03 (# of elements : 20342)
[Open3D DEBUG] ICP Iteration #19: Fitness 0.7475, RMSE 0.0631
[Open3D DEBUG] Residual : 1.29e-03 (# of elements : 20341)
[Open3D DEBUG] ICP Iteration #20: Fitness 0.7475, RMSE 0.0630
[Open3D DEBUG] Residual : 1.29e-03 (# of elements : 20339)
[Open3D DEBUG] ICP Iteration #21: Fitness 0.7473, RMSE 0.0629
[Open3D DEBUG] Residual : 1.29e-03 (# of elements : 20335)
[Open3D DEBUG] ICP Iteration #22: Fitness 0.7473, RMSE 0.0629
[Open3D DEBUG] Residual : 1.28e-03 (# of elements : 20334)
[Open3D DEBUG] ICP Iteration #23: Fitness 0.7472, RMSE 0.0628
[Open3D DEBUG] Residual : 1.28e-03 (# of elements : 20331)
[Open3D DEBUG] ICP Iteration #24: Fitness 0.7471, RMSE 0.0627
[Open3D DEBUG] Residual : 1.28e-03 (# of elements : 20329)
[Open3D DEBUG] ICP Iteration #25: Fitness 0.7470, RMSE 0.0627
[Open3D DEBUG] Residual : 1.27e-03 (# of elements : 20326)
[Open3D DEBUG] ICP Iteration #26: Fitness 0.7469, RMSE 0.0626
[Open3D DEBUG] Residual : 1.27e-03 (# of elements : 20325)
[Open3D DEBUG] ICP Iteration #27: Fitness 0.7469, RMSE 0.0626
[Open3D DEBUG] Residual : 1.27e-03 (# of elements : 20324)
[Open3D DEBUG] ICP Iteration #28: Fitness 0.7469, RMSE 0.0626
[Open3D DEBUG] Residual : 1.26e-03 (# of elements : 20323)
[Open3D DEBUG] ICP Iteration #29: Fitness 0.7469, RMSE 0.0626
[Open3D DEBUG] Residual : 1.26e-03 (# of elements : 20323)
[Open3D DEBUG] ICP Iteration #0: Fitness 0.5852, RMSE 0.0139
[Open3D DEBUG] Residual : 1.17e-04 (# of elements : 15924)
[Open3D DEBUG] ICP Iteration #1: Fitness 0.6369, RMSE 0.0121
[Open3D DEBUG] Residual : 7.15e-05 (# of elements : 17332)
[Open3D DEBUG] ICP Iteration #2: Fitness 0.6395, RMSE 0.0102
[Open3D DEBUG] Residual : 3.27e-05 (# of elements : 17402)
[Open3D DEBUG] ICP Iteration #3: Fitness 0.6390, RMSE 0.0101
[Open3D DEBUG] Residual : 3.13e-05 (# of elements : 17388)
[Open3D DEBUG] ICP Iteration #4: Fitness 0.6392, RMSE 0.0101
[Open3D DEBUG] Residual : 3.13e-05 (# of elements : 17392)
[Open3D DEBUG] ICP Iteration #5: Fitness 0.6391, RMSE 0.0101
[Open3D DEBUG] Residual : 3.13e-05 (# of elements : 17390)
Build o3d.pipelines.registration.PoseGraph
Apply point-to-plane ICP
[Open3D DEBUG] ICP Iteration #0: Fitness 0.5669, RMSE 0.1655
[Open3D DEBUG] Residual : 1.78e-02 (# of elements : 15427)
[Open3D DEBUG] ICP Iteration #1: Fitness 0.6107, RMSE 0.1603
