∎

11institutetext: J. Tu 22institutetext: G. Mei 33institutetext: School of
Engineering and Technolgy,
China University of Geosciences, Beijing, China
33email<EMAIL_ADDRESS>44institutetext: F. Piccialli 55institutetext:
Department of Mathematics and Applications “R. Caccioppoli”,
University of Naples Federico II, Italy

# An Efficient Deep Learning Approach Using Improved Generative Adversarial
Networks for Incomplete Information Completion of Self-driving Vehicles

Jingzhi Tu  Gang Mei  Francesco Piccialli

(Received: date / Accepted: date)

###### Abstract

Autonomous driving is the key technology of intelligent logistics in
Industrial Internet of Things (IIoT). In autonomous driving, the appearance of
incomplete point clouds losing geometric and semantic information is
inevitable owing to limitations of occlusion, sensor resolution, and viewing
angle when the Light Detection And Ranging (LiDAR) is applied. The emergence
of incomplete point clouds, especially incomplete vehicle point clouds, would
lead to the reduction of the accuracy of autonomous driving vehicles in object
detection, traffic alert, and collision avoidance. Existing point cloud
completion networks, such as Point Fractal Network (PF-Net), focus on the
accuracy of point cloud completion, without considering the efficiency of
inference process, which makes it difficult for them to be deployed for
vehicle point cloud repair in autonomous driving. To address the above
problem, in this paper, we propose an efficient deep learning approach to
repair incomplete vehicle point cloud accurately and efficiently in autonomous
driving. In the proposed method, an efficient downsampling algorithm combining
incremental sampling and one-time sampling is presented to improves the
inference speed of the PF-Net based on Generative Adversarial Network (GAN).
To evaluate the performance of the proposed method, a real dataset is used,
and an autonomous driving scene is created, where three incomplete vehicle
point clouds with 5 different sizes are set for three autonomous driving
situations. The improved PF-Net can achieve the speedups of over 19x with
almost the same accuracy when compared to the original PF-Net. Experimental
results demonstrate that the improved PF-Net can be applied to efficiently
complete vehicle point clouds in autonomous driving.

###### Keywords:

Industrial Internet of Things (IIoT) Autonomous driving Incomplete point
clouds Deep learning Generative Adversarial Network (GAN) Efficient
downsampling

##  1 Introduction

With the wide use of internet-based sensors, a new concept termed as the
Internet of Things (IoT) has emerged to facilitate the development of modern
industry 1 ; 19 . The ingenious application of intelligent logistics by
introducing Industrial Internet of Things (IIoT) significantly promotes the
development of the transportation industry, where autonomous driving is the
key technology. 3D vision using LiDAR has widely used in autonomous driving
due to its lower cost, more robust, richer information, and meeting the mass-
production standards 2 . Typically, to detect obstacles and other relevant
driving information, the computer vision system receives and analyzes the
original point cloud from LiDAR, where the appearance of incomplete point
clouds is inevitable owing to limitations of weather, sensor capability, and
viewing angle 3 . The emergence of incomplete point clouds, especially
fragmentary vehicle point clouds, may cause the reduction of the accuracy of
autonomous driving vehicles in object detection, traffic alert, and collision
avoidance.

For the above problem, traditional methods, such as interpolation algorithms
20 ; 21 ; 22 , cannot describe the complex geometric characteristics of the
vehicle without reference points. In recent years, deep learning is gradually
widely applied to 3D vision systems with the rapid development of machine
learning. Since the advent of the classic PointNet 4  showing powerful point
clouds operating ability, various deep-learning based approaches are developed
to solve 3D vision tasks directly 5 ; 6 ; 7 ; 8 . For the point cloud
completion, Panos et al. 1  proposed the first deep-learning based network by
utilizing an Encoder-Decoder framework. Point Completion Network (PCN) 10
performs shape completion tasks by combining the advantages of Latent-space
Generative Adversarial Network (L-GAN) 9  and FoldingNet 11 . Moreover, the
extensions of Convolutional Neural Network (CNN) in 3D have been demonstrated
to perform well when 3D voxel grids are used to represent 3D shapes 12 ; 13 ;
14 , where the CNN is computationally expensive for high voxel resolution.
Muhammad et al. 15  introduced the first reinforcement learning agent
controlled Generative Adversarial Network (GAN) to generate point clouds
quickly. Moreover, to repair the incomplete point cloud without modifying the
position of known points, an unsupervised point repair network based on GAN,
Point Fractal Network (PF-Net) 3 , is proposed by paying attention to the
local details of an object, which makes it perform well in accuracy.

However, these existing deep-learning based networks for point cloud
completion focus on the accuracy of point cloud completion, without
considering the efficiency of the inference process, which makes it difficult
for them to be deployed for vehicle point cloud repair in autonomous driving,
e.g., the state-of-the-art point cloud repair network, PF-Net, has
unsatisfactory inference speed due to the low efficiency of its downsampling
module.

Downsampling is a basic operation for large-scale point clouds, which can
improve the efficiency of subsequent algorithms, including 3D reconstruction
28 ; 29 , point cloud generation 30 ; 31 , and recognition 32 ; 33 . Uniform
downsampling, one of downsampling, is used to obtain uniform sparse point
clouds consistent with the geometric shape of the target, so as to remove
noise while preserving the geometric features of the target. In the uniform
downsampling algorithms, there are two commonly used algorithms: Iterative
Farthest Point Sampling (IFPS) 17  and cell sampling 34 . As an incremental
sampling algorithm 35 ; 36 , the IFPS is widely applied in point cloud
networks such as PointNet++ 17  and PF-Net because of its capability to
control number of sampling points. However, the IFPS has poor performance in
efficiency due to the characteristics of the incremental sampling algorithm.
Cell sampling, as a one-time sampling method 36 , has an excellent performance
in efficiency, but it cannot precisely control the number of sampling points.

