1 Introduction
With the wide use of internetbased 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 massproduction 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 deeplearning 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 deeplearning based network by utilizing an EncoderDecoder framework. Point Completion Network (PCN) 10 performs shape completion tasks by combining the advantages of Latentspace Generative Adversarial Network (LGAN) 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. 15introduced 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 (PFNet)
3 , is proposed by paying attention to the local details of an object, which makes it perform well in accuracy.However, these existing deeplearning 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 stateoftheart point cloud repair network, PFNet, has unsatisfactory inference speed due to the low efficiency of its downsampling module.
Downsampling is a basic operation for largescale 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 PFNet 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 onetime 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 selfdriving vehicles using the deep learning approach, i.e., the improved PFNet. In the improved method, we proposed an efficient uniform downsampling algorithm (CellIFPS) by combining the advantages of the IFPS and cell sampling, which significantly improves the inference efficiency of original PFNet.
The contributions of this paper can be summarized as follows:
(1) We employ a deep learning approach (i.e., the improved PFNet) to repair incomplete vehicle point clouds that cannot be addressed by traditional methods in autonomous driving.
(2) We improve the efficiency of original PFNet to meet the requirement of point cloud completion of selfdriving 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 realworld vehicle point cloud collected from a real vehicle selfdriving process and three incomplete vehicle point clouds with 5 different sizes collected from highfidelity 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 PFNet 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 selfdriving 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 selfdriving 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 PFNet) to repair the point incomplete cloud. Finally, the selfdriving vehicle design a safe route according to the complete vehicle point cloud to avoid collision (see Fig. 1 Case 2).
2.2 Improved GANbased Point Cloud Completion
In this section, the specific framework of improved PFNet will be introduced (see Fig. 2), which predicts the missing part of the point cloud from its incomplete known configuration. Compared with the original PFNet, we mainly modified the sampling step in the overall architecture. The overall architecture of improved PFNet consists of three fundamental parts, including MultiResolution Encoder (MRE), Point Pyramid Decoder (PPD), and Discriminator Network. The PFNet is a generative adversarial network 16 , and the Generator consists of MRE and PPD.
First, the improved PFNet uses CellIFPS 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
() by three independent Combined MultiLayer Perceptions (CMLPs). Finally, the combined latent vector is mapped into the final feature vector by a MultiLayer Perception (MLP) after those three individual latent vectors are concatenated (see Fig. 2). In the improved PFNet, CMLP is proposed as the feature extractor. The common MLP, such as PointNetMLP, cannot combine the lowlevel and middlelevel 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 (lowlevel, middlelevel, and highlevel features), which leads to better use of multilayer 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 obtained in the previous step. Therefore, the vector is first transformed into three feature results with different dimensions (where neurons, and ) by three fullyconnected layers. Then, point clouds with different resolutions are predicted according to different features .
The loss function is created by combining multistage completion loss (MCS) and adversarial loss in the improved PFNet. 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:
(1) 
where is the primary center points which be predicted by , is the secondary center points which be predicted by and . The generation of similar to . Moreover, is the ground truth of missing point cloud, and and are obtained from by applying IFPS.
is the hyperparameter.
The equation of Chamber Distance (CD) is as follows:
(2) 
where is the predicted point cloud, and is the ground truth point cloud.
The adversarial loss which is inspired by GAN is defined as follows:
(3) 
where which is the partial input, which is the real missing region, ( is the dataset size of ,). is the discriminator which is used to distinguish the predicted missing point cloud and the real missing point cloud. The function is defined as which maps the partial input into predicted missing region .
Finally, the joint loss of the MCS and the adversarial loss is defined as:
(4) 
where is the weight of completion loss , is the weight of adversarial loss , .
2.3 CellIFPS
Herein, the proposed CellIFPS is introduced in detail because it is the key to improve the efficiency of the original PFNet.
