目录

1 从triangle meshes中创建体素

2 从点云中创建体素

3 体素包含测试（Inclusion test）

4 Voxel carving

        在点云处理的内容中，简单介绍了open3d中对点云下采样使用了体素的操作，这里对体素化进行详细的介绍。

点云和三角面片（triangle meshes）表达的数据是无序的几何结构；而体素则是另一种表达三维数据的几何结构，体素类似于图片中的像素，具有规则性。因此，open3d中提供了VoxelGrid几何类型用于对体素的表达。

1 从triangle meshes中创建体素

        方法create_from_triangle_mesh可以从mesh中创建体素，任何一个mesh与体素相交，则该体素置为1（存在）；否则置为0（不存在）。该方法包含一个参数voxel_size用于设置体素的分辨率。

import copyimport open3d as o3d
import numpy as npif __name__ == "__main__":# bunny = o3d.data.BunnyMesh()armadillo_data = o3d.data.ArmadilloMesh()mesh = o3d.io.read_triangle_mesh(armadillo_data.path)# 计算顶点的法向量mesh.compute_vertex_normals()# Fit to unit cube.mesh.scale(1 / np.max(mesh.get_max_bound() - mesh.get_min_bound()),center=mesh.get_center())print('Displaying input mesh ...')# o3d.visualization.draw_geometries([mesh])"""create_from_triangle_mesh param:voxel_size：设置每个体素的长宽高为0.5返回值类型为o3d.geometry.VoxelGrid"""mesh_for_voxelGrid: o3d.geometry.TriangleMesh = copy.deepcopy(mesh)mesh_for_voxelGrid.translate([1, 0, 0])voxel_grid: o3d.geometry.VoxelGrid = o3d.geometry.VoxelGrid.create_from_triangle_mesh(mesh_for_voxelGrid, voxel_size=0.05)print('Displaying voxel grid ...')o3d.visualization.draw_geometries([mesh,voxel_grid])

2 从点云中创建体素

        使用方法create_from_point_cloud可以实现从点云中创建voxelgrid，一个voxel被占用的话，则至少该voxel中存在一个点云。voxel的颜色则是对该voxel中所有点云的颜色做平均；参数voxel_size设置voxelgrid的分辨率。

import open3d as o3d
import numpy as npif __name__ == "__main__":N = 3000armadillo_data = o3d.data.ArmadilloMesh()pcd = o3d.io.read_triangle_mesh(armadillo_data.path).sample_points_poisson_disk(N)# Fit to unit cube.pcd.scale(1 / np.max(pcd.get_max_bound() - pcd.get_min_bound()),center=pcd.get_center())pcd.colors = o3d.utility.Vector3dVector(np.random.uniform(0, 1,size=(N, 3)))print('Displaying input point cloud ...')o3d.visualization.draw_geometries([pcd])print('Displaying voxel grid ...')voxel_grid = o3d.geometry.VoxelGrid.create_from_point_cloud(pcd,voxel_size=0.05)o3d.visualization.draw_geometries([voxel_grid])

3 体素包含测试（Inclusion test）

        voxel grid可以用于测试一个点云是否被体素所包含；方法check_if_included接受一个（n,3）的array；并返回array中每个点是否在voxelgrid中。

import copyimport open3d as o3d
import numpy as npif __name__ == "__main__":N = 3000armadillo_data = o3d.data.ArmadilloMesh()pcd = o3d.io.read_triangle_mesh(armadillo_data.path).sample_points_poisson_disk(N)# Fit to unit cube.pcd.scale(1 / np.max(pcd.get_max_bound() - pcd.get_min_bound()),center=pcd.get_center())pcd.colors = o3d.utility.Vector3dVector(np.random.uniform(0, 1,size=(N, 3)))# print('Displaying input point cloud ...')# o3d.visualization.draw_geometries([pcd])pcd_for_voxelgrid = copy.deepcopy(pcd)pcd_for_voxelgrid.translate([1, 0, 0])print('Displaying voxel grid ...')voxel_grid = o3d.geometry.VoxelGrid.create_from_point_cloud(pcd_for_voxelgrid,voxel_size=0.05)# o3d.visualization.draw_geometries([pcd, voxel_grid])queries = np.asarray(pcd.points)output = voxel_grid.check_if_included(o3d.utility.Vector3dVector(queries))print(output[:10])queries = np.asarray(pcd_for_voxelgrid.points)output = voxel_grid.check_if_included(o3d.utility.Vector3dVector(queries))print(output[:10])"""输出结果Displaying voxel grid ...[False, False, False, False, False, False, False, False, False, False][True, True, True, True, True, True, True, True, True, True]"""