In this paper, our objective is to repair incomplete vehicle point clouds
accurately and efficiently, which can serve object detection, traffic alert,
and collision avoidance to improve driving safety in autonomous driving. To
address the problem, we proposed to complete incomplete vehicle point clouds
of self-driving vehicles using the deep learning approach, i.e., the improved
PF-Net. In the improved method, we proposed an efficient uniform downsampling
algorithm (Cell-IFPS) by combining the advantages of the IFPS and cell
sampling, which significantly improves the inference efficiency of original
PF-Net.

The contributions of this paper can be summarized as follows:

(1) We employ a deep learning approach (i.e., the improved PF-Net) to repair
incomplete vehicle point clouds that cannot be addressed by traditional
methods in autonomous driving.

(2) We improve the efficiency of original PF-Net to meet the requirement of
point cloud completion of self-driving vehicles, where an efficient uniform
downsampling algorithm by combining the advantages of the IFPS and cell
sampling (i.e., the high efficiency and the ability to precisely control the
number of sampling points) is presented.

(3) We evaluate the method on a real-world vehicle point cloud collected from
a real vehicle self-driving process and three incomplete vehicle point clouds
with 5 different sizes collected from high-fidelity vehicle models.

The rest of the paper is organized as follows. In Section 2, the significance
and the implementation process of incomplete vehicle information completion,
and the architecture of the improved PF-Net are introduced. In Section 3, the
experimental design and data are briefly introduced, then the repair results
of incomplete vehicle point clouds are shown. In Section 4, we had some
discussions based on the experimental results. In Section 5, some conclusions
are obtained.

##  2 Method

###  2.1 Overview

In this paper, we propose to complete incomplete vehicle point clouds of self-
driving vehicles using the deep learning approach due to the limitations of
traditional data completion methods, such as interpolation algorithm. As
demonstrated in Fig. 1, the incomplete point cloud obtained by using LiDAR is
inevitable owing to limitations of viewing angle (see Fig. 1(a)-(c)), which
may cause the self-driving vehicle to misjudge the size of the surrounding
car, resulting in the appearance of collision (see Fig. 1 Case 1). To avoid
this potentially dangerous situation, we first normalize the incomplete
vehicle point cloud obtained by using LiDAR and then input it into the point
cloud completion networks based on GAN (i.e., the improved PF-Net) to repair
the point incomplete cloud. Finally, the self-driving vehicle design a safe
route according to the complete vehicle point cloud to avoid collision (see
Fig. 1 Case 2).

Figure 1: Illustration of the proposed deep learning approach using improved
GAN for incomplete information completion of self-driving vehicle

###  2.2 Improved GAN-based Point Cloud Completion

In this section, the specific framework of improved PF-Net will be introduced
(see Fig. 2), which predicts the missing part of the point cloud from its
incomplete known configuration. Compared with the original PF-Net, we mainly
modified the sampling step in the overall architecture. The overall
architecture of improved PF-Net consists of three fundamental parts, including
Multi-Resolution Encoder (MRE), Point Pyramid Decoder (PPD), and Discriminator
Network. The PF-Net is a generative adversarial network 16 , and the Generator
consists of MRE and PPD.

Figure 2: The overall architecture of improved PF-Net

First, the improved PF-Net uses Cell-IFPS to extract feature points from the
input point cloud in the MRE, which are representative points that can map the
whole shape of the input. Then, three scales point clouds including the
extracted feature points and the original points are mapped into three
individual latent vectors $F_{i}$ ($i=1,2,3$) by three independent Combined
Multi-Layer Perceptions (CMLPs). Finally, the combined latent vector is mapped
into the final feature vector $V$ by a Multi-Layer Perception (MLP) after
those three individual latent vectors $F_{i}$ are concatenated (see Fig. 2).
In the improved PF-Net, CMLP is proposed as the feature extractor. The common
MLP, such as PointNet-MLP, cannot combine the low-level and middle-level
features well when it only applies the final single layer to obtain the latent
vector. Compared with common MLP, the CMLP is found to be able to extract
combined latent vector after concatenating multiple dimensional potential
vectors stemed from the last four layers (low-level, middle-level, and high-
level features), which leads to better use of multi-layer features.

The objective of PDD is to output point clouds with three different
resolutions which represent the shape of the missing region by the final
feature vector $V$ obtained in the previous step. Therefore, the vector $V$ is
first transformed into three feature results ${FC}_{i}$ with different
dimensions (where ${FC}_{i}=1024,512,256$ neurons, and $i=1,2,3$) by three
fully-connected layers. Then, point clouds with different resolutions are
predicted according to different features ${FC}_{i}$.

