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\begin{document}

\title{Research on Partial Missing Reconstruction of 3D Point Cloud Model Based
on Point Fractal Network}



\author[1]{jian wang}%
\author[1]{Zhenglin LI}%
\author[1]{Zhijie FANG}%
\author[1]{Yuan MA}%
\author[1]{Binjie SHI}%
\author[1]{Qingqing FAN}%
\author[1]{Zhiwen WANG}%
\affil[1]{Guangxi University of Science and Technology}%


\vspace{-1em}



  
  \date{June 16, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
In order to solve the problem of partial loss of data information and
structure of 3D point cloud model due to subjective and objective
factors such as occlusion and noise, a partial deletion reconstruction
method of 3D point cloud model based on PF-Net was proposed, and a model
deletion reconstruction system was developed. Based on the deep learning
PF-Net network architecture, the Batch Normal layer and the Dropout
layer are introduced to normalize the original datasets in batches,
which further improves the reconstruction efficiency and accuracy of
some missing point cloud models. In this paper, 11 point cloud models
are selected to carry out reconstruction experiments with some missing
data information and structural features, and the experiments show that
the proposed method has higher reconstruction efficiency than the L-Gan
and PCN methods when the same dataset is used for training and testing.
In the eleven test categories, the average improvement of the
refactoring method in this paper is 12\%-27\%. The proposed method has a
significant effect in dealing with the partial deletion reconstruction
of small-scale models, and at the same time improves the efficiency and
accuracy of reconstruction, which has good application value.%
\end{abstract}%



\sloppy


\textbf{Research on Partial Missing Reconstruction of 3D Point Cloud
Model Based on Point Fractal Network}

WANG Jian\textsuperscript{1},LI Zhenglin\textsuperscript{1**},FANG
Zhijie\textsuperscript{2**},MA Yuan\textsuperscript{1},SHI
Binjie\textsuperscript{1},FAN Qingqing\textsuperscript{1},WANG
Zhiwen\textsuperscript{2}

(1.School of Automation, Guangxi University of Science and
Technology,Liuzhou,Guangxi,545616,China;2. School of Electronic
Engineering, Guangxi University of Science and
Technology,Liuzhou,Guangxi,545616,China)

Corresponding author:LI Zhenglin,E-mail:13407885535@163.com.

FANG Zhijie, E-mail: nnfang@semi.ac.cn.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflict of interest.

Acknowledgements

National Natural Science Foundation of China (12364011); Guangxi Key
Research and Development Project (GuIKE AB23026146); Guangxi Higher
Education Project(2020JGB238); Central Government Special Fund for
Guiding Local Science and Technology Development (2023PRJ1013); Funding
and support of Guangxi Key Laboratory of Big Data of Finance and
Economics Open Fund Project (FEDOP2022A06).

\textbf{Abstract:} In order to solve the problem of partial loss of data
information and structure of 3D point cloud model due to subjective and
objective factors such as occlusion and noise, a partial deletion
reconstruction method of 3D point cloud model based on PF-Net was
proposed, and a model deletion reconstruction system was developed.
Based on the deep learning PF-Net network architecture, the Batch Normal
layer and the Dropout layer are introduced to normalize the original
datasets in batches, which further improves the reconstruction
efficiency and accuracy of some missing point cloud models. In this
paper, 11 point cloud models are selected to carry out reconstruction
experiments with some missing data information and structural features,
and the experiments show that the proposed method has higher
reconstruction efficiency than the L-Gan and PCN methods when the same
dataset is used for training and testing. In the eleven test categories,
the average improvement of the refactoring method in this paper is
12\%-27\%. The proposed method has a significant effect in dealing with
the partial deletion reconstruction of small-scale models, and at the
same time improves the efficiency and accuracy of reconstruction, which
has good application value.

