# 3D Facial Imperfection Regeneration: Deep learning approach and 3D printing
prototypes

Phuong D. Nguyen1,, Thinh D. Le1,11footnotemark: 1, Duong Q. Nguyen2, Thanh Q.
Nguyen1, Li-Wei Chou3, H. Nguyen-Xuan1,4,
1CIRTECH Institute, HUTECH University, Ho Chi Minh City, Viet Nam
2Department of Mathematics and Statistics, Quy Nhon University, Quy Nhon City,
Viet Nam
3Department of Physical Medicine and Rehabilitation, China Medical University
Hospital, Taichung, Taiwan
4Department of Medical Research, China Medical University Hospital, China
Medical University, Taichung, Taiwan Co-first author.Corresponding author:
CIRTECH Institute, HUTECH University (Email: ngx.hung@hutech.edu.vn).

###### Abstract

This study explores the potential of a fully convolutional mesh autoencoder
model for regenerating 3D nature faces with the presence of imperfect areas.
We utilize deep learning approaches in graph processing and analysis to
investigate the capabilities model in recreating a filling part for facial
scars. Our approach in dataset creation is able to generate a facial scar
rationally in a virtual space that corresponds to the unique circumstances.
Especially, we propose a new method which is named 3D Facial Imperfection
Regeneration(3D-FaIR) for reproducing a complete face reconstruction based on
the remaining features of the patient face. To further enhance the applicable
capacity of the present research, we develop an improved outlier technique to
separate the wounds of patients and provide appropriate wound cover models.
Also, a Cir3D-FaIR dataset of imperfect faces and open codes was released at
https://github.com/SIMOGroup/3DFaIR. Our findings demonstrate the potential of
the proposed approach to help patients recover more quickly and safely through
convenient techniques. We hope that this research can contribute to the
development of new products and innovative solutions for facial scar
regeneration.

_K_ eywords Fully convolutional mesh autoencoder $\cdot$ 3D object
regeneration $\cdot$ imperfect face $\cdot$ deep learning $\cdot$ graph
processing $\cdot$ facial scar restoration

##  1 Introduction

The field of reconstructing physical flaws in the human body plays significant
importance due to its widespread relevance to daily life. Physical
disabilities are frequently caused by various factors such as job accidents,
traffic accidents, and wars. The presence of disability in the body patient
can cause numerous challenges in life, both physically and mentally. One such
manifestation is the formation of scars, which are the marks left behind
following the healing process of external injuries due to trauma. Except for
minor traumas, all wounds originating from accidents, infections, or surgery
often produce scars. When the skin is wounded, its recovery and regeneration
should meet four stages, including the hemostasis stage, inflammatory stage,
proliferative stage, and regeneration stage, as depicted in Fig. 1. The shape
of the scar and how to treat scars are determined by a variety of factors,
including the depth, size, and location of the wound as well as the age, sex,
and genetics of each patient. Among the steps, step 3 is almost the most
important one, which consists of fibroblast proliferation, formation of
connective tissue, formation of capillaries, and wound healing. The patient
care method must be very attentive throughout this period in order for the
wound to heal spontaneously. In accordance with the request of the treating
doctor, wounds must be cleaned and disinfected on a regular basis. When the
wound dressing process is ineffective, the dressing process may be tough, and
it may not be safe to clean the wound. Such an issue becomes problematic and
has not been entirely resolved. Scars are unattractive and may lead to
physical and emotional symptoms such as itching, pain, sleep disturbance,
anxiety, depression, and disruption of daily activities. These psychological
sequelae may lead to a lower quality of life. The desire for aesthetic beauty
is increasing throughout the world, especially in developing countries. Scars,
particularly in areas that cannot be covered by clothing, may affect
significantly the life quality of the human.

Figure 1: The wound healing process of the patient.

Of all these commonly injured parts of the human body, the head region at the
head and face is the most important and dangerous. Many studies have tried to
regenerate damaged structures in this part of the body to help patients
recover. As analyzed before, the reconstruction of the human body parts is
divided into 3 main research directions [1, 2, 3], including body
reconstruction [4, 5, 6], reconstruction of the extremities [7, 8] and
reconstruction of the head as shown in Fig. 3. Reconstruction of the
extremities has been the subject of numerous publications, particularly with
regard to the hands [9, 10, 11, 12, 13] and legs [14, 15, 16, 17, 18]. Most
studies concerned on limb reconstruction due to the relative safety of these
areas compared to other parts of the body. In addition, this area is easy to
handle and assemble and is less dangerous for the patient. Similarly,
reconstruction of the body area is divided into the reconstruction of the
spine [19, 20, 21, 22, 23, 24, 25] and the rib cage [26, 27, 28, 29, 30]. More
importantly, two main research directions concerning on the head region
consists of facial reconstruction [31, 32, 33] and skull reconstruction [34,
35]. Also, injuries to the head can be particularly dangerous and may cause a
higher death rate than in other areas. Therefore, research on the
reconstruction of the face and skull has still been very challenging. That is
a reason why studies on head injuries are also much fewer than injuries to
other areas of the body.