The loss function is created by combining multi-stage completion loss (MCS)
and adversarial loss in the improved PF-Net. The MCS is used to minimize the
difference between the predicted three stages of point cloud and Ground Truth
(GT). The combined loss for three stages is as follows:

$\begin{split}L_{com}=&d_{CD1}\left(Y_{detail},Y_{GT}\right)+{\alpha
d}_{CD2}\left(Y_{primary},Y^{{}^{\prime}}_{GT}\right)\\\ &+2{\alpha
d}_{CD3}(Y_{secondary},Y^{{}^{\prime\prime}}_{GT})\end{split}$ (1)

where $Y_{primary}$ is the primary center points which be predicted by
${FC}_{3}$, $Y_{secondary}$ is the secondary center points which be predicted
by $Y_{primary}$ and ${FC}_{2}$. The generation of $Y_{detail}$ similar to
$Y_{secondary}$. Moreover, $Y_{GT}$ is the ground truth of missing point
cloud, and $Y^{{}^{\prime}}_{GT}$ and $Y^{{}^{\prime\prime}}_{GT}$ are
obtained from $Y_{GT}\ $by applying IFPS. $\alpha$ is the hyperparameter.

The equation of Chamber Distance (CD) is as follows:

$d_{CD}(S_{1},S_{2})=\frac{1}{S_{1}}\sum_{x\in
S_{1}}{{\mathop{\mathrm{min}}_{y\in
S_{2}}{\big{\|}x-y\big{\|}}^{2}_{2}+\frac{1}{S_{2}}\sum_{y\in
S_{2}}{{\mathop{\mathrm{min}}_{x\in S_{1}}{\big{\|}y-x\big{\|}}^{2}_{2}\ }}\
}}$ (2)

where $S_{1}$ is the predicted point cloud, and $S_{2}$ is the ground truth
point cloud.

The adversarial loss which is inspired by GAN is defined as follows:

$L_{adv}=\sum_{1\leq i\leq
S}{{\mathrm{log}\left(D\left(y_{i}\right)\right)+\sum_{1\leq j\leq
S}{{\mathrm{log}\left(1-D\left(F(x_{i})\right)\right)\ }}\ }}$ (3)

where $x_{i}\in X$ which is the partial input, $y_{i}\in Y$ which is the real
missing region, $i=1,2,\cdots,S$ ($S$ is the dataset size of $X$,$\ Y$). $D$
is the discriminator which is used to distinguish the predicted missing point
cloud and the real missing point cloud. The function $F$ is defined as
$F(){{:=}}PPD(MRE())$ which maps the partial input $X$ into predicted missing
region $Y^{{}^{\prime}}$.

Finally, the joint loss of the MCS and the adversarial loss is defined as:

$L={\lambda}_{c}L_{com}+{\lambda}_{a}L_{adv}$ (4)

where ${\lambda}_{c}$ is the weight of completion loss $L_{com}$,
${\lambda}_{a}$ is the weight of adversarial loss $L_{adv}$,
${\lambda}_{c}+{\lambda}_{a}=1$.

###  2.3 Cell-IFPS

Herein, the proposed Cell-IFPS is introduced in detail because it is the key
to improve the efficiency of the original PF-Net.

In the original PF-Net, the inefficient IFPS is used due to its ability to
precisely control the number of samples, resulting in the original PF-Net
inefficiencies for autonomous driving scenarios. As shown in Fig. 3(a), the
IFPS uses a circular iterative approach to sampling, the characteristics of
which make it inefficient and difficult to accelerate using parallel
strategies 23 ; 24 ; 25 . In the IFPS, we first establish the point cloud set
$C$ and the sampling set $S$ where the sampling points are stored, and then
randomly sample a point from $C$ as the seed (the starting sampling point) and
puts it into set $S$. Finally, we sample one farthest point at a time and puts
it into set $S$ until the number of sampling points meets the requirements.
The farthest point is the one with the greatest distance from the set $S$
among the remaining points set $S_{re}$, and the greatest distance is defined
as follows:

$d_{max}\mathrm{=}{\mathop{\mathrm{max}}_{x_{i}\in
S_{re}}({min(dist(x_{i},S))\ })\ }$ (5)

where $dist(x_{i},S)$ indicates that the distance between $x_{i}$ and each
point in the set $S$ is calculated.

Figure 3: An illustration of downsampling algorithms ((a) IFPS; (b) Cell
sampling; (c) Cell-IFPS.)

As shown in Fig. 3(b), there is another common method: cell sampling, which
downsamples the point cloud by constructing spheres with a specified radius,
and outputs the point in each sphere closest to the center of the sphere as
the sampling point. The sampling method is extremely efficient, but the number
of samples can only be controlled by adjusting the radius of the sphere.

Therefore, to sample efficiently and exactly control the number of samples,
the efficient Cell-IFPS by combining the advantages of the IFPS and cell
sampling is proposed, as shown in Fig. 3(c), the sampling steps are as
follows:

(1) Set number of samples $N$.

(2) Sample the point cloud using the cell sampling, and create the point cloud
$C$, the sampling set $S$, and the remaining points set $S_{re}$.

(3) Determine whether the current number of samples $N_{cur}$ in the set $S$.
is greater than the number of samples $N$. If it is equal, the sampling is
finished, if not, the next step is performed.

(4) Randomly sample a point from $S$ as the seed, and determine whether the
current number of samples $N_{cur}$ in the set $S$ is equal to the number of
samples $N$. If $N_{cur}>N$, the IFPS is used to sample $(N_{cur}-N$) points
from $S$ and these points are moved to $S_{re}$; If $N_{cur}<N$, the IFPS is
used to sample $(N-N_{cur}$) points from $S_{re}$ and these points are moved
to $S$.

##  3 Results

In this section, to evaluate the performance of the improved PF-Net, we use a
real-world vehicle point cloud and three incomplete vehicle point clouds
collected from high-fidelity models to test it.