\textbf{Keywords:} 3D point cloud; deep learning; network architecture;
missing refactoring; reconfiguration system

\textbf{1 Introduction}

In recent years, the method of using 3D point cloud for data acquisition
has been widely used. The realization of this method relies on scanning
3D objects or scenes, so as to obtain massive point sets with rich 3D
information and process them. The point set data collected in this
process is called the point cloud\textsuperscript{{[}1{]}}. Advanced
acquisition equipment can easily and quickly obtain the information and
structural characteristics of the point cloud model of the object, so
that the point cloud model is presented in the form of three-dimensional
spatial coordinates, and there are many application
scenarios\textsuperscript{{[}2{]}}. At present, the most commonly used
3D point cloud data acquisition equipment is 3D laser scanner, which
uses the time difference of laser echo to calculate the distance between
the scanned object and the scanning center point, so as to quickly
obtain the 3D spatial coordinates of the object
surface\textsuperscript{{[}3{]}}. However, in the scanning process, due
to the influence of factors such as material surface occlusion, light
reflection and sensor transmission stability, the collected point cloud
data is often missing, which will cause certain difficulties in the use
process. Therefore, it is very necessary to reconstruct the point cloud
model\textsuperscript{{[}4{]}}.

At present, the methods of point cloud model missing reconstruction
mainly include the following: surface reconstruction method based on
implicit function, surface reconstruction method based on Delaunay
triangulation and reconstruction method based on deep learning network.
Most of the first two methods use the traditional way to divide and
organize the point cloud data through the structure of
octree\textsuperscript{{[}5{]}}, and perform surface fitting for each
cell to generate a signed distance field\textsuperscript{{[}6{]}} to
restore the sharp features in the point cloud\textsuperscript{{[}7{]}}.
The first method is sensitive to noise and can not deal well with
surfaces with complex or irregular topologies. The second method may
produce too many quadrangles during triangulation, resulting in a
decrease in mesh quality. The resulting triangular mesh topology may not
be smooth enough, especially when dealing with surfaces with large
curvature changes, and the computational complexity is high. In the
delaunay triangulation process, it is necessary to make several
traversal and judgment. With the increase of the scale of point set, the
amount of calculation increases exponentially, which requires high
computer configuration and high cost. The third method can generate
high-quality 3D models in a relatively short time by computing
large-scale point cloud data in parallel; It can learn the potential
features in the point cloud data, so as to reconstruct the
three-dimensional model more accurately. It can understand the point
cloud data from multiple angles and levels, improve the accuracy of the
missing reconstruction of the high point cloud model, and cope with a
certain degree of data noise, missing and incomplete, and has a certain
robustness to the noise and missing data. Therefore, the reconstruction
method based on deep learning network has become the first choice of
most researchers\textsuperscript{{[}8{]}}.

In recent years, deep learning has become more and more widely used in
the field of point cloud. Among them, the PointNet model proposed in
literature {[}9{]} solves the problem of processing disordered point
sets, and makes remarkable progress in the algorithm of directly
executing shape completion of disordered point sets, which can generate
point clouds from input data, but is not comprehensive enough in point
cloud reconstruction. In literature {[}10{]}, a point cloud autoencoder
framework named L-GAN was proposed based on PointNet architecture and a
new measurement index was adopted. This method was trained by finding
the best match between the cloud convergence at two different points,
but it performed poorly in the reconstruction performance of the point
cloud model. The Point Completion Network (PCN) in literature {[}11{]}
mainly studies the shape completion problem of point cloud and proposes
an architecture based on deep learning, but it is not satisfactory in
terms of point cloud reconstruction accuracy. The SPD method proposed in
literature {[}12{]} is superior to most point cloud reconstruction
methods in widely used benchmark tests, but the data set used is larger,
the network structure is more complex, and the training time is longer.
Literature {[}13{]} designed a new point cloud complement model named
PointTr, which adopted the structure of geometric perception transform
encoder-decoder to realize point cloud complement, and could achieve the
missing reconstruction performance of point cloud model well, but the
effect was not ideal in the missing reconstruction of small-scale point
cloud model.

Point Fractal Network (PF-Net) proposed by Huang et
al.\textsuperscript{{[}14{]}} uses part of the point cloud as input, and
only the missing part of the point cloud is in the output, rather than
the whole object. In this way, the structural features of the original
point cloud can be retained after repair, and the network can focus on
learning the missing location and structural features. However, for some
known points and inferred points, they are only related at the semantic
level, but not the same in space. It combines feature extractor and
multi-layer perceptron (CMLP) to extract multi-layer features from
partial point cloud and low resolution feature points, greatly enhancing
the ability of semantic and geometric information extraction by the
network. The network also designed a Point Pyramid Decoder (PPD) to
efficiently estimate missing point clouds using network layering. It can
retain the spatial arrangement of incomplete point clouds and calculate
the detailed geometric information of predicting missing regions.
Compared with the previous methods, it greatly improves the accuracy of
partial missing reconstruction of three-dimensional point cloud models.

