Skull ethnic classification by combining skull auxiliary image with deep learning

Abstract

Background: China is a multi-ethnic country. It is of great significance for the skull identification to realize the skull ethnic classification through computers, which can promote the development of forensic anthropology and accelerate the exploration of national development.

Methods: In this paper, the 3D skull model is transformed into 2D auxiliary image including curvature, depth and elevation information, and then the deep learning method of the 2D auxiliary image is used for ethnic classification. We construct a convolution neural network structure inspired by VGGNet16 which has achieved excellent performance on image classification. In order to optimize the network, Adam algorithm is adopted to avoid falling into local minimum, and to ensure the stability of the algorithm with regularization terms.

Results: Experiments on 400 skull models have been conducted for ethnic classification by our method. We set different learning rates to compare the performance of the model, the highest accuracy of ethnic classification is 98.75%, which have better performance than other five classical neural network structures.

Conclusions: Deep learning based on skull auxiliary image for skull ethnic classification is an automatic and effective method with great application significance.

Graphical abstract

Keywords

skull auxiliary image / deep learning / skull ethnic classification / convolutional neural network

1 INTRODUCTION

China is a multi-ethnic country with prosperous national culture. Due to the living environment, genetic and other factors, the appearance characteristics of different nationalities are very different. Skull is an important research object in the fields of forensic anthropology, archaeology, facial reconstruction and so on. Skull is very hard to be damaged and it is easy to preserve skull features, it can better preserve the characteristics, so the identification of gender, race or ethnic through the skull is a reliable method and it has gradually become a research hotspot. In the criminal cases of forensic anthropology, many corpses are seriously damaged, even leaving only the skeleton, so it is impossible to identify the face and gender. The identification of skull ethnic can help to identify the victim and speed up the process of case investigation. In the field of archaeology, skull is an important unearthed cultural relic, which plays a positive role in understanding the historical development process, excavating the national culture and promoting national unity.

Chinese anthropologists have done a lot of research on the characteristics of different nationalities. In the 1980s, Zhang put forward the research on the physical characteristics of Tibetan people [1], Zhuang people [2] and Li people [3]. In the 1990s, Ai and Zheng respectively studied the physiological characteristics of Uygur people [4] and Hui people [5]. In recent years, the research on the physiological characteristics of Han people in different regions [6–9] has gradually increased. According to the relevant research, there are significant differences between the minority ethnic groups and Han facial appearances [10].

At present, the research on ethnic classification mainly focuses on 2D face images. Li et al. [11] used C5.0 algorithm to discriminate three ethnic images of Tibetan, Uyghur and Zhuang ethnicities, with an average accuracy of 90.95%. Compared with 2D face image, 3D skull model is more complex and difficult to obtain, so there is little research on 3D skull data classification of different ethnic (the same race). As the similarity between the ethnic classification and gender identification or race identification of skull, related references are investigated here.

Gender and race classification methods mainly include observation and measurement classification method and computer-aided classification method.

1.1 Observation and measurement classification method

In gender identification, Williams [12] identified the gender of European Caucasians by observing the size of mastoid, the structure of supraorbital ridge, the concave convex degree of zygomatic extension and the shape of nostril, with average accuracy of 90%. Walker [13] selected five features including nuchal spine, mastoid process, eyebrow/supraorbital region, supraorbital margin and chin eminence skull for gender classification, and the final accuracy was 88%. In race identification, Zhou and Wu [14] compared the skulls of Chinese and Europeans, and found that the bulge of the canine fossa and the lateral part of the piriform foramen was more likely to appear on the skulls of modern Europeans, while the probability of the zygomatic process appearing on the skulls of Chinese and Europeans was almost the same. Weinberg et al. [15] studied about 70 skulls, which were black-and-white fetuses about eight months old. The results showed that the lower occipital bone of white fetuses was narrower than that of black fetuses, and the vomer bone was longer, the anterior nasal spine was prominent, the bone ridge under the nasal bone was thick, and the edge of temporal scale was semicircular.