Processes to reconstruct virtual structures in the human body are being
developed quickly with the help of machine learning models. 3D prototypes for
research purposes can be then created by additive manufacturing technologies
or 3D printing. The use of machine learning approaches to upgrade 2D models
into 3D models of the human facial area is a very potential topic that has
been interested in research over the past few decades. Investigating this
tough model requires both the recognition algorithm and the correctness of the
product after the reconstruction model. The difficulty of the 3D structural
reconstruction stems from associated concerns such as the position of facial
features, the convexity of the model, and the use of multiple colors to
identify the most correct 3D model. In other words, the nature of the problem
is heavily influenced by the algorithm model used. Table 1 lists the key
algorithms employed for the reconstruction of the face model.

Table 1: Some algorithms for the reconstruction of face used in recent years Period |  Restrictions |  External links |  Sources
---|---|---|---
Up to 2016 |  - Machine learning models have been widely adopted and proven to be useful in solving various features of detection problems. - Several advanced methods have been proposed in the previous states including creating 3D models from signals and recreating 3D models using RGBD scanning. In addition, some applications for recreating human faces, as well as applications that operate on human faces recreated through video. - The development during this period is mainly inhibited by the hardware limitations of devices such as smartphones and scanners. |  Artificial Neural Network Deep Learning  Ensemble Methods  Dimensionality Reduction Bayesian  Decision Tree  Regression |  [36, 37, 38, 39] [40, 41, 42, 43] [44, 45, 46, 47, 48] [49, 50, 51, 52] [53, 54, 55, 56] [57, 58, 59] [60, 61]
Up to 2022 |  - New algorithms related to artificial intelligence have been extensively developed, and they are being integrated to create remarkable technological advancements. - The hardware systems, including machines that offer high accuracy, convenience, and safety for users, have been developed. - Several applications directly interact with the human body with the aid of current 3D printing technology and the development of bio and metal materials. |  Deep Learning |  [62, 63, 13, 42, 26, 41, 12, 45, 39, 64, 65, 66]
Figure 2: Some studies in the direction of 3D reconstruction.

As illustrated in Table 1 and Fig. 2, the relevant studies on the
reconstruction of 3D human facial have been extensively devised for a long
time. However, the above studies still exist the following gaps:

  * -

The dataset of faces and facial scars is lacking due to medical research
ethics. The ethical considerations in medical research aim to protect the
privacy and dignity of human subjects participating in the studies. In the
case of facial scars, the inclusion of images of individuals with such scars
may lead to stigmatization and discrimination, particularly in employment and
social settings. This potential harm to the participants’ well-being may
outweigh the benefits of having a comprehensive dataset for facial recognition
or other related applications. As a result, the lack of a dataset of faces
with facial scars may limit the accuracy and effectiveness of facial
recognition technologies in identifying individuals with such scars.

  * -

The facial reconstruction process is still inaccurate due to facial defects
because the filling-removal process were designed manually. When addressing
facial imperfections, the manual processes of filling and sculpting are
typically carried out by a surgical physician. However, Such a manual approach
is prone to inaccuracies and inconsistencies, which can lead to suboptimal
outcomes for the patient. Additionally, the level of skill and experience of
the surgeon can further impact the precision of the procedure, increasing the
likelihood of errors. While technology such as computer-aided design (CAD) and
3D printing can partially address these shortcomings, they still require an
expert in both the medical and technological fields. Currently, there is no
automated method for generating filling material to support the surgeon in the
most optimal way.

  * -

Currently, the majority of research is centered around the manual design of 3D
discrete components, with a lack of comprehensive solutions for specific body
parts, especially for the facial part. At present, the bulk of research
efforts in the realm of 3D design are focused on the manual creation of
discrete components as nose, chin, finger joint, ankle bone, etc. Regrettably,
there is a paucity of comprehensive solutions that address specific body
parts, particularly the all facial region. Despite the increased utilization
of 3D printing technologies in the medical field, there remains a significant
gap in the development of automated methods for generating filling material
that is optimized for facial imperfection correction procedures. This gap
highlights a critical need for further research to develop effective
techniques for automating the generation of 3D models that accurately capture
the intricacies of the facial region. Such advances would be invaluable in
streamlining the surgical process, increasing accuracy, and ultimately leading
to improved patient outcomes.