Combined with the above introduction to deep learning, this paper
improved its algorithm by combining the characteristics of
PF-Net\textsuperscript{{[}14{]}} and the accuracy of point cloud model
reconstruction, and developed a partial missing reconstruction system of
3D point cloud model. The reconstruction results were compared with the
two typical methods, and a better reconstruction effect was obtained.

The structure of this paper is as follows: the second section describes
the improvement of the algorithm, the third section describes the
reconstruction system developed on the basis of the improved algorithm,
the fourth section describes the whole experiment and result analysis,
the fifth section makes a summary of the whole paper and draws the
conclusion of this paper.

\textbf{2 Algorithm improvement}

Based on the study of PF-Net\textsuperscript{{[}14{]}}, this paper
introduces the Batch Normal (Batch Normal) layer and Dropout layer. By
adding Batch Normal layers to the Linear layer of the PPD and
Multi-Resolution Encoder (MRE), and adding Dropout layers to the Linear
layer of the discriminator, The purpose of introducing these two network
layers is to improve the efficiency and accuracy of partial missing
point cloud reconstruction, so that it can be applied to more scenarios.
The algorithm improvement design is shown in Figure 1.

Fig. 1 Method design drawing

\textbf{2.1 Adding the Bath Normal Layer}

The Batch Normal layer was proposed in literature {[}15{]} in 2015,
which aims to limit the activation value within a certain range to
ensure that the expression ability and information transmission ability
of the network are not too large or too small. Through normalization,
the network can be more stable in the training process and help to
improve the generalization ability of the model. The MobileNets model in
reference {[}16{]} uses Batch Normal to carry out standard batch
normalization operation in its two-layer convolution to reduce
computational cost and improve execution efficiency. Inspired by the
literature, this paper proposes a method to add Batch Normal layer,
which can further optimize the performance of PF-Net, improve the
training and inference efficiency of the network, and greatly improve
the efficiency and accuracy of partial missing reconstruction of the
point cloud model.

Batch Normal Normalizes the input data set to ensure that the
statistical characteristics of the network remain stable for each small
batch of data. It computes the mean and variance on each small batch of
data and normalizes the input so that the mean of the input is close to
0 and the variance is close to 1. A learnable scaling factor (Gamma) and
offset parameter (Beta) are introduced to re-scale and shift the
normalized data to preserve the expressibility of the network. There are
also two non-learnable parameters, which are saved as part of the batch
normalization state and used to normalize the new sample during the
inference phase, as shown in Figure 2.

Fig. 2 Parameter setting diagram

Bath Normal performs regularization according to mini-batch when
learning, and provides a small batch of data to the network at a time
during training, as shown in Figure 3.

Fig. 3 Data processing mode

Combined with the characteristics of Bath Normal layer, its main
functions after adding PF-Net are as follows:

(1) Improve model stability: By standardizing each feature in
small-batch data, Bath Normal layer makes the distribution of each
feature more stable, which helps to reduce model fluctuations in the
training process, improve the stability of the model, and make the model
better adapt to various data changes in the training process, reducing
the risk of overfitting.

(2) Accelerate model convergence: After the Bath Normal layer is added,
the problem of disappearing gradient is reduced, so that the model can
find the optimal solution faster, thus accelerating the convergence
speed of the training process. This means that the model can learn the
underlying patterns of the data more quickly, which in turn improves the
ability of point cloud refactoring.

(3) Enhance the generalization ability of the model: it can make the
feature distribution close to the natural distribution of human
perception, and improve the generalization ability of the model. This
means that the model can also perform well when dealing with previously
unseen point cloud data, which increases the usefulness of the model.

(4) Improve the quality of point cloud reconstruction: By normalizing
the output of each feature layer, the model's ability to learn features
can be enhanced, so as to improve the model's ability to reconstruct
point cloud data. The main performance is to generate more accurate and
complete point cloud data, and improve the accuracy of point cloud
segmentation and completion tasks.