###  3.1 Experimental Environment

The details of the experimental environment are listed in Table 1.

Table 1: The platforms used for testing Specifications |  Details
---|---
CPU |  Intel Xeon 5118
CPU RAM |  128 GB
CPU Frequency |  2.30 GHz
GPU |  Quadro P6000
CUDA Cores |  3840
GPU RAM |  24 GB
OS |  Window 10
Python |  Version 3.7
Pytorch |  Version 1.8
CUDA version |  Version 10.2

###  3.2 Data Description

The training dataset of the model is the ShapeNet Part 39 , which is a dataset
that selects 16 categories from the ShapeNetCore dataset 40  and annotated
with semantic information for the semantic segmentation task of point clouds.

As shown in Fig. 4, to simulate real autonomous driving scenarios, we set up a
two-way road with two lanes in an industrial estate (see Fig. 3(d)). In our
experiment, there are three different cars around the red autonomous vehicle,
and in addition, we obtained point clouds of 5 different scales from each car.
The missing regions of the vehicle point clouds obtained by LiDAR scanning are
also different due to the limitation of viewing angle (LiDAR Scan in Fig. 4).
Therefore, we have completed these three missing vehicle point clouds that are
common in the real world (see Fig. 4(a)-(c)). It should be noted that the
vehicle point clouds with missing regions are actually complete, but for
testing, incomplete vehicle point clouds are assumed.

Figure 4: An Illustration of three incomplete vehicle point clouds completion
for the experimental test in autonomous driving

As shown in Fig. 5, there is an incomplete vehicle point cloud with 2341
points from the famous KITTIT dataset 37 ; 38 , which is the real dataset
collected in the self-driving scenarios. Thus, it should be noted that the
real vehicle point cloud is incomplete, and we don’t have its real missing
region.

Figure 5: An incomplete vehicle point cloud from the real self-driving dataset
KITTIT

###  3.3 Completion Results on Vehicle Point Clouds of Different Scales

In this section, we used the original PF-Net and the improved PF-Net to
complete the vehicle point clouds of different sizes, where we utilized the
original PF-Net as a baseline. Then, we used Pred $\mathrm{\to}$ GT
(prediction to ground truth) error and GT $\mathrm{\to}$ Pred (ground truth to
prediction) error to evaluate the results of completion. Finally, we obtained
the running time of each step of the models.

####  3.3.1 Completion Accuracy on Vehicle Point Clouds of Different Scales

To evaluate the accuracy of completion results in autonomous driving, we use
Pred $\mathrm{\to}$ GT error and GT $\mathrm{\to}$ Pred error as evaluation
metrics, which are widely used to evaluate the quality of point cloud
generation 10 ; 17 . Pred $\mathrm{\to}$ GT error means the mean squared
distance between each predicted point and its nearest point in the ground
truth. It measures the difference between the prediction and the truth. GT
$\mathrm{\to}$ Pred error is similar to the Pred → GT error.

Table 2: The completion errors (Pred $\mathrm{\to}$ GT/GT $\mathrm{\to}$ Pred) of the incomplete vehicle point clouds in autonomous driving Number of Points |  Algorithm |  Vehicle 1 |  Vehicle 2 |  Vehicle 3 |  Mean
---|---|---|---|---|---
2048 |  Original PF-Net |  1.030/0.995 |  1.300/1.505 |  1.292/1.220 |  1.207/1.240
Improved PF-Net |  1.092/0.985 |  1.270/1.354 |  1.322/1.200 |  1.228/1.180
4048 |  Original PF-Net |  0.744/0.937 |  0.937/1.600 |  0.910/1.223 |  0.864/1.253
Improved PF-Net |  0.775/0.922 |  0.971/1.435 |  0.898/1.236 |  0.881/1.198
6048 |  Original PF-Net |  0.627/0.934 |  0.804/1.571 |  0.738/1.222 |  0.723/1.242
Improved PF-Net |  0.659/0.924 |  0.820/1.453 |  0.760/1.222 |  0.746/1.200
8048 |  Original PF-Net |  0.582/0.936 |  0.785/1.539 |  0.704/1.247 |  0.690/1.240
Improved PF-Net |  0.641/0.934 |  0.753/1.536 |  0.704/1.244 |  0.699/1.238
10048 |  Original PF-Net |  0.584/0.945 |  0.682/1.603 |  0.653/1.218 |  0.640/1.255
Improved PF-Net |  0.620/0.952 |  0.694/1.502 |  0.651/1.219 |  0.655/1.224

As listed in Table 2, the point cloud repair for Vehicle 1 has the best
performance, and the accuracy of the point cloud completion for Vehicle 2 is
the lowest. Moreover, when completing the same vehicle, as the point cloud
size (number of points) increases, the Pred $\mathrm{\to}$ GT error of
completion tends to decrease significantly, and the GT $\mathrm{\to}$ Pred
error of completion doesn’t decrease or increase significantly (see Fig. 6).

Figure 6: Average Pred $\mathrm{\to}$ GT error and GT $\mathrm{\to}$ Pred
error of point cloud completion for different sizes ((a) Average Pred
$\mathrm{\to}$ GT error; (b) Average GT →$\mathrm{\to}$ Pred error.)

In conclusion, as shown in Fig. 6, The average Pred $\mathrm{\to}$ GT error of
the improved PF-Net is slightly larger (approximately 2.1%) than that of the
original PF-Net, and the average GT $\mathrm{\to}$ Pred error of the improved
PF-Net is slightly smaller (approximately 3.1%) than that of the original PF-
Net. The results indicated that there is no significant difference in the
accuracy of the improved PF-Net and the original PF-Net, and both increase
with the increase of the number of points.

