『OPEN3D』1.6 Voxelization体素化

    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 copy

import open3d as o3d
import numpy as np

if __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 np

if __name__ == "__main__":

    N = 3000
    armadillo_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 copy

import open3d as o3d
import numpy as np

if __name__ == "__main__":
    N = 3000
    armadillo_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

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import open3d as o3d
import numpy as np

def 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] = r
    trans[:3, 3] = t
    return trans

def preprocess(model):
    min_bound = model.get_min_bound()
    max_bound = model.get_max_bound()
    center = min_bound + (max_bound - min_bound) / 2.0
    scale = np.linalg.norm(max_bound - min_bound) / 2.0
    vertices = np.asarray(model.vertices)
    vertices -= center
    model.vertices = o3d.utility.Vector3dVector(vertices / scale)
    return model

def 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 = True
    ctr = 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 = trans
        c = 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 = 2.0
    voxel_resolution = 128.0

    carved_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