Although this kind of method is simple, it relies too much on experts’ experience and subjectivity, which makes the classification results not objective and accurate.

1.2 Computer-aided classification method

In recent years, statistical theory is closely combined with computer technology. The feature extraction from observation and measurement has gradually developed into automatic feature extraction by computer according to statistical algorithm, which makes the gender and race recognition of skull tend to be automated. Literature [16–19] extracted different characteristic variables to establish discriminant equations for race identification, and the accuracy rate of race identification was more than 80%. Yasar and Steyn [17] established discriminant equations for black and white people in Southern Africa, with the highest average accuracy rate of 96.8%. Literature [20–26] used discriminant analysis to identify the gender of different skull features. In 2016, Liu [20] established a discriminant equation for 12 characteristic indexes including nose width and mastoid width, and the accuracy of gender identification could reach 95%. Luo [27] and Yang [28] used principal component analysis (PCA) to establish statistical shape model, and obtained skull feature vector to identify skull gender, and the identification rate was more than 90%. Luo [29] used the method of sparse principal component analysis (SPCA) to extract skull features and find four optimal regions. The final gender identification rate was about 97%.

With the rapid development of computer technology, machine learning methods have been widely used in classification problems. Yang et al. [30] combined convolution neural network with least square method to identify gender, and the average accuracy rate was 94.4%. In 2019, Yang et al. [31] measured six skull features, including sagittal arc, sagittal chord, sagittal arc, sagittal chord, sagittal arc and sagittal chord, as input of neural network for gender identification, and the accuracy of the test reached 96.764%. In race identification, Joseph et al. [32] used random forest algorithm to identify race with multiple features, and the average accuracy was 89.6%. Casper et al. [33] used the same feature vector as Luo [27] for race identification, with an average accuracy of 79%.

Compared with other classification methods, deep learning method has stronger learning ability and generalization ability. The operation is relatively simple and fast, and has more application value. Compared with the traditional method, literature [34] uses back propagation neural network for ethnic classification, which improves the automation and convenience to a certain extent. But this method requires researchers to understand the characteristics of different nationalities and extract skull features with significant differences. Because there are many nationalities and races in the world, this is complex and difficult to achieve. Therefore, in this paper, the deep learning method is used to study the classification of skull ethnic. We propose to transform the Han and Uygur 3D skull models into 2D skull auxiliary images containing depth, curvature and elevation information, and input them into VGGNet16, which has superior performance in the field of image classification (Fig.1).

2 RESULTS AND DISCUSSION

In this paper, 400 skull models were used for Han and Uygur classification experiments, including 200 Uygur and 200 Han, and they were randomly divided into 80% train data and 20% test data. We transform the 3D skull data into 2D skull auxiliary images and input them into neural network for experimental analysis. The specific network structure is described in the materials and methods section. At the same time, in order to verify the performance of the network selected in this paper, we compare it with a variety of different convolutional neural network structures.

2.1 Experimental results and analysis under different parameters

In the process of network model training, the setting of network parameters is particularly important, which directly affects the results of the network model. The optimal parameter setting is different for different tasks. Therefore, in this section, we select the optimal combination of super parameters for skull ethnic discrimination task through many experiments. Firstly, we consider the influence of the number of iterations. Because we used small sample data, we controlled the number of iterations between 1 and 40 during the experiment. Then we analyzed the influence of different learning rates on network performance. If the convergence time of loss function is too long, the learning rate can be increased appropriately. When the loss function cannot converge, the learning rate can be reduced appropriately. Through several experiments, the Figs. Fig.2 and Fig.3 show the change of training loss and average training accuracy under three different learning rates when the number of iterations is 40.

It can be seen from Fig.2 that different learning rates lead to different network convergence rates. On the whole, when the number of iterations is 40, the training loss has decreased to a very small value, indicating that the model has basically reached a stable state. When the learning rate is 0.0001, the training accuracy can reach up to 100%, while when the learning rate is 0.001 and 0.01, the training accuracy can only reach about 50% (Fig.3). This shows that different learning rates have different effects on the network performance, and choosing the appropriate learning rate can greatly improve the classification effect. Therefore, we set the learning rate at 0.0001.

