点云处理——将激光雷达数据投影到二维图像

“前视图”投影

为了将激光雷达传感器的“前视图”展平为2D图像，必须将3D空间中的点投影到可以展开的圆柱形表面上，以形成平面。
以下代码改编自论文：Vehicle Detection from 3D Lidar Using Fully Convolutional Network

# h_res = horizontal resolution of the lidar sensor
# v_res = vertical resolution of the lidar sensor
x_img = arctan2(y_lidar, x_lidar)/ h_res 
y_img = np.arctan2(z_lidar, np.sqrt(x_lidar**2 + y_lidar**2))/ v_res

问题在于这样做会将图像的接缝直接放在汽车的右侧。将接缝定位在汽车的最后部更有意义，因此前部和侧部更重要的区域是不间断的。让这些重要区域不间断将使卷积神经网络更容易识别那些重要区域中的整个对象。
以下代码解决了这个问题。

# h_res = horizontal resolution of the lidar sensor
# v_res = vertical resolution of the lidar sensor
x_img = np.arctan2(-y_lidar, x_lidar)/ h_res # seam in the back
y_img = np.arctan2(z_lidar, np.sqrt(x_lidar**2 + y_lidar**2))/ v_res

沿每个轴配置刻度

变量 $h_{res}$和 $v_{res}$ 非常依赖于所使用的LIDAR传感器。在KTTI数据集中，使用的传感器是Velodyne HDL 64E。根据Velodyne HDL 64E的规格表，它具有以下重要特征：

• 垂直视野为26.9度，分辨率为0.4度，垂直视野被分为传感器上方+2度，传感器下方-24.9度
• 360度的水平视野，分辨率为0.08-0.35（取决于旋转速度）
• 旋转速率可以选择在5-20Hz之间

可以按以下方式更新代码：

# Resolution and Field of View of LIDAR sensor
h_res = 0.35         # horizontal resolution, assuming rate of 20Hz is used 
v_res = 0.4          # vertical res
v_fov = (-24.9, 2.0) # Field of view (-ve, +ve) along vertical axis
v_fov_total = -v_fov[0] + v_fov[1] 

# Convert to Radians
v_res_rad = v_res * (np.pi/180)
h_res_rad = h_res * (np.pi/180)

# Project into image coordinates
x_img = np.arctan2(-y_lidar, x_lidar)/ h_res_rad
y_img = np.arctan2(z_lidar, d_lidar)/ v_res_rad

然而，这导致大约一半的点在x轴负方向上，并且大多数在y轴负方向上。为了投影到2D图像，需要将最小值设置为（0,0），所以需要做一些改变：

# SHIFT COORDINATES TO MAKE 0,0 THE MINIMUM
x_min = -360.0/h_res/2    # Theoretical min x value based on specs of sensor
x_img = x_img - x_min     # Shift
x_max = 360.0/h_res       # Theoretical max x value after shifting

y_min = v_fov[0]/v_res    # theoretical min y value based on specs of sensor
y_img = y_img - y_min     # Shift
y_max = v_fov_total/v_res # Theoretical max x value after shifting
y_max = y_max + 5         # UGLY: Fudge factor because the calculations based on
                          # spec sheet do not seem to match the range of angles
                          # collected by sensor in the data.

绘制二维图像

将3D点投影到2D坐标点，最小值为（0,0），可以将这些点数据绘制成2D图像。

pixel_values = -d_lidar # Use depth data to encode the value for each pixel
cmap = "jet"            # Color map to use
dpi = 100               # Image resolution
fig, ax = plt.subplots(figsize=(x_max/dpi, y_max/dpi), dpi=dpi)
ax.scatter(x_img,y_img, s=1, c=pixel_values, linewidths=0, alpha=1, cmap=cmap)
ax.set_axis_bgcolor((0, 0, 0)) # Set regions with no points to black
ax.axis('scaled')              # {equal, scaled}
ax.xaxis.set_visible(False)    # Do not draw axis tick marks
ax.yaxis.set_visible(False)    # Do not draw axis tick marks
plt.xlim([0, x_max])   # prevent drawing empty space outside of horizontal FOV
plt.ylim([0, y_max])   # prevent drawing empty space outside of vertical FOV
fig.savefig("/tmp/depth.png", dpi=dpi, bbox_inches='tight', pad_inches=0.0)