4 Voxel carving

        上述两种方法创建的voxelGrid只在点云或mesh占用该voxel时，才会将该voxel设置为被占用的状态；因此会出现物体的中心在voxelGrid为空洞的情况，只有表面的voxelGrid被占据；但是也可以从多个深度图（depth maps）或者轮廓图(silhouettes)中雕刻出体素网格；在open3d中提供了该实现分别为carve_depth_map和carve_silhouette。

下面已depth map为示例进行展示

# ----------------------------------------------------------------------------
# -                        Open3D: www.open3d.org                            -
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# The MIT License (MIT)
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# Copyright (c) 2018-2021 www.open3d.org
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# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
# IN THE SOFTWARE.
# ----------------------------------------------------------------------------import open3d as o3d
import numpy as npdef xyz_spherical(xyz):x = xyz[0]y = xyz[1]z = xyz[2]# 计算得到球体的半径r = np.sqrt(x * x + y * y + z * z)# 半径与x轴的夹角r_x = np.arccos(y / r)# 半径在y轴的夹角r_y = np.arctan2(z, x)return [r, r_x, r_y]def get_rotation_matrix(r_x, r_y):rot_x = np.asarray([[1, 0, 0], [0, np.cos(r_x), -np.sin(r_x)],[0, np.sin(r_x), np.cos(r_x)]])rot_y = np.asarray([[np.cos(r_y), 0, np.sin(r_y)], [0, 1, 0],[-np.sin(r_y), 0, np.cos(r_y)]])return rot_y.dot(rot_x)def get_extrinsic(xyz):rvec = xyz_spherical(xyz)# 计算该相机位姿下的旋转矩阵和平移向量并拼接成T矩阵r = get_rotation_matrix(rvec[1], rvec[2])t = np.asarray([0, 0, 2]).transpose()trans = np.eye(4)trans[:3, :3] = rtrans[:3, 3] = treturn transdef preprocess(model):min_bound = model.get_min_bound()max_bound = model.get_max_bound()center = min_bound + (max_bound - min_bound) / 2.0scale = np.linalg.norm(max_bound - min_bound) / 2.0vertices = np.asarray(model.vertices)vertices -= centermodel.vertices = o3d.utility.Vector3dVector(vertices / scale)return modeldef voxel_carving(mesh, cubic_size, voxel_resolution, w=300, h=300):# 计算mesh的顶点法向量mesh.compute_vertex_normals()# 创建球体camera_sphere = o3d.geometry.TriangleMesh.create_sphere(radius=1.0,resolution=10)# o3d.visualization.draw_geometries([camera_sphere], mesh_show_back_face=True)# Setup dense voxel grid.voxel_carving = o3d.geometry.VoxelGrid.create_dense(width=cubic_size,height=cubic_size,depth=cubic_size,voxel_size=cubic_size / voxel_resolution,origin=[-cubic_size / 2.0, -cubic_size / 2.0, -cubic_size / 2.0],color=[1.0, 0.7, 0.0])# Rescale geometry.camera_sphere = preprocess(camera_sphere)mesh = preprocess(mesh)# Setup visualizer to render depthmaps.vis = o3d.visualization.Visualizer()vis.create_window(width=w, height=h, visible=False)vis.add_geometry(mesh)vis.get_render_option().mesh_show_back_face = Truectr = vis.get_view_control()param = ctr.convert_to_pinhole_camera_parameters()# Carve voxel grid.centers_pts = np.zeros((len(camera_sphere.vertices), 3))for cid, xyz in enumerate(camera_sphere.vertices):# Get new camera pose.trans = get_extrinsic(xyz)param.extrinsic = transc = np.linalg.inv(trans).dot(np.asarray([0, 0, 0, 1]).transpose())centers_pts[cid, :] = c[:3]# 转换相机的参数到成open3d中的相机内外参ctr.convert_from_pinhole_camera_parameters(param)# Capture depth image and make a point cloud.vis.poll_events()vis.update_renderer()# 根据当前的位姿来进行渲染拍摄得到深度图depth = vis.capture_depth_float_buffer(False)# Depth map carving method.voxel_carving.carve_depth_map(o3d.geometry.Image(depth), param)print("Carve view %03d/%03d" % (cid + 1, len(camera_sphere.vertices)))vis.destroy_window()return voxel_carving"""
流程：
1 先创建一个固定大小的稠密（dense）voxleGrid对象
2 创建一个球形用于虚拟相机的位姿来拍摄拍摄深度图
3 根据拍摄得到的深度图与相机位姿使用carve_depth_map融合到dense voxelGrid中
"""
if __name__ == "__main__":armadillo_data = o3d.data.ArmadilloMesh()mesh = o3d.io.read_triangle_mesh(armadillo_data.path)cubic_size = 2.0voxel_resolution = 128.0carved_voxels = voxel_carving(mesh, cubic_size, voxel_resolution)print("Carved voxels ...")print(carved_voxels)o3d.visualization.draw_geometries([carved_voxels])

生成的voxelGird内部也是被填充的，可以自行方法查看