As a result, to compensate for the deficiencies of earlier studies on this
topic, the current work suggests the use of 3D object reconstruction of the
fully convolutional mesh autoencoder model in the face regeneration problem
for trauma patients. The research has exploited advanced machine learning
models in image processing and analysis to rebuild facial scars. Facial wound
patient models, replicated in virtual space using artificial intelligence, can
match true scar states and form more complicated scar models. The findings
also show that the proposed method delivers a complete face reconstruction
based on the remainder of the face, as opposed to reconstructing by joining
one human body component to another. To optimize the present research model,
we utilized an improved outlier technique to isolate patients’ wounds and
generate suitable wound cover models. The obtained results show the potential
for developing safe and convenient products to assist patients in their
recovery.

Figure 3: Some studies on restructuring the human body. Figure 4: Overview of
the data flow process for problem processing.

##  2 Materials and methods

In this section, we present an efficient method to create a human head mesh
dataset based on the MICA model by Zielonka et al. [62]. The research
direction in the field of defective faces has been severely limited due to the
lack of data, mostly caused by patient privacy concerns. To address this
issue, we have generated the Cir3D-FaIR dataset using the technique we called
Virtual Space. This dataset not only ensures patient privacy but can also be
made available publicly to support other researchers. Four main processes
including dataset construction, mesh preprocessing, training, and application
have been solved. As shown in Fig. 4 shows, we have started processing and
building the data by collecting the data of the human face image and using the
MICA model to get the original 3D face object. Scar Generation is responsible
for creating random scars for 3D face objects. Next, in the mesh preprocessing
part, we have to refine the data to better fit the Fully Convolution Mesh
Autoencoder model such as removing eyeballs and filling holes to fix the non-
watertight error. In the Training part, we introduce a new training strategy
by changing the calculation object of the loss function. Finally, in the
Application part, we offer a method to bring this problem to life by
extracting the fill and sending it to 3D printing for further treatment
purposes.

###  2.1 Generation of dataset

For the first phase, we collected photographs of the faces of 3687 individuals
from various nations around the world in order to assure the coverage of
facial information of all races. Using the MICA model - Towards Metrical
Reconstruction of Human Faces model delivers SOTA - State of the Art results
on datasets converted from 2D models to 3D models [62], these 3687 photographs
of human faces were converted to 3D models as displayed in Fig. 5.

Figure 5: Some input and output of MICA model.

The MICA model is divided into 2 main parts: Identity Encoder and Geometry
Decoder as shown in Fig. 6.

  * $\bullet$

Identity Encoder: The research adopts the work of Deng et al [63] sub-center
ArcFace network in pre-trained facial recognition on large-scale 2D picture
datasets. The previous research has revealed the individual characteristics of
every single face which can significantly differ in expression, light, and
image capability from the Glint360K dataset [67]. According to the present
study, the ArcFace sub-center is constructed on the ResNet100 architecture,
which is capable of being robust to photographs obtained in surroundings with
low stability. Furthermore, the author has extended the architecture of Sub-
center ArcFace with a mapping network, which maps the features that Sub-center
ArcFace wants to be discernable by their geometry decoder. The network is made
up of three fully connected linear hidden layers, and ReLU is used for
activation.

  * $\bullet$

Geometry Decoder: Since the 3DMM model was too good for facial representation,
the author focused on model-based decoder development. In this model, the
author uses FLAME [68], which is a model that uses linear shape space trained
from 3800 human head scans, and combines that linear shape space with jaws,
necks, eyeballs, pose-dependent corrective blend shapes, and additional global
expression blend shapes. In addition, the model was trained at over 33,000
scans and produced more outstanding results than models such as the Face Ware
House [69] and Basel Face Model [70].

Figure 6: A description of the MICA model.

(a) Model filled with holes

(b) Model of eyeball removing

Figure 7: Geometrical figures

The present study gathers data after using the MICA model, and the replicable
model is presented in Fig. 6. The findings acquired from Fig. 6 are per capita
mesh models, and two eyeballs are isolated from the main mesh, yielding a
total number of mesh points of 5023. According to the above studies, two
eyeballs are not truly required in the human face restructuring model, so this
research deleted two eyeballs and the recovery model produced the same
findings as Fig. 7(a). Because the fully convolutional mesh autoencoder model
only accepts watertight mesh data [71], this research needs to address the gap
that is causing present mesh data to be non-watertight as Fig. 7(b). The
proposed method introduces a simpler and easier-to-execute strategy for
filling holes in the mesh than earlier studies, including: 1) Find all the
edges at the edge hole, so that all the edges in the mesh model are in one
face. 2) Connect the edges with corresponding spots, forming sets of holes on
the mesh. 3) Take the midway of the pore and connect all the points on the
pore to that midpoint, forming a sheet pattern to cover these voids from the
extracted points on the edges of the corresponding pores.