In the original PFNet, the inefficient IFPS is used due to its ability to precisely control the number of samples, resulting in the original PFNet 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 and the sampling set where the sampling points are stored, and then randomly sample a point from as the seed (the starting sampling point) and puts it into set . Finally, we sample one farthest point at a time and puts it into set until the number of sampling points meets the requirements. The farthest point is the one with the greatest distance from the set among the remaining points set , and the greatest distance is defined as follows:
(5) 
where indicates that the distance between and each point in the set is calculated.
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 CellIFPS 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 .
(2) Sample the point cloud using the cell sampling, and create the point cloud , the sampling set , and the remaining points set .
(3) Determine whether the current number of samples in the set . is greater than the number of samples . If it is equal, the sampling is finished, if not, the next step is performed.
(4) Randomly sample a point from as the seed, and determine whether the current number of samples in the set is equal to the number of samples . If , the IFPS is used to sample ) points from and these points are moved to ; If , the IFPS is used to sample ) points from and these points are moved to .
3 Results
In this section, to evaluate the performance of the improved PFNet, we use a realworld vehicle point cloud and three incomplete vehicle point clouds collected from highfidelity models to test it.
3.1 Experimental Environment
The details of the experimental environment are listed in Table 1.
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 twoway 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.
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 selfdriving scenarios. Thus, it should be noted that the real vehicle point cloud is incomplete, and we don’t have its real missing region.
3.3 Completion Results on Vehicle Point Clouds of Different Scales
In this section, we used the original PFNet and the improved PFNet to complete the vehicle point clouds of different sizes, where we utilized the original PFNet as a baseline. Then, we used Pred GT (prediction to ground truth) error and GT 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 GT error and GT
Pred error as evaluation metrics, which are widely used to evaluate the quality of point cloud generation
10 ; 17 . Pred 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 Pred error is similar to the Pred → GT error.Number of Points  Algorithm  Vehicle 1  Vehicle 2  Vehicle 3  Mean 
2048  Original PFNet  1.030/0.995  1.300/1.505  1.292/1.220  1.207/1.240 
Improved PFNet  1.092/0.985  1.270/1.354  1.322/1.200  1.228/1.180  
4048  Original PFNet  0.744/0.937  0.937/1.600  0.910/1.223  0.864/1.253 
Improved PFNet  0.775/0.922  0.971/1.435  0.898/1.236  0.881/1.198  
6048  Original PFNet  0.627/0.934  0.804/1.571  0.738/1.222  0.723/1.242 
Improved PFNet  0.659/0.924  0.820/1.453  0.760/1.222  0.746/1.200  
8048  Original PFNet  0.582/0.936  0.785/1.539  0.704/1.247  0.690/1.240 
Improved PFNet  0.641/0.934  0.753/1.536  0.704/1.244  0.699/1.238  
10048  Original PFNet  0.584/0.945  0.682/1.603  0.653/1.218  0.640/1.255 
Improved PFNet  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 GT error of completion tends to decrease significantly, and the GT Pred error of completion doesn’t decrease or increase significantly (see Fig. 6).
In conclusion, as shown in Fig. 6, The average Pred GT error of the improved PFNet is slightly larger (approximately 2.1%) than that of the original PFNet, and the average GT Pred error of the improved PFNet is slightly smaller (approximately 3.1%) than that of the original PFNet. The results indicated that there is no significant difference in the accuracy of the improved PFNet and the original PFNet, 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 selfdriving 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).Number of Points  Algorithm  Vehicle 1  Vehicle 2  Vehicle 3  
t1  t2  t3  t1  t2  t3  t1  t2  t3  
2048  Original PFNet  271.1  5.9  277.0  263.3  6.0  269.3  279.2  5.0  284.2 
Improved PFNet  6.0  7.0  13.0  14.9  5.0  19.9  6.0  5.0  11.0  
4048  Original PFNet  392.9  6.9  399.8  396.9  5.0  401.9  411.0  5.9  416.9 
Improved PFNet  7.9  6.0  13.9  9.0  6.0  15.0  8.9  5.9  14.8  
6048  Original PFNet  527.6  6.0  533.6  533.7  6.0  539.7  524.6  6.0  530.6 
Improved PFNet  11.1  6.0  17.1  15.0  6.0  21.0  11.0  6.0  17.0  
8048  Original PFNet  637.3  6.0  643.3  652.2  6.0  658.2  639.8  6.0  645.8 
Improved PFNet  14.0  5.1  19.1  15.9  5.0  20.9  11.9  6.0  17.9  
10048  Original PFNet  759.9  5.3  765.2  775.9  6.0  781.9  790.9  6.8  797.7 
Improved PFNet  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 PFNet are much larger than those of the improved PFNet when the number of points is the same (see Fig. 7). In any case, the generation module running time is always approximately 6 ms.