In addition, we also consider the impact of batch-size on recognition accuracy. Appropriate batch-size can improve training speed and accuracy. Most experiments have shown that GPU can perform better when batch-size is a power of 2. Therefore, this paper sets batch-size to 8, 16, 32, 64 to experiment and record the training accuracy.

The experimental results are shown in Fig.4 and Fig.5. From the figure, it can be seen that four different batch-size values can achieve the highest training accuracy. When batch-size is 16, accuracy increases the fastest and changes steadily. In summary, the experimental results show that when the learning rate is 0.0001 and the batch-size is 16, the network performance is the best, and it is the optimal combination of network parameters for ethnic discrimination problems. At this time, the accuracy of the network on the test set can reach 98.75%.

2.2 Comparison of different network structures

In order to compare the performance of our and other network structures in skull ethnic classification problem, we compare the experimental results of VGGNet19 [35], LeNet [36], AlexNet [37], ResNet [38] and GoogLeNet [39] when the learning rate is 0.0001. The same data are used in the experiments. After 40 iterations, the average training accuracy of each network is shown in the Fig.4, and the performance of the final network model on the test data is in Tab.1.

Fig.5 shows the change in training accuracy when the training data and parameters are the same. LeNet has two convolution layers and three full connection layers, and AlexNet includes five convolution layers and three full connected layers. Their convolution kernel size is 5 * 5. VGG19 has 16 convolution layers and 3 full connection layers, the convolution kernel size is 3 * 3; GoogLeNet adopts the improved Inception Module; ResNet is the ResNet-101 network structure. As shown in Fig.5, the accuracy of our network used in this paper is significantly higher than that of other image classification networks. The performance of each network in the test data (Tab.1) also verifies the superior performance of our method, the accuracy of our network used in this paper is 98.75%. As can be seen from Fig.6, the accuracy ranked from high to low is our method, AlexNet, VGGNet19, LeNet, GoogLeNet, ResNet. It shows that the small convolution kernel can extract skull features better, and the depth of the network has a great impact on the classification performance of the model. So, our method is more robust to complex data like skull, and more suitable for the study of skull ethnic classification.

3 CONCLUSIONS

As deep learning is robust to noise and has better generalization, we put forward a method of ethnic classification which combines 2D auxiliary image of skull with deep learning. The 3D skull model of Uygur and Han is converted to 2D image which contains curvature, elevation and depth information as input of convolution neural network. The skull features are automatically extracted and classified by neural network instead of extracting features of different ethnics by hand and can be applied to other different ethnic groups easily and quickly, which greatly improves the generalization ability.

This paper utilizes 16 layers network structure to extract features and classify ethnic. All convolution kernels in the network are as small as 3*3, which reduces the amount of calculation and speeds up the training process. It improves the network performance by deepening the network level, and the final average accuracy is up to 98.44%. Compared with other five network models, our method is superior to the state-of-the-art classification networks, and it is more suitable for ethnic classification.

Due to the limitation of the existing data, we only carried out the classification experiment on Uygur and Han, which will be extended to multi ethnic classification in the future. We will also continue to explore the deep learning methods, continuously try to adjust and explore the optimal network structure, so as to improve the recognition rate and form a more perfect and meaningful automated classification method.