The creation of the Cir3D-FaIR dataset involves a multi-step process. First, a
simulated MRI scan is created from an actual patient, with the patient’s
consent, and is then converted into a 3D format. Next, a large number of 3D
faces are generated in Virtual Space with MICA dataset, which each product
containing different errors in specific parts of the face, such as the eyes,
nose, and mouth. This is done to ensure that dataset covers a wide range of
possible faces. Once the 3D faces have been generated, random errors are
introduced wherever possible to further increase the variability of dataset.
These random errors can include anything from subtle asymmetries to more
severe defects. The resulting dataset is intended to be representative of a
broad range of facial defects that might be encountered in clinical practice.
Throughout the process of generating the Cir3D-FaIR dataset, medical
professionals are consulted to ensure that the dataset is both feasible and
useful for research purposes. This includes assessing the accuracy and realism
of the simulated defects, as well as evaluating the potential impact of the
dataset on patient privacy. Ultimately, the goal of the Cir3D-FaIR dataset is
to provide researchers with a comprehensive and privacy-protected resource for
studying facial defects. By generating a diverse and realistic dataset, this
research aims to enable further advancements in the diagnosis and treatment of
facial abnormalities. The steps to implement in Virtual Space:

  1. 1.

Choosing a focal point for facial scars;

  2. 2.

Assembling the nearby locations of the scar center specified in step 1 to
construct a scar region. The pattern spread out throughout the full scar
region generated on the face by adjusting the height of the points in the scar
area with the assumption that the scar center is the deepest spot;

  3. 3.

At step 3, a concave scar region on the face with the shape, size, and depth
of the scar area within a particular range is received after the
reconstruction of the scar model from step 2. Random parameters, in
particular, are chosen through many trials in order to achieve an empirical
visual of the true structure of the actual wound that humans may encounter;

  4. 4.

The investigation produces the results shown in Fig. 8 after employing the
strategy presented in this work. The results revealed that while some aspects
of the face are deformed, some regions on the face remain fixed and focused on
the face. Although the data is not gathered directly from actual patients, we
demonstrate that the proposed model is sufficient to assist the research model
in simulating and solving real-world problems.

Finally, we modify the structure of the fully convolutional mesh autoencoder
model by Zhou et al. [71] to train on our dataset, allowing the model to
reconstruct incomplete faces.

Figure 8: Some simulated models of the actual scarring process.

###  2.2 Fully Convolutional Mesh Antoencoder

The fully convolutional mesh autoencoder model by Zhou et al. [71] is the
basis for training in this study, which aims to address the lack or limitation
of using real data for ethical reasons in research. Therefore, this paper
presents a new technique, that incorporates convolutional neural networks with
graph models, specifically the mesh model.

####  2.2.1 vcConv and vcTransConv

In a regular mesh, if the topology of all neighbors is identical, the learned
weight matrix determined for each neighbor vertex can be determined
consistently and shared in all vertices of the grid. However, in reality, the
vertices are unevenly distributed in space, and each vertex has a different
connection and orientation. Therefore, we cannot directly apply the same
weighting schemes. Research by Zhou et al. [71] has provided a solution to
this problem by allowing the weights to vary spatially so that each vertex is
free to determine its own convolution weights. At the same time, they
introduced two operators, convolution and transposition, denoted vcConv and
vcTransConv respectively, and called the “coefficients of transformation” (vc)
the local coefficients. These coefficients are in the range of the shared
weight basis and are sampled by a set of local coefficients per neighbor. In
addition, Zhou et al. [71] gave a definition of a Weight Basis (WB), which is
a network formed by a virtual space of a defined size on a real-space network,
where the real vertices in the mesh within the influence area of a weight
basis belongs to that weight basis. The weights in WB are shared across the
entire mesh, but the weights of real vertices are calculated inside that
weight basis using different functions from vertex to vertex. It was shown
that WB is like a pixel in a 2D CNN network, as the model directly computes on
WB and then evaluates the weights back for the vertices affected by that
weight basis.