####  3.3.2 Completion Efficiency on Vehicle Point Clouds of Different Scales

Since the point cloud completion serves self-driving vehicles, we focus on the
inference efficiency of deep neural networks in this paper. The inference
process of completion networks consists of two modules: (1) sampling module
and (2) generation module. As shown in Fig. 2, the sampling module includes
two downsampling processes. First, the input vehicle point cloud needs to be
downsampled into a point cloud with 1024 points. Second, the point cloud 1024
points are downsampled into a point cloud with 512 points. Finally, we can
obtain three scales point clouds that meet the input requirements of the
generation module (i.e., the generator).

Table 3: Running time (ms) of point cloud completion on vehicle point clouds of different scales (Where $t_{1}$ is the sampling module running time, $t_{2}$ is the generation module running time, and $t_{3}$ is the total time, i.e., $t_{3}=t_{1}+t_{2}$.) Number of Points |  Algorithm |  Vehicle 1 |  Vehicle 2 |  Vehicle 3
---|---|---|---|---
t1 |  t2 |  t3 |  t1 |  t2 |  t3 |  t1 |  t2 |  t3
2048 |  Original PF-Net |  271.1 |  5.9 |  277.0 |  263.3 |  6.0 |  269.3 |  279.2 |  5.0 |  284.2
Improved PF-Net |  6.0 |  7.0 |  13.0 |  14.9 |  5.0 |  19.9 |  6.0 |  5.0 |  11.0
4048 |  Original PF-Net |  392.9 |  6.9 |  399.8 |  396.9 |  5.0 |  401.9 |  411.0 |  5.9 |  416.9
Improved PF-Net |  7.9 |  6.0 |  13.9 |  9.0 |  6.0 |  15.0 |  8.9 |  5.9 |  14.8
6048 |  Original PF-Net |  527.6 |  6.0 |  533.6 |  533.7 |  6.0 |  539.7 |  524.6 |  6.0 |  530.6
Improved PF-Net |  11.1 |  6.0 |  17.1 |  15.0 |  6.0 |  21.0 |  11.0 |  6.0 |  17.0
8048 |  Original PF-Net |  637.3 |  6.0 |  643.3 |  652.2 |  6.0 |  658.2 |  639.8 |  6.0 |  645.8
Improved PF-Net |  14.0 |  5.1 |  19.1 |  15.9 |  5.0 |  20.9 |  11.9 |  6.0 |  17.9
10048 |  Original PF-Net |  759.9 |  5.3 |  765.2 |  775.9 |  6.0 |  781.9 |  790.9 |  6.8 |  797.7
Improved PF-Net |  14.9 |  5.0 |  19.9 |  17.9 |  6.0 |  23.9 |  14.0 |  6.0 |  20.0

As listed in Table 3, when the number of points and the model are the same,
there is little difference in the running time of each module for the
completion of different vehicle point clouds. As the number of points
increases, the sampling module running time and the total time tend to
increase when the model is the same, and the sampling module running time and
the total time of the original PF-Net are much larger than those of the
improved PF-Net when the number of points is the same (see Fig. 7). In any
case, the generation module running time is always approximately 6 ms.

Figure 7: Average total time and average sampling module running time in
original PF-Net and improved PF-Net ((a) Average total time; (b) Average
sampling module running time.)

As shown in Fig. 8(a), for the original PF-Net, the sampling module running
time is much larger (265.6$\sim$
769.6 ms) than the generation module running time, and the difference between
them increases as the number of points increases (the percentage of the
sampling module running time in the total time increases from 97.98% to
99.23%), which means that the sampling module is the key factor in the
efficiency of point cloud completion, and its impact increases with the number
of points. As shown in Fig. 8(b), for the improved PF-Net, the sampling module
running time is only a little larger (2.2$\sim$9.9 ms) than the generation
module running time, and the difference between them increases as the number
of points increases (the percentage of the sampling module running time in the
total time increases from 60.96% to 73.24%).

Figure 8: Average running time (ms) bar plots of sampling module and
generation module ((a) Original PF-Net; (b) Improved PF-Net.)

As shown in Fig. 9, compared with the original PF-Net, the efficiency of the
proposed completion networks (the improved PF-Net) is greatly improved, and
the speedup of overall completion is 19$\sim$36.7. Moreover, compared with the
IFPS algorithm, the efficiency of the proposed Cell-IFPS is greatly improved,
the speedup of the sampling module using the proposed Cell-IFPS is
30.5$\sim$49.7.

Figure 9: Speedups of overall completion and sampling module in the improved
PF-Net ($speedup\mathrm{=}\frac{t_{P}}{t_{IP}}$, where $t_{P}$ is the running
time of overall completion or sampling module in the original PF-Net, and
$t_{IP}$ is the running time of overall completion or sampling module in the
improved PF-Net.)

The aforementioned comparative results indicate that:

(1) The efficiency of the sampling module is the key factor in the efficiency
of point cloud completion, and its impact increases with the number of points.

(2) Compared with the original PF-Net, the efficiency of the improved PF-Net
is greatly improved due to the efficient Cell-IFPS, and the maximum speedup is
36.7.

(3) Compared with the IFPS algorithm, as the scale of the point clouds
increases, the acceleration effect of the proposed Cell-IFPS increases, and
the maximum speedup is 49.7.

