How can I align / register two meshes in Open3d? (Python)

I have two .ply files that contain mesh of objects that are similar in shape. They are initially unaligned. I would like to achieve global registration for the two mesh objects. Is there a way that I can do this without having to initially import the point cloud data, do global registration, and then reconstruct the mesh?

I have tried the steps listed in the open3d documentation (http://www.open3d.org/docs/0.12.0/tutorial/pipelines/global_registration.html) and it works well for the point clouds. However, reconstructing a mesh from the point clouds is challenging, as they are a relatively complex shape, so I would like to avoid that.

Thank you in advance!

The main idea is you don't need to reconstruct mesh from point cloud.

Mark the data you have as mesh_a, mesh_b, pcl_a, pcl_b.

1. if your pcl_a/b is extracted directly from mesh_a/b or pcl_a/b and mesh_a/b has the same Transformation Matrix, You can simply apply the transformation matrix obtained from the point cloud alignment to the mesh.

2. if your point cloud data has no relations with your mesh data. You can first sample mesh_a/b to point cloud and do registration or directly get mesh vertex as point cloud from mesh data. The rest of the work is the same as in case one.

Here are the example of situation two.

import copy

import numpy as np
import open3d as o3d


def draw_registration_result(source, target, transformation):
    source_temp = copy.deepcopy(source)
    target_temp = copy.deepcopy(target)
    source_temp.paint_uniform_color([1, 0.706, 0])
    target_temp.paint_uniform_color([0, 0.651, 0.929])
    source_temp.transform(transformation)
    o3d.visualization.draw_geometries([source_temp, target_temp])


def preprocess_point_cloud(pcd, voxel_size):
    print(":: Downsample with a voxel size %.3f." % voxel_size)
    pcd_down = pcd.voxel_down_sample(voxel_size)

    radius_normal = voxel_size * 2
    print(":: Estimate normal with search radius %.3f." % radius_normal)
    pcd_down.estimate_normals(
        o3d.geometry.KDTreeSearchParamHybrid(radius=radius_normal, max_nn=30))

    radius_feature = voxel_size * 5
    print(":: Compute FPFH feature with search radius %.3f." % radius_feature)
    pcd_fpfh = o3d.pipelines.registration.compute_fpfh_feature(
        pcd_down,
        o3d.geometry.KDTreeSearchParamHybrid(radius=radius_feature, max_nn=100))
    return pcd_down, pcd_fpfh


def execute_global_registration(source_down, target_down, source_fpfh,
                                target_fpfh, voxel_size):
    distance_threshold = voxel_size * 1.5
    print(":: RANSAC registration on downsampled point clouds.")
    print("   Since the downsampling voxel size is %.3f," % voxel_size)
    print("   we use a liberal distance threshold %.3f." % distance_threshold)
    result = o3d.pipelines.registration.registration_ransac_based_on_feature_matching(
        source_down, target_down, source_fpfh, target_fpfh, True,
        distance_threshold,
        o3d.pipelines.registration.TransformationEstimationPointToPoint(False),
        3, [
            o3d.pipelines.registration.CorrespondenceCheckerBasedOnEdgeLength(
                0.9),
            o3d.pipelines.registration.CorrespondenceCheckerBasedOnDistance(
                distance_threshold)
        ], o3d.pipelines.registration.RANSACConvergenceCriteria(100000, 0.999))
    return result


def main():
    voxel_size = 0.01
    print(":: Load two mesh.")
    target_mesh = o3d.io.read_triangle_mesh('bunny.ply')
    source_mesh = copy.deepcopy(target_mesh)
    source_mesh.rotate(source_mesh.get_rotation_matrix_from_xyz((np.pi / 4, 0, np.pi / 4)), center=(0, 0, 0))
    source_mesh.translate((0, 0.05, 0))
    draw_registration_result(target_mesh, source_mesh, np.identity(4))

    print(":: Sample mesh to point cloud")
    target = target_mesh.sample_points_uniformly(1000)
    source = source_mesh.sample_points_uniformly(1000)
    draw_registration_result(source, target, np.identity(4))

    source_down, source_fpfh = preprocess_point_cloud(source, voxel_size)
    target_down, target_fpfh = preprocess_point_cloud(target, voxel_size)
    result_ransac = execute_global_registration(source_down, target_down,
                                                source_fpfh, target_fpfh,
                                                voxel_size)
    print(result_ransac)
    draw_registration_result(source_down, target_down, result_ransac.transformation)
    draw_registration_result(source_mesh, target_mesh, result_ransac.transformation)


if __name__ == '__main__':
    main()