Assuming that graph $\mathcal{O}$ is the output sampled from input graph
$\mathcal{I}$; $\mathcal{O}$ has $N$ vertices and each vertex $y_{i}$ is
computed from a local region $\mathcal{N}(i)$ in $\mathcal{I}$;
$\mathcal{N}(i)$ has $E_{i}$ vertices $x_{i,j},j=1,..,E_{i}$. Each convolution
layer has one kernel basis defined as
$B=\left\\{\mathbf{B}_{k}\right\\}_{k=1}^{M}$, where
$\mathbf{B}_{k}\in\mathbb{R}^{I\times O}$ with local variant coefficients(vc)
$A_{i,j}=\left\\{\alpha_{i,j,k}\right\\}_{k=1}^{M},\alpha_{i,j,k}\in\mathbb{R}$.
$M$ is chosen close to the average size of a neighborhood. Then, the weight
$\mathbf{W}_{i,j}$ on each edge is computed as:

$\mathbf{W}_{i,j}=\sum_{k=1}^{M}\alpha_{i,j,k}\mathbf{B}_{k},$ (1)

and then the convolution is determined by

$\mathbf{y}_{i}=\sum_{x_{i,j}\in\mathcal{N}(i)}\mathbf{W}_{i,j}^{T}\mathbf{x}_{i,j}+\mathbf{b}.$
(2)

where $\mathbf{x}_{i,j}\in\mathbb{R}^{I}$ are the input feature; $\mathbf{b}$
is the learned bias; $A_{i,j}$ are different for each vertex $x_{i,j}$ in
$\mathcal{N}(i)$ of each $y_{i}$, but $B$ is shared globally in one layer. The
parameters used in this approach are learnable and shared across the entire
dataset.

####  2.2.2 vdPool, vdUnpool, vdUpRes, and vdDownRes

To preserve the functionality of traditional Convolutional Neural Networks
(CNNs), Pool and Unpool Layers are commonly used. Common types of pooling
include max pooling and average pooling. Given a mesh with $n$ vertices
$V={v_{1},v_{2},\ldots,v_{n}}$ and their corresponding features
$F={f_{1},f_{2},\ldots,f_{n}}$. Two pooling layers, maximum and average can be
defined, respectively, as follows

$f_{i,~{}maxpool}=\max_{j\in\mathcal{N}(i)}f_{j},$ (3)
$f_{i,~{}avgpool}=\frac{1}{|\mathcal{N}(i)|}\sum_{j\in\mathcal{N}(i)}f_{j},$
(4)

where $\mathcal{N}(i)$ represents the set of neighboring vertices of vertex
$i$ in the mesh and $|\mathcal{N}(i)|$ is the number of neighboring vertices.
This creates a coarser representation of the original mesh with fewer
vertices, as each pooled vertex represents the average or maximum feature
value of the neighborhood. The corresponding unpooling layer restores the
original resolution of the mesh by copying the pooled features to their
corresponding vertices. However, max or average pooling can be less effective
when applied to grids with uneven peak density because they treat all regions
of the input grid equally, regardless of their importance. This can result in
important features being averaged out or overlooked, leading to a loss of
information and a decrease in performance. To address this issue, various
pooling methods have been proposed that take into account the local density of
peaks or the spatial relationships between features. Thus, Zhou et al. [71]
described a technique for feature aggregation using Monte Carlo sampling. The
approach is inspired by the work of Hermosilla et al. [72], who estimated the
vertex density using 3D coordinates of neighboring vertices. However, in more
general cases, such information may not be available for each layer. In [71],
instead of designing a density estimation function, the authors propose to
learn the optimal variant density coefficients (vd) across all training
samples. These coefficients are defined per node after pooling or unpooling,
and they allow the network to adaptively adjust the density of features for
each node. By learning the optimal vd coefficients, the network can better
capture the important features of the input and improve performance. It is
worth noting that vd is defined per node after pooling or unpooling. In [71],
vdPool and vdUnpool layers act as pooling and unpooling layers in CNN,,
respectively. Accordingly, each local vertex $j$ has a density coefficient is
defined as follows

$\rho_{i,j}^{\prime}=\frac{\left|\rho_{i,j}\right|}{\sum_{j=1}^{E_{i}}\left|\rho_{i,j}\right|},$
(5)

where $\rho_{i,j}\in\mathbb{R}$ are training parameters, shared across the
dataset. Specifically, Eq. (5) is an aggregate function used in vdPool and
vdUnpool layers. Due to the $vd$ coefficient normalization, the vdPool and
vdUnpool do not perform any rescaling nor change the mean values of the input
feature map. Similarly, the residual layer is written as:

$\mathbf{y}_{i}=\sum_{x_{i,j}\in\mathcal{N}(i)}\rho_{i,j}^{\prime}\mathbf{Cx}_{i,j}.$
(6)

If the input and output feature dimensions are identical, then $\mathbf{C}$
represents an identity matrix. However, if the input and output feature
dimensions differ, then $\mathbf{C}$ is a learned $O\times I$ matrix that is
learned and shared across all graph nodes.

Figure 9: The coaching model we recommend.