###  3.4 Completion Results on a Real-world Vehicle Point Cloud

In this section, for the incomplete vehicle point cloud from the real self-
driving process, we specifically introduce the completion efficiency of the
original PF-Net and the improved PF-Net, and briefly describe the completion
effect.

As shown in Fig. 10, for the incomplete vehicle point cloud, both original PF-
Net and improved PF-Net successfully complete the missing area of the vehicle
so that the point cloud has the complete shape of the vehicle after the
repair, and the missing point clouds generated by the original PF-Net and the
improved PF-Net are almost identical.

Figure 10: An Illustration of vehicle point cloud completion on a real-world
vehicle point cloud in self-driving

As listed in Table 4, the total running time of the improved PF-Net is much
less than that of the original PF-Net, and the speedup is 30.9; the sampling
module running time of the improved PF-Net is much less than that of the
original PF-Net, and the speedup is 21.7. The improved PF-Net performs a point
cloud completion in only 20 ms during autonomous driving, i.e., the speed of
the improved PF-Net is approximately 46 fps during autonomous driving, which
satisfies the requirement for real-time vehicle point cloud completion for
autonomous driving.

Table 4: Running time (ms) of point cloud completion on a real self-driving vehicle point cloud ($speedup\mathrm{=}\frac{t_{P}}{t_{IP}}$, where $t_{P}$ is the total running time or the sampling module running time in the original PF-Net, and $t_{IP}$ is the total running time or the sampling module running time in the improved PF-Net.) Module |  Original PF-Net |  Improved PF-Net |  Speedup
---|---|---|---
Sampling Module |  368.1 |  11.9 |  30.9
Generation Module |  4.9 |  5.3 |  0.9
Total |  373.0 |  17.2 |  21.7

##  4 Discussion

###  4.1 Advantages of the proposed deep learning method

The advantage of the proposed method is to consider the efficiency of point
cloud completion networks for self-driving vehicles. More specifically, in
this paper, we found that the sampling algorithm is the key factor that
restricts the efficiency of point cloud completion networks. Therefore, we
proposed an efficient sampling algorithm Cell-IFPS by combining the one-time
sampling algorithm Cell sampling with the incremental sampling algorithm IFPS,
which can precisely control the number of sampling points. The proposed Cell-
IFPS substantially improves the inference speed of the original PF-Net without
using a parallel strategy for acceleration. In autonomous driving scenarios,
the tasks are generally time-critical. As listed in Table 4, the point cloud
completion efficiency of the original PF-Net is difficult to meet the needs of
self-driving, only 3 fps, and the point cloud completion efficiency of the
improved PF-Net is 46 fps, which is enough to meet the requirement of speed.
Moreover, as shown in Fig. 7, the efficiency of the improved PF-Net is
insensitive to changes in the size of the point cloud, i.e., an increase in
the number of points doesn’t lead to a sharp decrease in its efficiency, which
gives it the potential to serve tasks such as the 3D reconstruction of large-
scale point clouds.

On the other hand, for the incomplete vehicle point cloud repair, the accuracy
of improved PF-Net is almost the same as that of the original PF-Net, which
performs well in accuracy and surpassing the widely used point cloud
generation model PCN [3,10]. The improved PF-Net with high accuracy can be
effectively used to realize the real-time vehicle point cloud completion to
enhance the safety of autonomous driving.

###  4.2 Shortcomings of the proposed deep learning method

The shortcoming of the proposed method is that the accuracy of the point cloud
completion may be reduced or even the point cloud completion may fail when the
scale of the input point cloud is too small. According to the network
architecture, the input point cloud needs to use downsampling to extract the
feature points, in this paper, the input point cloud is downsampled by 1024
points and 512 points, which means that the improved PF-Net cannot complete
the point cloud when the size of the input point cloud is less than 1024
points. On the other hand, for the real self-driving data, we lack the real
point cloud of the missing part of the incomplete vehicle point cloud.
Therefore, we don’t use the corresponding evaluation metric to evaluate the
completion accuracy.

###  4.3 Outlook and Future Work

In the future, we plan to apply the improved PF-Net to repair incomplete point
clouds that include more kinds of obstacles (e.g., trees, roadblocks,
telegraph poles) in autonomous driving. Further, the proposed efficient
uniform sampling method, Cell-IFPS, will be applied to more tasks for point
cloud (e.g., 3D reconstruction, object recognition, point cloud segmentation)
due to the sampling being one of the foundations of point cloud processing.

There are several techniques to improve the efficiency of deep learning,
including CPU/GPU-accelerated parallel technology and TensorRT technology 18 ;
26 ; 27 . In the future, we will use parallel technology to speed up the
sampling process or use the TensorRT technology to accelerate the generation
process at the cost of slightly reducing the accuracy.

Moreover, the deployment of deep learning in actual production is still
difficult. Compared with Python language, the deployment of deep learning
algorithms developed by C/C++ language is more convenient. Therefore, we will
consider developing or using API to convert the Python version of the improved
PF-Net to the C/C++ version to facilitate deployment.