[Open3D DEBUG] Residual : 1.72e-02 (# of elements : 16617)
[Open3D DEBUG] ICP Iteration #2: Fitness 0.6706, RMSE 0.1484
[Open3D DEBUG] Residual : 1.47e-02 (# of elements : 18249)
[Open3D DEBUG] ICP Iteration #3: Fitness 0.7393, RMSE 0.1341
[Open3D DEBUG] Residual : 9.62e-03 (# of elements : 20117)
[Open3D DEBUG] ICP Iteration #4: Fitness 0.8061, RMSE 0.1313
[Open3D DEBUG] Residual : 7.39e-03 (# of elements : 21934)
[Open3D DEBUG] ICP Iteration #5: Fitness 0.8341, RMSE 0.1120
[Open3D DEBUG] Residual : 5.13e-03 (# of elements : 22697)
[Open3D DEBUG] ICP Iteration #6: Fitness 0.8784, RMSE 0.0993
[Open3D DEBUG] Residual : 3.11e-03 (# of elements : 23901)
[Open3D DEBUG] ICP Iteration #7: Fitness 0.9177, RMSE 0.0846
[Open3D DEBUG] Residual : 1.47e-03 (# of elements : 24972)
[Open3D DEBUG] ICP Iteration #8: Fitness 0.9376, RMSE 0.0795
[Open3D DEBUG] Residual : 9.79e-04 (# of elements : 25512)
[Open3D DEBUG] ICP Iteration #9: Fitness 0.9463, RMSE 0.0789
[Open3D DEBUG] Residual : 9.53e-04 (# of elements : 25750)
[Open3D DEBUG] ICP Iteration #10: Fitness 0.9491, RMSE 0.0788
[Open3D DEBUG] Residual : 9.87e-04 (# of elements : 25827)
[Open3D DEBUG] ICP Iteration #11: Fitness 0.9499, RMSE 0.0787
[Open3D DEBUG] Residual : 1.00e-03 (# of elements : 25849)
[Open3D DEBUG] ICP Iteration #12: Fitness 0.9503, RMSE 0.0787
[Open3D DEBUG] Residual : 1.01e-03 (# of elements : 25858)
[Open3D DEBUG] ICP Iteration #13: Fitness 0.9504, RMSE 0.0788
[Open3D DEBUG] Residual : 1.01e-03 (# of elements : 25862)
[Open3D DEBUG] ICP Iteration #14: Fitness 0.9505, RMSE 0.0788
[Open3D DEBUG] Residual : 1.01e-03 (# of elements : 25863)
[Open3D DEBUG] ICP Iteration #15: Fitness 0.9505, RMSE 0.0787
[Open3D DEBUG] Residual : 1.01e-03 (# of elements : 25863)
[Open3D DEBUG] ICP Iteration #16: Fitness 0.9505, RMSE 0.0788
[Open3D DEBUG] Residual : 1.01e-03 (# of elements : 25863)
[Open3D DEBUG] ICP Iteration #0: Fitness 0.6932, RMSE 0.0152
[Open3D DEBUG] Residual : 1.42e-04 (# of elements : 18863)
[Open3D DEBUG] ICP Iteration #1: Fitness 0.7057, RMSE 0.0106
[Open3D DEBUG] Residual : 3.39e-05 (# of elements : 19203)
[Open3D DEBUG] ICP Iteration #2: Fitness 0.7052, RMSE 0.0104
[Open3D DEBUG] Residual : 3.06e-05 (# of elements : 19190)
[Open3D DEBUG] ICP Iteration #3: Fitness 0.7054, RMSE 0.0104