4 MATERIALS AND METHODS

4.1 3D skull dataset

The experimental data used in this paper include 400 non pathological skull CT raw data, of which 200 Han head CT data are from the craniofacial CT database of the Engineering Research Center of Virtual Reality Application Ministry of Education in China; 200 Uyghur head CT data were obtained from the radiation center of the people’s Hospital of Toxon County, Xinjiang, China. The collected CT images is 512 × 512, the color and depth are the same 16 bits. Firstly, the skull contour boundary [40] is extracted from the collected CT data, and then Marching Cube algorithm [41] is used reconstructs 3D model to get 3D skull and face model. The main idea of the algorithm is to detect the voxels intersecting with the iso-surface and calculate the coordinates of the intersection point, and then use the look-up table to construct the mesh topological relations in the voxels for different intersecting situations. Then we need to preprocess the 3D skull model. First, in order to avoid the influence of posture, scale and coordinate system, we adjust all the skulls to the same Frankfurt coordinate system [42]. The Frankfurt coordinate system is determined by the left ear hole point, right ear hole point, left eye orbital lower edge point and eyebrow center point. All skull data can be adjusted to Frankfurt coordinate system by rotation and translation, so that all the skull models can be unified in posture. Second, non-rigid data registration method based on TPS is used for registration [43]. TPS is a region registration algorithm based on the correspondence between feature points calibrated manually. The algorithm calculates the coefficients of the TPS transformation function from the feature points. After obtaining the coefficients, transform the target skull to complete the registration. After data preprocessing, each skull model has 41,059 points, and they had the same pose and scale.

4.2 2D skull auxiliary image generation

The skull model is complex high data, which contains a lot of redundant information. Directly feeding the whole model into the convolution neural network for training requires a large amount of computation and training time, and the design of the convolution neural network model is also very complex. In this paper, 3D skull model is transformed into 2D image and then input into convolutional neural network for skull ethnic classification. The method is inspired by the approach in Gilani et al. [44] and Galteri et al. [45].

The specific calculation process of converting the preprocessed and registered 3D skull data into 2D auxiliary image including depth, curvature and elevation information is as follows.

4.2.1 Calculate depth

Suppose that the 3D skull data is represented as matrix S_{n\times 3}:

(1)S=\left[\begin{array}{c}{x}_1,y_1,{\mathit{\text{z}}}_1\\ x_2,y_2,{\mathit{\text{z}}}_2\\ ⋮⋮⋮\\ x_n,y_n,{\mathit{\text{z}}}_n\end{array}\right]

Then each line of S is the three-dimensional coordinates of a vertex. The 2D auxiliary image is represented as D_{m\times n}, we need to project the skull data S to D. Suppose i is a vertex in skull data S, x_i and {\mathit{\text{z}}}_i can be transformed into 2D auxiliary image coordinates by formula:

(2)a=-{\mathit{\text{z}}}_i\ast (m/2)+n/2

(3)b=x_i\ast (m/2)+n/2

(a, b) are the coordinate values of vertex i in the image, m and n are the length and width of the image respectively. We directly take the y-axis value of each vertex as the depth value.

4.2.2 Calculate mean curvature

Curvature is a measure or amount of curving of the geometry. Mean curvature is the mean of any two orthogonal curvatures perpendicular to each other at a point on a surface in space. At present, there are many algorithms to solve curvature. We use the method proposed by Cohen Steiner and Morvan [46] to calculate the mean curvature. For each vertex p_i on the mesh, we take all the points in the ball with radius r_i as a geodesic neighborhood around the point p_i, and then we can define the following matrix:

(4)E_{p_i}(B)=\frac{1}{\left|B\right|}\sum _{e\in B}\beta (e)\Vert e\cap B\Vert {\overline{e}}^{\mathrm{T}}\cdot \overline{e}

where \left|B\right| is the area of B, e is the edge of the mesh in B. \Vert e\cap \beta \Vert is the length of the mesh, always between 0 and \left|e\right|. \beta (e) is the angle between the normal directions of two triangles with e as the common edge. We calculate the eigenvalues and eigenvectors of the matrix E_{p_i}(B). The minimum eigenvalue k_{min} and the maximum eigenvalue k_{max} are taken as the principal curvatures k_1 and k_2, from which the mean curvature of each vertex can be calculated:

(5)k_H=\frac{k_1+k_2}{2}

4.2.3 Calculate elevation

Elevation is the angle between the projection of the vector from the vertex to the origin on the XY plane and the X axis. First, the normal vector (n_x,n_y,n_z) of each vertex is calculated and transformed into spherical coordinates (n_{\theta },n_{\phi },n_r) , where \phi is the azimuth, \theta is the elevation, and r is the radius,

(6)\{\begin{array}{c}r=\sqrt{x^2+y^2+{\mathit{\text{z}}}^2}\\ \mathit{\text{z}}=r\ast \cos (\phi )\\ x=r\ast \sin \phi \ast \cos \theta \\ y=r\ast \sin \phi \ast \sin \theta \end{array}

The elevation angle \theta can be calculated from the above formula.