##  5 Conclusion

In this paper, to meet the requirements of algorithm efficiency for incomplete
point cloud completion in the process of self-driving, we proposed the
improved PF-Net to repair incomplete vehicle point cloud accurately and
efficiently in autonomous driving. The essential idea of the method is to use
efficient deep learning for real-time incomplete vehicle point cloud
completion to improve the safety of self-driving vehicles. In the proposed
method, an efficient down sampling combining incremental sampling and one-time
sampling, Cell-IFPS, is presented to significantly improve the inference speed
of the original PF-Net. To evaluate the performance of the proposed method, a
real dataset is used, and an autonomous driving scene is created, where three
incomplete vehicle point clouds with 5 different sizes are set for three
autonomous driving situations. The results show that: (1) inefficient sampling
module is the key to restrict the efficiency of the original PF-Net; (2) the
proposed Cell-IFPS can greatly improve the efficiency of the original PF-Net
without using a parallel strategy for acceleration, and the enhancement effect
increases with the increase of point cloud scale; (3) the improved PF-Net has
far greater speed than the original PF-Net and almost the same accuracy as the
original PF-Net, which is the state-of-the-art point cloud repair network in
accuracy. The improved PF-Net has the capability to complete incomplete
vehicle point clouds of self-driving vehicles.

###### Acknowledgements.

This research was jointly supported by the National Natural Science Foundation
of China (Grant No. 11602235), and the Fundamental Research Funds for China
Central Universities (2652018091).

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# Study of the performance of the HEPD apparatus for the CSES mission

Beatrice Panico  INFN Napoli, I-80126 Naples, Italy - *Corr. author  Francesco
Palma  Alessandro Sotgiu  University of Rome Tor Vergata, Via della ricerca
scientifica, 00133 Roma, Italy  INFN Roma Tor Vergata, Via della ricerca
scientifica, 00133 Roma, Italy

###### Abstract

The High-Energy Particle Detector (HEPD) is one of the payloads of the CSES
space mission. The CSES (China Seismo-Electromagnetic Satellite) mission will
investigate the structure and the dynamic of the topside ionosphere, will
monitor electric and magnetic field and high energy particle fluctuations,
searching for their correlations with the geophysical activity, in order to
contribute to the monitoring of earthquakes from space. The HEPD is built by
the Italian collaboration and has different goals. It will study the temporal
stability of the inner Van Allen radiation belts, the precipitation of trapped
particles in the atmosphere and the low energy component of the cosmic rays (5
- 100 MeV for electrons and 15 - 300 MeV for protons). Here is presented a
study of the performance of the apparatus to separate electrons and protons
and identify nuclei up to iron.

##  I The CSES Mission

The China Seismo-Electromagnetic Satellite (CSES) is a space mission dedicated
to Wang :

  1. 1.

measurement of signals from electromagnetic emission and its disturbances in
ionosphere;

  2. 2.

measurement of background magnetic field in space;

  3. 3.

measurement of the disturbance of plasma in ionosphere, such as contents,
density and temperature of the ions, density and temperature of the electron;

  4. 4.

measurement of energetic particles precipitation.

Some studies Zhang ; Sgrigna ; Alex  show a correlation between the
electromagnetic anomalies from Earth and ionosphere perturbations and the
earthquakes. In DeSantis , a review of the searches for correlation between
phenomena in the atmosphere, ionosphere, magnetosphere and seismic events is
reported. Different observables are studied: the precipitation of low energy
electrons (E $>$ 0.3 MeV) trapped within the Van Allen Belts Battiston ; the
depletion in the intensity of VLF electric field at satellite altitudes in
Nemec ; Pisa ; time/space localized OLR anomalies Guo .

CSES will also complement the cosmic ray measurements in an energy range up to
few hundreds of MeV and will contribute to the study of the solar-terrestrial
environment with the observation of Coronal Mass Ejections.

The satellite is based on the Chinese CAST2000 platform. It is a 3-axis
attitude stabilized satellite and will be placed in a 97,4∘ inclination Sun-
synchronous circular orbit, at an altitude of $\sim$500 km. The working zone
is in the latitude range [-65∘;+65∘], where there is no rotation of solar
panel and no action for attitude and orbit control system of satellite.

The launch is scheduled for 2017, July-August and the expected lifetime is 5
years.

CSES hosts several instruments on board, as reported in Tab. 1.

Category | Payloads
---|---
ElectroMagnetic field | Electric field detector
| High precision magnetometer
| Search coil magnetometer
In-situ plasma | Plasma analyzer package
| Langmuir probe
Plasma construction | GNSS occultation receiver
| Tri-band beacon
Energetic particle | High energy particle package
Table 1: CSES payloads.

##  II The High-Energy Particle Detector

The High-Energy Particle Detector (HEPD) is one of the payloads of the CSES
space mission. The HEPD is built by the Italian collaboration; its main
characteristics are reported in Table 2.

Parameter | Value
---|---
Energy Range | Electrons: 3-100 MeV
Energy Range | Protons: 30-200 MeV
Angular resolution |  $<8^{\circ}$ at 5 MeV
Energy resolution |  $<10\%$ at 5 MeV
Particle identification | $>90\%$
Free field of view | $\geq 70^{\circ}$
Pointing | Zenith
Operative temperature | -10∘+45∘
Table 2: HEPD main technical characteristics.

To study the low energy component of the cosmic rays, the HEPD detector is
composed by different instruments: a tracker, made of two planes of double-
side silicon micro-strip sensors, at the top of the instrument; the trigger
plane made by a plastic scintillator read by 2 PMTs and divided into 6
segments; a calorimeter, composed by 16 plastic scintillators with dimensions
(15x15x1) cm3 and a layer of 9 LYSO cubes, for a resulting plane of dimension
(15x15x4) cm3; a scintillator veto system, 5 mm thick, at sides and at the
bottom of the instrument.