\textbf{2.2 Add Dropout layer}

In the process of training a model in deep learning, it is often the
case that the model learns very well on some specific data, but has poor
generalization performance for other data. To avoid this phenomenon,
some scholars have proposed a method of
Dropout\textsuperscript{{[}17{]}}, which randomly deletes neurons during
the learning process, and the deleted neurons no longer transmit
signals, thus maintaining the universality of the network model. Neuron
Specific Dropout\textsuperscript{{[}18{]}} is a solution proposed on the
basis of Dropout method to deal with missing or inaccessible data during
training. By comparing the average value of each neuron in each category
of the data set, the network can selectively delete the target unit,
reducing the complexity of the network. The operation efficiency has
been greatly improved. It is able to predict which features or noise are
not present in the model's validation sample during testing, allowing
similar test accuracy to be achieved with less data. Combining the
characteristics of the method and the requirement of the algorithm in
this paper, a Dropout layer is added to effectively improve the
reconstruction efficiency and accuracy. The network calculation formula
of Dropout is:

(1)

(2)

(3)

(4)

In the above equation, the probability \emph{r} vector is generated by
Bernoulli function, \emph{p} represents the probability,
\emph{l}represents the hidden layer index, \emph{y} represents the
output of each layer, \emph{z} represents the vector input of layer
\emph{l} ,\emph{f} represents the activation function, \emph{w} and
\emph{b} are the weight values\textsuperscript{{[}19{]}}.

Combined with the advantage of Dropout introduced above, adding a layer
behind the Linear layer of the discriminator can more accurately
calculate the error between the predicted value and the true value. The
error between the true value and the predicted value can be greatly
reduced by changing the parameter values according to the size of the
error, which effectively improves the efficiency and accuracy of partial
missing reconstruction of the point cloud model.

Dropout is a common regularization technique that reduces the risk of
overfitting the model to the training data by randomly discarding the
output of neurons with a certain probability during the training phase.

(2) Increase the generalization ability of the model: the Dropout layer
randomly drops a portion of the neuron output at each training step,
which is equivalent to training a collection of multiple submodels,
which learn different feature representations on different training
sample subsets, thereby increasing the generalization ability of the
network;

(3) Prevent strong dependence between neurons: The introduction of
Dropout layers helps to break the strong coupling between neurons.
Randomly discarding the output of a subset of neurons can prompt each
neuron to learn useful features independently, without being overly
dependent on the presence of other neurons. This randomness helps the
model better learn the diversity and variability of the data, and
improves the ability of point cloud reconstruction.

(4) Enhance the robustness of the model: The addition of the Dropout
layer can enhance the robustness of the model, so that it can show good
performance in the face of noise, deformation, or incomplete point cloud
data. By randomly discarding the output of neurons, the model can be
robust to small perturbations and improve the processing ability of
noise and incomplete point cloud data.

\textbf{2.3 Using the weighted loss function}

The purpose of adding the loss function is to measure the similarity
between the output point cloud and the original point cloud. This paper
adopts the calculation method of loss function in literature {[}14{]},
which includes multi-stage completion loss and adversarial loss. The
multi-stage completion loss is used to evaluate the difference between
the actual value and the predicted value of the object. The smaller the
loss value is, the closer the predicted value is to the true value.
Adversarial losses are used to optimize the MRE and PPD modules in
PF-Net to bring the predicted values closer to the true values.

Multi-stage loss recovery using CD and EMD\textsuperscript{{[}20{]}}. CD
is an indicator to measure the average nearest point distance between
the original point cloud \emph{P\textsubscript{gt}} and the output point
cloud \emph{P\textsubscript{coarse}} , which is obtained by calculating
the symmetry between them\textsuperscript{{[}7{]}}. By using CD as a
measure of multi-stage completion loss, the point cloud generated by the
network can be pushed closer to the original point cloud and maintain
the shape and structural similarity between them.

(5)

The above equation\textsuperscript{{[}14{]}} is used to calculate the
average nearest squared distance between the predicted point
cloud\emph{s\textsubscript{1}} and the real point
cloud\emph{s\textsubscript{2}} by first calculating the minimum distance
from each point X in \emph{s\textsubscript{1}} to
\emph{s\textsubscript{2}} , then adding these minimum distances to
obtain the first term, then calculating the minimum distance from each
point Y to\emph{s\textsubscript{1}} in \emph{s\textsubscript{2}} , and
adding these minimum distances to obtain the second term.