According to this layer, a residual block is used for up-and-down sampling. At
this point, the input is run through vcConv for down-sampling or vcTransConv
for up-sampling and then the data is run through the activation layer
function.

We conduct the analysis to choose the appropriate activation function for the
problem. The Rectified Linear Unit (ReLU) and the Exponential Linear Unit
(ELU) are both popular activation functions used in neural networks. They are
both non-linear functions that introduce non-linearity into the output of a
neural network, which is necessary for the network to learn complex patterns
in the data. The ReLU function is defined as:

$f(x)=\max(0,x),$

where $x$ is the input to the activation function. The ReLU function is a
piecewise linear function that returns zero for negative inputs and the input
value itself for positive inputs. The ReLU function has several advantages,
including its simplicity, computational efficiency, and sparsity. The ELU
function, on the other hand, is defined as:

$\displaystyle f(x)=\begin{cases}x&\text{if }x>0,\\\
\alpha(\exp(x)-1)&\text{if }x\leq 0,\\\ \end{cases}$ (7)

where $\alpha$ is a hyperparameter that controls the value of the function for
negative inputs. The ELU function is a smooth and non-monotonic function that
returns the input value for positive inputs and has an exponential component
for negative inputs. The ELU function has several advantages, including its
smoothness, differentiability, and small negative output for negative inputs.
One key advantage of the ELU function over the ReLU function is its ability to
avoid the “dead ReLU” problem. In some cases, the ReLU function can cause
neurons to become permanently inactive if their output falls below zero. This
can lead to a reduction in the expressive power of the network and lower
performance. The ELU function avoids this problem by having a non-zero output
for negative inputs, which can help to prevent neurons from becoming inactive.
Another advantage of the ELU function is its small negative output for
negative inputs. This can help to improve the robustness of the network to
noise and outliers, which is important in many applications.

From the above analysis, we can see that ELU is roughly smooth while ReLU is
completely smooth. Therefore, ReLU is chosen as the activation function for
this problem. The output from the ELU activation layer is combined with the
output from the vdDownRes or vdUpRes layer and produces the final output. The
implementation process is shown in Figure 9.

###  2.3 Training strategy

The selection of an appropriate loss function is essential in many machine
learning problems, including mesh reconstruction. Let
$v_{i}(x,y,z)\in\mathcal{M}_{in}(V,E,F)$ and
$v^{\prime}_{i}(x^{\prime},y^{\prime},z^{\prime})\in\mathcal{M}_{out}(V^{\prime},E^{\prime},F^{\prime})$
be the vertices in the input and output mesh, respectively. In [71], the loss
function is calculated as the average of the sum of Euclidean distances
between the corresponding vertices in the input mesh and output mesh.
Accordingly, the loss function is written as follows:

$d(v_{i},v^{\prime}_{i})=||v_{i}-v^{\prime}_{i}||_{2}.$ (8)

Therefore, the loss function can be expressed as

$\mathcal{L}(\mathcal{M}_{in},\mathcal{M}_{out})=\dfrac{1}{n}\sum_{i=1}^{n}d(v_{i},v^{\prime}_{i}),$
(9)

where $n=n(E)=n(E^{\prime})$ is the number of vertices.

Zhou et al [71] described a training model in which both the input and the
comparison value are used to compute the output from the model. This approach
helps the model to learn similar to the structure of the input mesh. However,
our goal is to train a model to locate the wound and reconstruct it to
resemble a natural face. Therefore, this loss function needs to be justified.
To solve this problem, we introduce the loss function by modifying the
training architecture of the fully convolutional mesh autoencoder model.

According to Subsection 2.1, we get 3687 ground truth mesh faces of people
before the injury. In the problem of this research, the input and the ground
truth are two different meshes. Thus, the inclusion of the input is a human
head mesh with wounds and the ground truth is a human head mesh before the
injury, and then the output generated from the model is calculated with that
ground truth. Similar to $\mathcal{M}_{in}$, $\mathcal{M}_{out}$, let
$v^{\prime\prime}_{i}(x^{\prime\prime},y^{\prime\prime},z^{\prime\prime})\in\mathcal{M}_{gt}$
be the vertices in the ground truth mesh. Then, the loss function is adjusted
as follows:

$\mathcal{L}(\mathcal{M}_{out},\mathcal{M}_{gt})=\dfrac{1}{n}\sum_{i=1}^{n}d(v^{\prime}_{i},v^{\prime\prime}_{i})=||v^{\prime}_{i}-v^{\prime\prime}_{i}||_{2},$
(10)

where $d(v^{\prime}_{i},v^{\prime\prime}_{i})$ is the Euclidean distance of
the vertices on $\mathcal{M}_{out}$ and $\mathcal{M}_{gt}$;
$n=n(E^{\prime})=n(E^{\prime\prime})$ is the number of vertices. With this
correction, the model can learn how to repair the damage in a way that brings
the injured face back to its original state, rather than simply filling the
wound. The proposed training model from this research is exhibited in Fig. 9.