[Open3D DEBUG] Residual : 3.07e-05 (# of elements : 19195)
[Open3D DEBUG] ICP Iteration #4: Fitness 0.7055, RMSE 0.0105
[Open3D DEBUG] Residual : 3.07e-05 (# of elements : 19198)
[Open3D DEBUG] ICP Iteration #5: Fitness 0.7055, RMSE 0.0105
[Open3D DEBUG] Residual : 3.07e-05 (# of elements : 19197)
Build o3d.pipelines.registration.PoseGraph
Apply point-to-plane ICP
[Open3D DEBUG] ICP Iteration #0: Fitness 0.7980, RMSE 0.1231
[Open3D DEBUG] Residual : 1.23e-02 (# of elements : 15272)
[Open3D DEBUG] ICP Iteration #1: Fitness 0.9232, RMSE 0.1132
[Open3D DEBUG] Residual : 9.84e-03 (# of elements : 17668)
[Open3D DEBUG] ICP Iteration #2: Fitness 0.9638, RMSE 0.0957
[Open3D DEBUG] Residual : 4.76e-03 (# of elements : 18445)
[Open3D DEBUG] ICP Iteration #3: Fitness 0.9648, RMSE 0.0865
[Open3D DEBUG] Residual : 2.63e-03 (# of elements : 18464)
[Open3D DEBUG] ICP Iteration #4: Fitness 0.9576, RMSE 0.0784
[Open3D DEBUG] Residual : 1.34e-03 (# of elements : 18326)
[Open3D DEBUG] ICP Iteration #5: Fitness 0.9506, RMSE 0.0755
[Open3D DEBUG] Residual : 8.08e-04 (# of elements : 18191)
[Open3D DEBUG] ICP Iteration #6: Fitness 0.9446, RMSE 0.0746
[Open3D DEBUG] Residual : 5.87e-04 (# of elements : 18077)
[Open3D DEBUG] ICP Iteration #7: Fitness 0.9400, RMSE 0.0740
[Open3D DEBUG] Residual : 4.83e-04 (# of elements : 17989)
[Open3D DEBUG] ICP Iteration #8: Fitness 0.9381, RMSE 0.0739
[Open3D DEBUG] Residual : 4.41e-04 (# of elements : 17953)
[Open3D DEBUG] ICP Iteration #9: Fitness 0.9373, RMSE 0.0737
[Open3D DEBUG] Residual : 4.30e-04 (# of elements : 17937)
[Open3D DEBUG] ICP Iteration #10: Fitness 0.9372, RMSE 0.0738
[Open3D DEBUG] Residual : 4.29e-04 (# of elements : 17936)
[Open3D DEBUG] ICP Iteration #11: Fitness 0.9372, RMSE 0.0739
[Open3D DEBUG] Residual : 4.29e-04 (# of elements : 17936)
[Open3D DEBUG] ICP Iteration #0: Fitness 0.7654, RMSE 0.0129
[Open3D DEBUG] Residual : 9.10e-05 (# of elements : 14648)
[Open3D DEBUG] ICP Iteration #1: Fitness 0.7605, RMSE 0.0109
[Open3D DEBUG] Residual : 4.28e-05 (# of elements : 14553)
[Open3D DEBUG] ICP Iteration #2: Fitness 0.7594, RMSE 0.0108
[Open3D DEBUG] Residual : 4.23e-05 (# of elements : 14533)
[Open3D DEBUG] ICP Iteration #3: Fitness 0.7592, RMSE 0.0108
[Open3D DEBUG] Residual : 4.24e-05 (# of elements : 14528)
Build o3d.pipelines.registration.PoseGraph