EMD is a method used to measure the distance between two point clouds,
which can find a bijective \emph{s\textsubscript{1}}
and\emph{s\textsubscript{2}} to ensure the minimum average
distance\textsuperscript{{[}7{]}}.

(6)

In this paper, \emph{d\textsubscript{1}} and
\emph{d\textsubscript{2}}are used to construct a multi-stage completion
loss function, which is weighted by hyperparameters.

(7)

The first item represents the similarity between the original point
cloud \emph{P\textsubscript{gt}} and the output point
cloud\emph{P\textsubscript{coarse}} , which is the same size
as\emph{P\textsubscript{coarse}} . The second term represents the
similarity between the output and the original point
cloud\emph{P\textsubscript{gt}} , where the hyperparameter \selectlanguage{greek}\emph{β} \selectlanguage{english}is
used for weighting. In the experiment, \emph{d\textsubscript{1}} 's
similarity measure used CD and EMD, while \emph{d\textsubscript{2}} only
used CD.

The adversarial loss function was inspired by the creation of
adversarial networks (GAN)\textsuperscript{{[}21{]}}. First, a
function\emph{F} is defined, which consists of MRE and
PPD\textsuperscript{{[}14{]}}. The function \emph{F:X-Y'} maps part of
the input \emph{X} to the predicted missing region \emph{Y'} ,
where\emph{X} and \emph{Y'} represent the input and predicted point
clouds. Then, a Discriminator (\emph{D} ) is introduced, whose goal is
to distinguish between the predicted missing region \emph{Y'} and the
actual missing region \emph{Y} . The discriminator is structured like a
composite multilayer perceptron, which contains successive multilayer
perceptron layers {[}64-64-128-256{]}, and applies maximum pooling to
the last three layers to obtain the feature
vectors\emph{f\textsubscript{i}} , where the sizes of
\emph{f\textsubscript{i}} are 64, 128, and 256, respectively (\emph{i} =
1,2,3). This paper defines the adversarial loss function:

(8)

Where \emph{x\textsubscript{i}} [?]X, \emph{yi} [?]Y, i=1,\ldots{} , S. S is
the size of the data set for X, Y. F and D use alternate Adam for joint
optimization while training the data.

In summary, the weighted loss function adopted in this paper is as
follows:

(9)

In the above formula, \selectlanguage{greek}\emph{λ\textsubscript{adv}}\selectlanguage{english}
and\selectlanguage{greek}\emph{λ\textsubscript{com}}\selectlanguage{english} are the weights of adversarial losses and
multi-stage completion losses, and the condition
of\selectlanguage{greek}\emph{λ\textsubscript{com}}\selectlanguage{english} +\selectlanguage{greek}\emph{λ\textsubscript{adv}}\selectlanguage{english} =1 is
satisfied.

Adding this loss function effectively measures the similarity between
the output point cloud and the original point cloud, making the
predicted value closer to the real value, and greatly improving the
reconstruction efficiency and accuracy.

\textbf{3 Reconstructing the System}

This paper develops a partial missing reconstruction system of 3D point
cloud model combined with the improved algorithm, which is more
convenient to use the reconstruction method. Through the experimental
verification in Section 3, a good reconstruction effect is achieved,
which makes the reconstruction operation more simple and has good use
value. The development of the system is based on PyTorch and utilizes
the GPU for computational acceleration, alternating training between
modules using the Adam optimizer. When executing the algorithm, the
initial learning rate is set to 0.0002 and adjusted each time according
to the attenuation factor of 0.6, a total of 20,000 large loop
iterations are performed, and the Epoch number in each large loop is
560.

The specific design framework of the system is shown in Figure 4, which
is mainly composed of three levels, namely application layer,
development layer and system layer. Among them, the application layer is
the most important part of the whole system, covering the core functions
such as parameter calculation, algorithm processing and missing
reconstruction algorithm of 3D point cloud model. In the development
layer, the appropriate development environment and system library are
selected according to the requirements of the system, so as to
facilitate the subsequent secondary development work and ensure the
scalability and flexibility of the system.