Figure 10: Results obtained from the proposed model.

###  2.4 Filling extraction

Fig. 10 showed results derived from the training model in Section 2.3. For the
surgery of patients, the wound filling part can be then reproduced by the use
of 3D printing technology. We introduce a new technique called “filling
extraction” which has been implemented to fill in the missing parts with high
accuracy and low computational cost. In particular, the input mesh and the
ground truth mesh are both created from the same original mesh, as given in
Section 2.1. The output mesh tends to reform like the ground truth mesh.
Therefore, the model can take the output mesh “minus” the input mesh to obtain
the filling part of the wound on the face. Because the output mesh is
generated from a deep learning model, it itself exists certain errors, which
need to be fixed to achieve the most accurate model. Therefore, when taking
the output mesh “minus” the input mesh, in addition to filling the wound area,
the wrong parts are also removed according to the concatenate mesh as
illustrated in Fig. 11a. To remedy this, the outlier method was used to
eliminate the underlying errors. It is noted that the fully convolutional mesh
autoencoder [71] model is characterized by the fact that the output and the
input have the same number of points and different point order. Accordingly,
we concatenate both the input and the output in three-dimensional space. We
assume that $D$ is the set of distances of
$v_{i}(x,y,z)\in\mathcal{M}_{in}(V,E,F)\text{ and
}v^{\prime}_{i}(x^{\prime},y^{\prime},z^{\prime})\in\mathcal{M}_{out}(V^{\prime},E^{\prime},F^{\prime})$
described by:

$D:=\left\\{d(v_{i},v^{\prime}_{i})\right\\}^{n}_{i=1}=\left\\{||v_{i}-v^{\prime}_{i}||_{2}\right\\}^{n}_{i=1}=\left\\{\sqrt{(x_{i}-x^{\prime}_{i})^{2}+(y_{i}-y^{\prime}_{i})^{2}+(z_{i}-z^{\prime}_{i})^{2}}\right\\}^{n}_{i=1}$
(11)

where $n$ is the number of vertices of input and output meshes. We calculate
the mean $\mu_{D}$ and variance $\sigma_{D}$ from the set $D$, respectively,
as follows

$\mu_{D}=\frac{1}{n}\sum_{i=1}^{n}D_{i},\quad\sigma_{D}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(D_{i}-\mu_{D})^{2}},$
(12)

where $n$ is the number of elements in the set $D$, and $D_{i}$ is the
$i$-element of the set $D$. We define the outlier extraction formula to show
the error correction as follows

$D_{outlier}:=\left\\{(v_{i},v^{\prime}_{i})\mid|d(v_{i},v^{\prime}_{i})-\mu_{D}|>2\sigma_{D}\right\\},$
(13)

where $1<i<n$. From $D_{outlier}$, we get the coordinates of the outliers on
the input mesh and output mesh respectively. The outliers are then
concatenated into space, which gets the same mesh as the concatenate outlier
mesh in Fig. 11. Since the concatenate outlier mesh is still two separated
mesh parts, we connect them by staying at the outer edges. Then, we take
additional vertices from the output mesh that are directly connected to each
vertex at the outer edge of the outlier output mesh. Then, the calculation
joins the outlier input mesh and the newly added vertices of the outlier
output mesh together with the result eventually formed a filling mesh for the
fig-like wound as shown in Fig. 11.

Figure 11: The procedure for the wound filling part.