As shown in Fig. 8(a), for the original PFNet, the sampling module running time is much larger (265.6
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 PFNet, the sampling module running time is only a little larger (2.29.9 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%).
As shown in Fig. 9, compared with the original PFNet, the efficiency of the proposed completion networks (the improved PFNet) is greatly improved, and the speedup of overall completion is 1936.7. Moreover, compared with the IFPS algorithm, the efficiency of the proposed CellIFPS is greatly improved, the speedup of the sampling module using the proposed CellIFPS is 30.549.7.
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 PFNet, the efficiency of the improved PFNet is greatly improved due to the efficient CellIFPS, 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 CellIFPS increases, and the maximum speedup is 49.7.
3.4 Completion Results on a Realworld Vehicle Point Cloud
In this section, for the incomplete vehicle point cloud from the real selfdriving process, we specifically introduce the completion efficiency of the original PFNet and the improved PFNet, and briefly describe the completion effect.
As shown in Fig. 10, for the incomplete vehicle point cloud, both original PFNet and improved PFNet 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 PFNet and the improved PFNet are almost identical.
As listed in Table 4, the total running time of the improved PFNet is much less than that of the original PFNet, and the speedup is 30.9; the sampling module running time of the improved PFNet is much less than that of the original PFNet, and the speedup is 21.7. The improved PFNet performs a point cloud completion in only 20 ms during autonomous driving, i.e., the speed of the improved PFNet is approximately 46 fps during autonomous driving, which satisfies the requirement for realtime vehicle point cloud completion for autonomous driving.
Module  Original PFNet  Improved PFNet  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 selfdriving 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 CellIFPS by combining the onetime sampling algorithm Cell sampling with the incremental sampling algorithm IFPS, which can precisely control the number of sampling points. The proposed CellIFPS substantially improves the inference speed of the original PFNet without using a parallel strategy for acceleration. In autonomous driving scenarios, the tasks are generally timecritical. As listed in Table 4, the point cloud completion efficiency of the original PFNet is difficult to meet the needs of selfdriving, only 3 fps, and the point cloud completion efficiency of the improved PFNet is 46 fps, which is enough to meet the requirement of speed. Moreover, as shown in Fig. 7, the efficiency of the improved PFNet 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 largescale point clouds.
On the other hand, for the incomplete vehicle point cloud repair, the accuracy of improved PFNet is almost the same as that of the original PFNet, which performs well in accuracy and surpassing the widely used point cloud generation model PCN [3,10]. The improved PFNet with high accuracy can be effectively used to realize the realtime 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 PFNet 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 selfdriving 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 PFNet 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, CellIFPS, 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/GPUaccelerated 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 PFNet 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 selfdriving, we proposed the improved PFNet 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 realtime incomplete vehicle point cloud completion to improve the safety of selfdriving vehicles. In the proposed method, an efficient down sampling combining incremental sampling and onetime sampling, CellIFPS, is presented to significantly improve the inference speed of the original PFNet. 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 PFNet; (2) the proposed CellIFPS can greatly improve the efficiency of the original PFNet without using a parallel strategy for acceleration, and the enhancement effect increases with the increase of point cloud scale; (3) the improved PFNet has far greater speed than the original PFNet and almost the same accuracy as the original PFNet, which is the stateoftheart point cloud repair network in accuracy. The improved PFNet has the capability to complete incomplete vehicle point clouds of selfdriving 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).References
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