Fig. 4 System architecture diagram

The main objective of the system is to realize the functions of point
cloud denoising, model missing reconstruction and burr removal.
According to the division of these functional modules, the system can be
divided into several main modules, including algorithm module, system
setting module, login module and data management module. When the system
is running, these modules collaborate with each other to process and
reconstruct the point cloud data, including removing noise, repairing
missing parts, and eliminating burrs. Figure 5 shows the schematic
diagram of the system module.

\par\null

Fig. 5 System module diagram

\textbf{4 Experiment and result analysis}

The experiment was conducted on a Windows x64 system using a hardware
configuration of a Core i9 processor, 64GB of memory, and an RTX3060
graphics card. The training and test models based on CUDA 11.3 and
Python 3.8 were run in the experimental environment.

\textbf{4.1 Data Generation}

ShapeNet data set is used to train and test the improved network
algorithm in this paper, and to organize it. There are 40 training sets
and 11 test sets (hats, airplanes, cars, guitars, lamps, motorcycles,
pistols, skateboards, round tables, cups, handbags).

\textbf{4.2 Result Analysis}

The 3D point cloud model partial missing reconstruction system can
reconstruct the complete data information and structural features
according to the previous learning effect and the imported local shape
model, and has obtained good results after several experiments. When it
is used, first open the system and click the file in the menu bar to
select the local point cloud model to be imported, which will be
displayed on the system interface after the import is completed. After
clicking the reconstruction button in the menu bar, the system will
reconstruct according to the training effect of the algorithm, and after
the reconstruction is completed, it will be displayed on the system
interface, as shown in Figure 6.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image15/image15}

\end{center}
\end{figure}

Fig. 6 System reconstruction interface

Figure 7 shows the visualization results of the local shape model
reconstructed by the algorithm in this paper. As can be seen from the
figure, part of the structural problems caused by the metric space can
be well captured, and it can show good generalization ability for
complex scenes. When extracting and processing partial feature problems,
this method can obtain the correlation of relative neighboring points in
the point cloud space. In addition, the reconstructed image is close to
the data set density, which can better restore the characteristics of
the original point cloud data density.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image16/image16}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image17/image17}

\end{center}
\end{figure}

Fig. 7 Visualization of the results graph

In order to verify the effectiveness of the proposed method, several
typical 3D point cloud model reconstruction methods were compared,
including L-Gan{[}10{]} and PCN{[}11{]}. Both methods were trained and
tested using the same data set to observe the refactoring effect. In
order to evaluate the quality of reconstruction results, the evaluation
measurement method mentioned in the reference {[}22, 23{]} uses two
indicators: Pred-GT (predicted value to true value) error and GT-Pred
(true value to predicted value) error. Pred-GT error First, the network
prediction results are spliced with some input point clouds to obtain
the complete point cloud data. Then, for each point, the square distance
from the point closest to the real ground is calculated. Finally, the
square distance of all points is summed and divided by the total number
of points to get the average square distance. GT-Pred error First, for
the real ground point, the square distance to the nearest predicted
point is calculated; The square distance of all real ground points is
then summed and divided by the total number of real ground points to get
the average square distance. The calculation formula uses the network
calculation formulas of (5), (6) and Dropout. The error pairs of
completion results for specific missing point clouds are shown in Table
1.

\textbf{Tab.1 Error contrast}\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
\begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Category Method\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
L-Gan\textsuperscript{{[}10{]}}\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
PCN\textsuperscript{{[}11{]}}\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Ours\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Cap\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
8.896/4.608\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
7.015/4.240\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
7.003/4.230\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Airplane\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.357/1.130\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
5.060/1.243\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.241/1.097\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Car\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
4.531/2.518\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2.741/2.123\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2.753/2.116\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Guitar\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
0.838/0.536\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
1.419/0.689\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
0.823/0.521\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Lamp\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
8.464/3.627\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
11.61/7.139\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
8.567/4.326\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Motorbike\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
4.914/2.036\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
4.962/1.922\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
4.032/1.892\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Pistol\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.944/1.424\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
4.484/1.414\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.021/1.134\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Skateboard\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
5.613/1.683\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.025/1.740\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2.154/1.414\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Table\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2.658/2.484\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2.503/2.452\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2.314/2.056\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Mug\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
6.139/4.735\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.590/3.591\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.214/3.463\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Bag\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
5.707/5.303\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.251/4.314\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.034/4.152\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Mean\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
5.006/2.735\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
4.515/2.806\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.651/2.400\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

As can be seen from the above table, the method in this paper is
superior to the previous two methods in most models. In the six
categories tested, the average value is improved by 1.5\% to 19\%, which
better improves the reconstruction accuracy and efficiency.