完整代码

把上面所有的代码放在一个函数中。

def lidar_to_2d_front_view(points,
                           v_res,
                           h_res,
                           v_fov,
                           val="depth",
                           cmap="jet",
                           saveto=None,
                           y_fudge=0.0
                           ):
    """ Takes points in 3D space from LIDAR data and projects them to a 2D
        "front view" image, and saves that image.

    Args:
        points: (np array)
            The numpy array containing the lidar points.
            The shape should be Nx4
            - Where N is the number of points, and
            - each point is specified by 4 values (x, y, z, reflectance)
        v_res: (float)
            vertical resolution of the lidar sensor used.
        h_res: (float)
            horizontal resolution of the lidar sensor used.
        v_fov: (tuple of two floats)
            (minimum_negative_angle, max_positive_angle)
        val: (str)
            What value to use to encode the points that get plotted.
            One of {"depth", "height", "reflectance"}
        cmap: (str)
            Color map to use to color code the `val` values.
            NOTE: Must be a value accepted by matplotlib's scatter function
            Examples: "jet", "gray"
        saveto: (str or None)
            If a string is provided, it saves the image as this filename.
            If None, then it just shows the image.
        y_fudge: (float)
            A hacky fudge factor to use if the theoretical calculations of
            vertical range do not match the actual data.

            For a Velodyne HDL 64E, set this value to 5.
    """

    # DUMMY PROOFING
    assert len(v_fov) ==2, "v_fov must be list/tuple of length 2"
    assert v_fov[0] <= 0, "first element in v_fov must be 0 or negative"
    assert val in {"depth", "height", "reflectance"}, \
        'val must be one of {"depth", "height", "reflectance"}'


    x_lidar = points[:, 0]
    y_lidar = points[:, 1]
    z_lidar = points[:, 2]
    r_lidar = points[:, 3] # Reflectance
    # Distance relative to origin when looked from top
    d_lidar = np.sqrt(x_lidar ** 2 + y_lidar ** 2)
    # Absolute distance relative to origin
    # d_lidar = np.sqrt(x_lidar ** 2 + y_lidar ** 2, z_lidar ** 2)

    v_fov_total = -v_fov[0] + v_fov[1]

    # Convert to Radians
    v_res_rad = v_res * (np.pi/180)
    h_res_rad = h_res * (np.pi/180)

    # PROJECT INTO IMAGE COORDINATES
    x_img = np.arctan2(-y_lidar, x_lidar)/ h_res_rad
    y_img = np.arctan2(z_lidar, d_lidar)/ v_res_rad

    # SHIFT COORDINATES TO MAKE 0,0 THE MINIMUM
    x_min = -360.0 / h_res / 2  # Theoretical min x value based on sensor specs
    x_img -= x_min              # Shift
    x_max = 360.0 / h_res       # Theoretical max x value after shifting

    y_min = v_fov[0] / v_res    # theoretical min y value based on sensor specs
    y_img -= y_min              # Shift
    y_max = v_fov_total / v_res # Theoretical max x value after shifting

    y_max += y_fudge            # Fudge factor if the calculations based on
                                # spec sheet do not match the range of
                                # angles collected by in the data.

    # WHAT DATA TO USE TO ENCODE THE VALUE FOR EACH PIXEL
    if val == "reflectance":
        pixel_values = r_lidar
    elif val == "height":
        pixel_values = z_lidar
    else:
        pixel_values = -d_lidar