##  3 Results and discussion

The present research reveals the results of training the model to restore the
facial structure when scarred in this part. The models were trained on the
2D-manifold training set and watertight mesh of the injured skull, as
described in Section 2.3. The scale used is that each human head mesh
generates 10 human head meshes with wounds at random in a virtual space
environment. Moreover, in the present approach, the visual model is likely to
mirror the reality of individuals with facial injuries. Thus, the final
dataset consists of 40458 human head mesh, including 3678 ground truth and
36780 input, derived from the starting dataset of 3687 human head mesh. As
compared to previous studies, the current work consider the most hypothetical
dataset of human faces available in the literature. The dataset generated by
this work does not violate medical research ethics. In addition, it is also
accessible to most models of injury in practice and those that are more
severely harmed than they actually are. We employ 80% of the aforesaid data as
a training model, 10% for validation, and the remaining 10% for testing using
this enormous data set. The facial selectivity model as shown in Fig. 12
uniformly divides the points in the middle layer, allowing the model to better
replicate the facial parts with the figure trained with $l_{1}$ reconstruction
loss and Adam optimizer. We test the model on the test data and generate the
statistics shown in Table 2, and the error used is Geometric Distance. The
results show that, while the single vertex error can be as high as 4.5643, the
mean error of the overall vertices of mesh is only $2.75\times 10^{-1}$. This
demonstrates the correctness of the model in the overall vertices of the mesh
in the majority of circumstances. Furthermore, this study may graphically
represent the results displayed in Table 2 and Fig. 15, where the chroma
statistics of meshes displayed in Fig. 13 are derived based on the geometric
distance of the vertices corresponding to output mesh and ground truth mesh.
The research then randomly retrieved the outputs of the model on the test set,
as shown in Fig. 14, to gain a better understanding of the outcomes.
Simultaneously, the test employs the extraction of the filler, as shown in
Fig. 16, to proceed to the 3D printing procedure for wound restoration.

Table 2: Statistics extracted from the test suite (3678 meshes). Method | Error (geometric distance) | Figure reference
---|---|---
Min vertices distance | $2.26\times 10^{-3}$ | Fig. 13a
Max vertices distance | $4.564300$ | Fig. 13b
Mean vertices distance | $2.75\times 10^{-1}$ | Fig. 13c
Min of Mean vertices distance | $1.35\times 10^{-1}$ | Fig. 13d
Max of Mean vertices distance | $6.64\times 10^{-1}$ | Fig. 13e
Figure 12: Illustration for the middle layer of the model. Figure 13: The
results are statistically extracted from the model with the test suite (3678
meshes). Figure 14: The results were randomly extracted from the model with
the test suite (3678 meshes). Figure 15: The loss function value corresponding
to each Epoch. Figure 16: 3D printer output from our model result.

##  4 Conclusions

This study explored the benefits of using the fully convolutional mesh
autoencoder model for 3D object regeneration of individuals with facial trauma
defects. The obtained results showed the most prominent features as follows

  * -

The virtual scar construction method allows the visual model in a virtual
environment to accurately replicate the scars of patients with facial
injuries. The research used a final dataset of 40,458 human head meshes, which
is considered the most comprehensive human face dataset currently available.
This dataset was created from an original set of 3,687 human head meshes and
did not violate research ethics in medicine as it did not involve direct
treatment of patients, but still provides access to a range of injury models
and severe cases.

  * -

The research results also support the proposed training method, which allows
for the regeneration of facial scars based on the rest of the actual face. The
model is able to accomplish this without mechanically reproducing scars or
attaching one part of the person to others. The present work suggests using
the outlier technique to separate the wound, which has been used to create a
wound model for the entire face. The results obtained may provide useful
insights for doctors during the re-surgery of patients’ wounds. However, the
model has limitations in its ability to accept a wide range of inputs, and
future studies aim to address this issue in order to improve its practicality
and overall strength.

  * -

The actual experiment results, as shown in Fig. 16, indicate that 3D printing
technology has the potential to improve the treatment process for patients.
Firstly, it supports surgeons and patients in gaining a better understanding
of the final results when the treatment process is completed. Secondly, this
technology replaces traditional molding methods, enabling quicker mold sample
creation and assisting surgeons in adapting to each stage of patient recovery.
Finally, the combination of this research with bioprinting technology has the
potential to create a filling part with biological materials that are not
irritating to human skin and are implanted in the face to construct a natural-
looking facial structure for patients. This is a promising development, as
bioprinting technology allows for the creation of complex tissue structures
that can be used for various medical applications such as drug testing,
developing new therapies, and creating replacement body parts. These findings
underscore the importance of ongoing research and development in the field of
3D printing technology and its potential to improve patient outcomes.

  * -

A novel wound-covering model has been developed through this research,
enabling patients to conceal facial imperfections. We hope this paper also
leads to the creation of products that simplify and ensure the safe treatment
of wounds during the healing process. The benefits of the current paper serve
as a valuable aid for individuals suffering from illnesses in underprivileged,
underdeveloped, and war-affected countries. The data generated from the
present method is enriched and stored on our app system https://ht3dprint.com.

## Acknowledgments

We would like to thank Vietnam Institute for Advanced Study in Mathematics
(VIASM) for hospitality during our visit in 2023, when we started to work on
this paper. It is important to highlight that the introduction of this article
underwent refinement to enhance its readability, using a Large Language Model
(LLM) called ChatGPT from OpenAI, based on our initial paper. Authors are
accountable for the originality, validity, and integrity of the content of our
submissions. The use of this AI-assisted technology is permitted by the
publisher’s policy.

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