##  III MC Simulation

A Monte Carlo simulation based on Geant4 toolkit was developed in order to
evaluate the HEPD performances. In Fig. 1A one veto plane has been removed to
show the calorimeter inside, the silicon planes are on the left; in Fig. 1B
the electronic box is showed; in Fig. 1C the 16 scintillator planes are
showed, the first plane is involved in the trigger configuration.

Figure 1: View of the HEPD electric box and detectors.

The interaction of particles inside the silicon tracker, the trigger plane,
the calorimeter planes and the veto systems, togheter with the mechanical
structure and the HEPD box were simulated.

In order to estimate the performances of HEPD, 109 events have been uniformly
generated according to a power law spectrum $E^{-\gamma}$, where:

  * •

$\gamma=2.2$, for electrons in the energy range [1-200] MeV;

  * •

$\gamma=2.7$, for protons in the energy range [10-500] MeV;

To ensure an uniform exposure for the detector, a spherical surface around
HEPD, with a different bin size at the poles and the equator, has been
considered. The simulation has been used to study the trigger mask efficiency,
the energy resolution of the calorimeter and the electron/proton
discrimination.

Figure 2: Trigger basic mask (T1 $\&\&$ P1) for simulated electrons (left) and
protons (right). The blue line represents all triggered events; the red line
represents the events without a signal into the lateral veto; the black line
represents events completely contained into the detector.

Figure 3: Trigger mask (T1 $\&\&$ P1 $\&\&$ P2) for simulated electrons (left)
and protons (right). The blue line represents all triggered events; the red
line represents the events without a signal into the lateral veto; the black
line represents events completely contained into the detector.

In Fig. 2 the trigger rate is reported with the basic trigger both for
electrons and protons. It requires the coincidence between the trigger plane
(T1) and the first calorimeter plane (P1) (blue line). The red line represents
the trigger rate for those events without a signal into the lateral veto; the
black line represents the trigger rate for events completely contained into
the detector. In Fig. 3 the trigger rate for a different mask is reported; it
requires the coincidence of the trigger plane (T1), of the first (P1) and the
second (P2) calorimeter plane.

###  III.1 Energy resolution

The HEPD calorimeter is composed by 2 different materials: the upper
calorimeter is made by plastic scintillator planes, while the lower
calorimeter is made by Lyso cristals. To study the different energy losses in
each detector, simulated samples at fixed energies have been used. The minimum
energy required for particles to entirely cross the 3.5 mm aluminium thickness
of the satellite wall is $\sim$2 MeV for electrons and $\sim$30 MeV for
protons.
The simulated energy range is [3-150] MeV for electrons and [30-200] MeV for
protons. In Fig. 4 the energy losses of electrons with energy E=100 MeV into
the upper and lower calorimeter are reported. The green line represents the
total energy released by the particle; the magenta line represents the energy
deposited into the upper calorimeter, while the blue line is the energy
released into the Lyso cristals. In Fig. 4 the profile of the energy released
into the upper calorimeter (CALO) vs the lower calorimeter (LYSO) is also
reported. In Fig. 5 the same plots are reported for protons with energy E=200
MeV.

Figure 4: Energy losses of electrons with energy E=100 MeV into the upper and
lower calorimeter (top). Profile of the energy released into the upper
calorimeter vs the lower calorimeter (down).

Figure 5: Energy losses of protons with energy E=200 MeV into the upper and
lower calorimeter (top). Profile of the energy released into the upper
calorimeter vs the lower calorimeter (down).

In Fig. 6 the energy resolution of the HEPD calorimeter is reported. Only
events completely contained into the calorimeter have been considered. The
energy resolution has to be $<10\%$ at 5 MeV. Both for electrons and for
protons it is in good agreement with these initial requests. The energy losses
inside the material of the mechanical structures are responsible of the low
energy tails observed in the distributions.

Figure 6: Energy resolution for the calorimeter for electrons (top) and
protons (bottom).

###  III.2 Electron/Proton discrimination

One of the most important features of HEPD is the separation between electrons
and protons.

Since, at these energies protons are slow and not relativistic within the HEPD
operational range, the _dE vs E_ method for discriminating electrons against
protons can be used. To normalize the simulated proton and electron spectra,
the results in lpsc  have been used. The normalization factor is chosen at 200
MeV, where proton spectrum is $\sim$45 times greater than the electron
spectrum.
The _dE_ is measured within the two layers of silicon tracker, while the sum
of the energy released in the detector provides the _E_ measurement. The veto
system allow to select events completely contained into the calorimeter. The
resulting plots for electrons and protons are shown in Fig. 7. Electron and
proton distributions are very different and particles lay in separate energy
bands.

Figure 7: Top: Distributions of the energy loss in the silicon tracker and the
total energy loss in the detector for electrons and protons. Bottom: Spectrum
used to normalize electron and proton MC simulation.

##  IV Conclusions

In this paper the study of the performances of the HEPD detector have been
described. The HEPD project involved the construction of 4 detector versions:
the Electrical Model, the Structural and Thermal Model, the Qualification
Model and the Flight Model.
The Qualification Model have been tested in April 2016 at the Beam Test
Facility (BTF) of the “Laboratori Nazionali di Frascati” of INFN. The Flight
Model has also been tested at the BTF in Frascati in September 2016 where it
was irradiated with electrons and positrons from 30 to 150 MeV. In November
2016, the Flight model has been also tested at Trento Facility with a proton
beam with energies in the range [35 - 220] MeV. The beam test data are under
analysis.

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