    # PLOT THE IMAGE
    cmap = "jet"            # Color map to use
    dpi = 100               # Image resolution
    fig, ax = plt.subplots(figsize=(x_max/dpi, y_max/dpi), dpi=dpi)
    ax.scatter(x_img,y_img, s=1, c=pixel_values, linewidths=0, alpha=1, cmap=cmap)
    ax.set_axis_bgcolor((0, 0, 0)) # Set regions with no points to black
    ax.axis('scaled')              # {equal, scaled}
    ax.xaxis.set_visible(False)    # Do not draw axis tick marks
    ax.yaxis.set_visible(False)    # Do not draw axis tick marks
    plt.xlim([0, x_max])   # prevent drawing empty space outside of horizontal FOV
    plt.ylim([0, y_max])   # prevent drawing empty space outside of vertical FOV

    if saveto is not None:
        fig.savefig(saveto, dpi=dpi, bbox_inches='tight', pad_inches=0.0)
    else:
        fig.show()

以下是一些用例：

import matplotlib.pyplot as plt
import numpy as np

HRES = 0.35         # horizontal resolution (assuming 20Hz setting)
VRES = 0.4          # vertical res
VFOV = (-24.9, 2.0) # Field of view (-ve, +ve) along vertical axis
Y_FUDGE = 5         # y fudge factor for velodyne HDL 64E

lidar_to_2d_front_view(lidar, v_res=VRES, h_res=HRES, v_fov=VFOV, val="depth",
                       saveto="/tmp/lidar_depth.png", y_fudge=Y_FUDGE)

lidar_to_2d_front_view(lidar, v_res=VRES, h_res=HRES, v_fov=VFOV, val="height",
                       saveto="/tmp/lidar_height.png", y_fudge=Y_FUDGE)

lidar_to_2d_front_view(lidar, v_res=VRES, h_res=HRES, v_fov=VFOV,
                       val="reflectance", saveto="/tmp/lidar_reflectance.png",
                       y_fudge=Y_FUDGE)

产生以下三个图像：
Depth

Height

Reflectance

未来的工作

目前创建每个图像非常慢，可能是因为matplotlib，它不能很好地处理大量的散点。
因此需要创建一个使用numpy或PIL的实现。

测试

需要安装python-pcl，加载PCD文件。

sudo apt-get install python-pip

sudo apt-get install python-dev

sudo pip install Cython==0.25.2

sudo pip install numpy

sudo apt-get install git

git clone https://github.com/strawlab/python-pcl.git

cd python-pcl/

python setup.py build_ext -i

python setup.py install

可惜，sudo pip install Cython==0.25.2这步报错：

Cannot uninstall ‘Cython’. It is a distutils installed project and thus we cannot accurately determine which files belong to it which would lead to only a partial uninstall.

换个方法，安装pypcd：

pip install pypcd

查看 https://pypi.org/project/pypcd/ ，用例如下：

Example
-------

.. code:: python

import pypcd
# also can read from file handles.
pc = pypcd.PointCloud.from_path('foo.pcd')
# pc.pc_data has the data as a structured array
# pc.fields, pc.count, etc have the metadata

# center the x field
pc.pc_data['x'] -= pc.pc_data['x'].mean()

# save as binary compressed
pc.save_pcd('bar.pcd', compression='binary_compressed')

测试数据结构：

>>> lidar = pypcd.PointCloud.from_path(‘～/pointcloud-processing/000000.pcd’)
>>> lidar.pc_data
array([(18.323999404907227, 0.04899999871850014, 0.8289999961853027, 0.0),
(18.3439998626709, 0.10599999874830246, 0.8289999961853027, 0.0),
(51.29899978637695, 0.5049999952316284, 1.944000005722046, 0.0),
…,
(3.7139999866485596, -1.3910000324249268, -1.7330000400543213, 0.4099999964237213),
(3.9670000076293945, -1.4739999771118164, -1.8569999933242798, 0.0),
(0.0, 0.0, 0.0, 0.0)],
dtype=[(‘x’, ‘<f4’), (‘y’, ‘<f4’), (‘z’, ‘<f4’), (‘intensity’, ‘<f4’)])
>>> lidar.pc_data[‘x’]
array([ 18.3239994 , 18.34399986, 51.29899979, …, 3.71399999,
3.96700001, 0. ], dtype=float32)

加载PCD：

import pypcd

lidar = pypcd.PointCloud.from_path('000000.pcd')

x_lidar：

x_lidar = points[’x‘]

结果：