\textbf{4.3 Ablation results and analysis}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image18/image18}

\end{center}
\end{figure}

\par\null

Fig. 8 Visualization of the results of ablation experiments

In order to further illustrate the improvement in the accuracy of
partial missing reconstruction of the 3D point cloud model by adding the
Batch Normal layer and Dropout layer, this paper chooses aircraft,
guitar and table as examples to perform ablation experiments, and
considers the following benchmark schemes. (1) The model obtained by
adding only Batch Normal layer is called B-Ours; (2) The model obtained
by adding only Dropout layer is called D-Ours; (3) The model obtained by
adding the Batch Normal layer and Dropout layer is called Ours. As can
be seen from Figure 8, the model obtained by the method in this paper is
in good agreement with the actual model, and relatively complete tail,
guitar and round table edges can be obtained. In short, adding the Batch
Normal layer and Dropout layer can generate fine local geometry. Table 2
shows the error results of the ablation experiment. Compared with
B-Ours, the reduction of Ours is 6.09\%/9.56\% for aircraft,
14.63\%/14.87\% for guitar and 7.25\%/12.17\% for round table. In
addition, compared to D-Ours, the aircraft decreased by 2.50\%/8.12\%,
the guitar decreased by 7.11\%/12.29\%, and the round table decreased by
3.70\%/7.09\%. These demonstrate the effectiveness of adding the Batch
Normal layer and Dropout layer.

\textbf{Tab.2 Comparison of errors in ablation experiments}\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
Category Method & \begin{CJK}{UTF8}{gbsn}飞机 \end{CJK}\selectlanguage{english}Airplane & \begin{CJK}{UTF8}{gbsn}吉他 \end{CJK}\selectlanguage{english}Guitar & \begin{CJK}{UTF8}{gbsn}圆桌
\end{CJK}\selectlanguage{english}Table\tabularnewline
B-Ours & 3.451/1.213 & 0.964/0.612 & 2.495/2.341\tabularnewline
D-Ours & 3.324/1.194 & 0.886/0.594 & 2.403/2.213\tabularnewline
Ours & 3.241/1.097 & 0.823/0.521 & 2.314/2.056\tabularnewline
\bottomrule
\end{longtable}

\textbf{5 Conclusion}

In this paper, the method of generating complete point cloud shape by
using partial missing of point cloud model is proposed on the basis of
PF-Net, which can restore 3D model to a large extent. In order to
realize the visualization operation, this paper develops a missing point
cloud model reconstruction system, which can better repair the semantic
contours and detailed features of some missing point cloud models, and
basically maintain the shape and local point density consistent with the
original model. Compared with L-Gan and PCN methods, in 11 test
categories, the average value of the reconstruction method proposed in
this paper is improved by 12\%-27\%, indicating that the proposed method
is effective in dealing with partial missing reconstruction of
small-scale models. Due to the lack of training times due to hardware
limitations, although the accuracy of reconstruction of some models has
been improved, the effect is worse than that of the PF-Net method, and
the error is relatively large. This paper still needs to do more
research and discussion to improve the efficiency and accuracy of
reconstruction.