Open3D 使用函数 global_optimization 来执行位姿图优化。可选择两种优化方法：GlobalOptimizationGaussNewton 或 GlobalOptimizationLevenbergMarquardt。推荐使用后者，因为它具有更好的收敛性质。GlobalOptimizationConvergenceCriteria 类可用于设置最大迭代次数及各种优化参数。

GlobalOptimizationOption 类定义了若干选项。max_correspondence_distance 决定对应关系的阈值；edge_prune_threshold 是剪除离群边的阈值；reference_node 是被视为全局空间的节点编号。

print("Optimizing PoseGraph ...")
option = o3d.pipelines.registration.GlobalOptimizationOption(
    max_correspondence_distance=max_correspondence_distance_fine,
    edge_prune_threshold=0.25,
    reference_node=0)
with o3d.utility.VerbosityContextManager(
        o3d.utility.VerbosityLevel.Debug) as cm:
    o3d.pipelines.registration.global_optimization(
        pose_graph,
        o3d.pipelines.registration.GlobalOptimizationLevenbergMarquardt(),
        o3d.pipelines.registration.GlobalOptimizationConvergenceCriteria(),
        option)

输出：

Optimizing PoseGraph ...
[Open3D DEBUG] Validating PoseGraph - finished.
[Open3D DEBUG] [GlobalOptimizationLM] Optimizing PoseGraph having 3 nodes and 3 edges.
[Open3D DEBUG] Line process weight : 15.334500
[Open3D DEBUG] [Initial     ] residual : 1.037615e+00, lambda : 2.960068e+00
[Open3D DEBUG] [Iteration 00] residual : 2.034300e-01, valid edges : 1, time : 0.000 sec.
[Open3D DEBUG] [Iteration 01] residual : 1.455356e-01, valid edges : 1, time : 0.000 sec.
[Open3D DEBUG] Delta.norm() < 1.000000e-06 * (x.norm() + 1.000000e-06)
[Open3D DEBUG] [GlobalOptimizationLM] total time : 0.000 sec.
[Open3D DEBUG] [GlobalOptimizationLM] Optimizing PoseGraph having 3 nodes and 3 edges.
[Open3D DEBUG] Line process weight : 15.334500
[Open3D DEBUG] [Initial     ] residual : 1.455332e-01, lambda : 3.051329e+00
[Open3D DEBUG] Delta.norm() < 1.000000e-06 * (x.norm() + 1.000000e-06)
[Open3D DEBUG] [GlobalOptimizationLM] total time : 0.000 sec.
[Open3D DEBUG] CompensateReferencePoseGraphNode : reference : 0

全局优化对位姿图执行两遍。第一遍在考虑所有边的情况下优化原始位姿图的位姿，并尽可能区分不确定边中的错误对齐；这些错误对齐具有较小的线过程权重，会在第一遍之后被剪除。第二遍在排除这些边的情况下运行，产生紧密的全局对齐。在本例中，所有边都被视为正确对齐，因此第二遍立即终止。

可视化优化结果

变换后的点云被列举出来，并使用 draw_geometries 进行可视化。

print("Transform points and display")
for point_id in range(len(pcds_down)):
    print(pose_graph.nodes[point_id].pose)
    pcds_down[point_id].transform(pose_graph.nodes[point_id].pose)
o3d.visualization.draw_geometries(pcds_down,
                                  zoom=0.3412,
                                  front=[0.4257, -0.2125, -0.8795],
                                  lookat=[2.6172, 2.0475, 1.532],
                                  up=[-0.0694, -0.9768, 0.2024])

输出：

Transform points and display
[[ 1.00000000e+00  1.62736205e-19  0.00000000e+00 -8.67361738e-19]
 [-5.41042295e-20  1.00000000e+00  1.08420217e-19 -8.67361738e-19]
 [-1.08420217e-19  0.00000000e+00  1.00000000e+00  0.00000000e+00]
 [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  1.00000000e+00]]
[[ 0.84016209 -0.14644296  0.52218973  0.34786264]
 [ 0.0061365   0.96535921  0.26085233 -0.39421642]
 [-0.54230065 -0.21595382  0.81195686  1.73016434]
 [ 0.          0.          0.          1.        ]]
[[ 0.9627171  -0.07182071  0.26080179  0.37666506]
 [-0.00193493  0.96225765  0.27213318 -0.48961689]
 [-0.27050331 -0.2624919   0.92624293  1.29777557]
 [ 0.          0.          0.          1.        ]]
[Open3D WARNING] GLFW initialized for headless rendering.

合并为单个点云

PointCloud 提供了一个便捷的 + 运算符，可以把两个点云合并为一个。下面的代码在合并之后使用 voxel_down_sample 对点进行均匀重采样。这是合并点云后推荐的后处理步骤，因为它能够缓解重复点或过度密集的点。

pcds = load_point_clouds(voxel_size)
pcd_combined = o3d.geometry.PointCloud()
for point_id in range(len(pcds)):
    pcds[point_id].transform(pose_graph.nodes[point_id].pose)
    pcd_combined += pcds[point_id]
pcd_combined_down = pcd_combined.voxel_down_sample(voxel_size=voxel_size)
o3d.io.write_point_cloud("multiway_registration.pcd", pcd_combined_down)
o3d.visualization.draw_geometries([pcd_combined_down],
                                  zoom=0.3412,
                                  front=[0.4257, -0.2125, -0.8795],
                                  lookat=[2.6172, 2.0475, 1.532],
                                  up=[-0.0694, -0.9768, 0.2024])

输出：

[Open3D WARNING] GLFW initialized for headless rendering.

说明

尽管本教程以点云演示多路配准，但同一流程同样适用于 RGBD 图像。相关示例请参见 Open3D 教程中的 Make fragments。