Finally, the curvature value, elevation value and depth value of each vertex of 3D skull model are used as RGB channel value of 2D auxiliary image. The 2D auxiliary image of skull is shown in the Fig.7.

4.3 Network structure of ethnic classification based on skull auxiliary image

Network structure based on skull auxiliary image is constructed for ethnic classification in this paper. Inspired by VGGNet16 [34], a 16-layer deep convolution neural network is constructed by stacking 3*3 small convolution kernels and 2*2 maximum pooling layers. Different from the previous convolutional neural network, large size kernels are not used in the network, but all 3 * 3 small kernels and 2 * 2 pooled kernels. The stacked small filter can not only keep the size of receptive field unchanged, but also reduce the number of parameters and increase the nonlinear operation, which makes the network model have stronger learning ability for features, increase the fitting expression ability of the network and improve the performance of the model. The specific network structure is shown in the Fig.7.

It can be seen from the Fig.8 that our network consists of 13 convolution layers (conv1−conv13) and 3 full connection layers. We input the 96 * 96 2D skull auxiliary image into the network, and then use 3 * 3 convolution kernel to obtain deeper and more detailed features of skull. In order to reduce the size of the feature map and improve the network anti-interference ability, the max pool layer (pool1−pool5) connects conv2, conv4, conv7, conv10 and conv13 respectively. The network ends with three full connection layers and a softmax classification layer. Finally, the input image can be divided into Han and Uygur by softmax layer to complete the ethnic classification.

Activation function: To speed up convergence and improve the sparse representation of the neural network, all the activation functions of convolution layer use ReLU function. ReLU function is defined as

(7)f\left(x\right)=max\left(0,x\right)

Loss function: Considering the cross-entropy loss function does not depend on the partial derivative of the activation function in the process of parameter updating, it is used as the following formula in our study

(8)C_0=\frac{1}{N}\sum _{i=1}^N-\left[y_i\log p_i+\left(1-y_i\right)\log \left(1-p_i\right)\right]

where N is the number of samples, y_i is the label value of samples, 1 represents Han and 0 represents Uygur, p_i is the probability that the prediction sample i is Han.

Optimization algorithm: The network uses Adam (adaptive motion estimation) optimization algorithm [47]. Adam is an adaptive optimization algorithm, which combines the gradient descent method with momentum and RMSprop (root mean square prop) algorithm to accelerate the gradient descent. Suppose that the derivative of the objective function C_{\text{0}} to the parameter \theta is g_t at time t. Calculating the estimation of the first moment m_t=E\left(g_t\right) and the second moment v_t=E\left({g_t}^2\right) of the gradient, m_t and v_t are corrected: {\hat{m}}_t={\displaystyle \frac{m_t}{1-{{\beta }_1}^t}}, {\hat{v}}_t={\displaystyle \frac{v_t}{1-{{\beta }_2}^t}}, where, {\beta }_1 and {\beta }_2 are the first-order moment attenuation coefficient and the second-order moment attenuation coefficient respectively, so

(12){\theta }_{t+1}={\theta }_t-\frac{\eta }{\sqrt{{\hat{v}}_t}+\epsilon }{\hat{m}}_t

where \eta is the learning rate and \epsilon is the minimum constant term, which is used to maintain numerical stability. Thus, Adam can design independent adaptive learning rates for different parameters to achieve more efficient training.

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The Authors (2022). Published by Higher Education Press.