前视图投影
为了将激光雷达传感器的前视图平展成二维图像，必须将三维空间中的点云投影到可以展开的圆柱形表面，一个平面上。根据论文Vehicle Detection from 3D Lidar Using Fully Convolutional Network所述，以下的代码完成了这部分功能。
# 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。 以下代码修复了这一点。
# 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沿每一个坐标轴设置刻度
变量h_res和v_res比较依赖于所使用的激光雷达传感器。KITTI数据集中，使用Velodyne 64E传感器，根据相关说明，它具有如下重要性质：
- 垂直视野为26.9度，分辨率为0.4度，垂直视野别分解为传感器上方+2度，下方-24.9度；
- 360度的水平视野，分辨率为0.08-0.35度（取决于旋转速度）；
- 可以选择旋转速率在5-20Hz之间。
现在将代码更新为：
# 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但是这使得一般的点被定位在x轴的负半轴，而且大部分在Y的负半轴，为了将其投影到二维图像上，必须将最小值设置为（0,0）。故：
# 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.作为二维图像校准
现在将三维点云投影到二维坐标系的点，最小值为（0,0），并且将这些点绘制成二维图像。
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)第一成果
将以上代码放进一个功能函数中：
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()以下为其使用的样例：
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)生成以下三种图像：
深度图：
高度图：
强度图：