\textbf{Reference}

\begin{enumerate}
\tightlist
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\item
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\item
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\item
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  Bei Zile, ZHAO Jieyu. A point cloud repair model based on deep
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\item
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\item
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\item
  Achlioptas P, Diamanti O, Mitliagkas I, et al. Learning
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\item
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\item
  Xumin Yu, Yongming Rao, Ziyi Wang, et al. AdaPoinTr: Diverse Point
  Cloud Completion with Adaptive Geometry-Aware Transformers{[}J{]}.
  Cornell University - arXiv, 2023, 11(09): 1-17.
\item
  Huang Z, Yu Y, Xu J, et al. PF-Net: Point Fractal Network for 3D Point
  Cloud Completion{[}C{]} // 2020 IEEE/CVF Conference on Computer Vision
  and Pattern Recognition (CVPR), Seattle, WA, USA. 2020: 7659-7667.
\item
  Ioffe S, Szegedy C. Batch Normalization: Accelerating Deep Network
  Training by Reducing Internal Covariate Shift{[}J{]}. arXiv: Learning,
  2015, 16(11): 73-84.
\item
  Howard A G, Zhu M, Chen B, et al. MobileNets: Efficient Convolutional
  Neural Networks for Mobile Vision Applications{[}J{]}. arXiv: Computer
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\item
  Srivastava N, Hinton G E, Krizhevsky A, et al. Dropout: a simple way
  to prevent neural networks from overfitting{[}J{]}. Journal of Machine
  Learning Research, 2014, 36(12): 345-356.
\item
  Shunk S, Joshua. Neuron-Specific Dropout: A Deterministic
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  \& Reduce Dependence on Large Training Samples{[}J{]}. Computer
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\item
  Chen Shenjin; Xue Yang. Short-time bus passenger flow prediction based
  on improved Convolutional neural networks {[}J{]}. Computer Science,
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\item
  Fan H, Su H, Guibas L. A Point Set Generation Network for 3D Object
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\item
  Yu P, Song K, Lu J. Generating Adversarial Examples With Conditional
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  Lin C, Kong C, Lucey S. Learning Efficient Point Cloud Generation for
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  Gadelha M, Wang R, Maji S. Multiresolution Tree Networks for 3D Point
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\end{enumerate}

\textbf{Figures}

Fig. 1 Method design drawing

Fig. 2 Parameter setting diagram

Fig. 3 Data processing mode

Fig. 4 System architecture diagram

Fig. 5 System module diagram\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image19/image19}

\end{center}
\end{figure}

Fig. 6 System reconstruction interface\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image20/image20}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image21/image21}

\end{center}
\end{figure}

Fig. 7 Visualization of the results graph\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image22/image22}

\end{center}
\end{figure}

Fig. 8 Visualization of the results of ablation experiments

\textbf{Tab.1 Error contrast}\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
\begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Category Method\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
L-Gan\textsuperscript{{[}10{]}}\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
PCN\textsuperscript{{[}11{]}}\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Ours\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Cap\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
8.896/4.608\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
7.015/4.240\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
7.003/4.230\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Airplane\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.357/1.130\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
5.060/1.243\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.241/1.097\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Car\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
4.531/2.518\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2.741/2.123\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2.753/2.116\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Guitar\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
0.838/0.536\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
1.419/0.689\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
0.823/0.521\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Lamp\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
8.464/3.627\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
11.61/7.139\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
8.567/4.326\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Motorbike\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
4.914/2.036\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
4.962/1.922\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
4.032/1.892\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Pistol\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.944/1.424\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
4.484/1.414\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.021/1.134\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Skateboard\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
5.613/1.683\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.025/1.740\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2.154/1.414\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Table\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2.658/2.484\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2.503/2.452\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2.314/2.056\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Mug\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
6.139/4.735\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.590/3.591\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.214/3.463\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Bag\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
5.707/5.303\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.251/4.314\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.034/4.152\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Mean\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
5.006/2.735\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
4.515/2.806\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.651/2.400\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}



\textbf{Tab.2 Comparison of errors in ablation experiments}\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
Category Method & \begin{CJK}{UTF8}{gbsn}飞机 \end{CJK}\selectlanguage{english}Airplane & \begin{CJK}{UTF8}{gbsn}吉他 \end{CJK}\selectlanguage{english}Guitar & \begin{CJK}{UTF8}{gbsn}圆桌
\end{CJK}\selectlanguage{english}Table\tabularnewline
B-Ours & 3.451/1.213 & 0.964/0.612 & 2.495/2.341\tabularnewline
D-Ours & 3.324/1.194 & 0.886/0.594 & 2.403/2.213\tabularnewline
Ours & 3.241/1.097 & 0.823/0.521 & 2.314/2.056\tabularnewline
\bottomrule
\end{longtable}

\selectlanguage{english}
\FloatBarrier
\end{document}

