Measurement and analysis of facial features of terracotta warriors based on high-precision 3D point clouds

The striking realism of the life-sized ceramic terracotta warriors has been attracting the interest of the public and archaeologists since they were discovered from the mausoleum complex of the first Chinese Emperor Qin Shihuang in the 1970s. It is still debated whether the life-size models were based on individual people or were just crafted from the standardized models. This research examined the facial features of the terracotta warriors in a quantitative and contactless way with the support of the High-precision 3D point cloud modelling technology and the anthropometric method. The similarities and dissimilarities were analyzed among the facial features of terracotta warriors and 29 modern Chinese ethnic groups using mathematical statistics methods such as MDS, ANOVA, ranking analysis and cluster analysis. The results reveal that the features of the terracotta warriors highly resemble those of contemporary Chinese people and indicate that terracotta warriors were crafted from real portraits and intended to constitute a real army to protect the Emperor Qin Shihuang in the afterlife.


Introduction
The discovery in 1974 of the terracotta army of the first emperor of China is known as one of the greatest finds in the history of twentieth-century archaeology. The army of terracotta warriors was created in the third century BC and comprises an estimated 7000 life-size soldiers standing in three pits that cover more than 20,000 square meters [1][2][3] and are located approximately 1.5 km from Qin Shihuang's mausoleum, as illustrated in Fig. 1. After discovery, the site became a museum and a UNESCO World Heritage Site in 1987; it remains one of the world's most impressive archaeological sites.
The terracotta warriors expertly crafted with intricate features and clothing demonstrate an extraordinarily high level of achievement from the artistic perspective and also provide an invaluable reference for studying the military, political, economic, cultural, scientific, and technological aspects of the Qin Dynasty [4,5]. Therefore, the terracotta army attracts the public and scholars with diverse interests in ancient Chinese art, afterlife beliefs, funerary culture, craft technology, materials, logistics management and labor organization of building a mausoleum with such an incredibly large scale during ancient times.
One of the most extraordinary features is the striking realism of the terracotta warriors [6][7][8]. Each warrior has intricate details with distinct styled hair and features [9,10]. They also have different builds, expressions and postures. Actually, the warriors were painted in proper colors when they were unearthed and originally equipped with real fully functional bronze weapons. Therefore, they should have appeared more realistic and individualized than now. But the colors have vanished after the warriors were exposed to the dry air. In addition, the armored soldiers present impressive funerary assemblage that Open Access *Correspondence: huyungang@bucea.edu.cn 1 School of Geomatics and Urban Spatial Informatics, Beijing University of Civil Engineering and Architecture, Beijing 100044, China Full list of author information is available at the end of the article includes chariots, cavalry, horses, and archers installed in battle formations to protect the first emperor of China in the afterlife [11]. Figure 2 shows the warriors unearthed in exploration T19 of Pit No. 1.
Despite that there are intensive studies from different sectors since the discovery of terracotta warriors, it remains open how they were crafted and invented into these incredible works of art [10,11]. Especially, it is still debated whether the life-size models were based on real humans or were just made from several standardized groups of models. It has led scholars to conduct related research into the realism of the terracotta army, delving into their purpose, materials used, the creative process, variability of figures, and similarity to the real humans.
Many researchers examined these sculptures of warriors in a qualitative way from the viewpoint of artistic sculpturing, purpose/function, cultural tradition, religious belief of an afterlife, and funeral ritual [6][7][8][9]. These related studies indicate that the terracotta warriors were intended to constitute a "real" underworld army to serve the first emperor in the netherworld after his death, as if he was alive. The constructed artificial army was more likely the substitution of his real army. Theoretically, this view conforms to the religious belief and funeral culture at that time [6,7].
On the other hand, some researchers analyzed the unearthed warriors in a quantitative way, compared them with real humans. So far, the analysis of the body dimensions of terracotta warriors has indicated there is a remarkable resemblance to the modern population [13]. More detailed, the variability of the ear shape of the warriors was also examined and reveals that no two ears are strictly the same [12].
However, the facial features of terracotta warriors have not been analyzed quantitatively so far. It is still unclear how the features of these figures are exactly similar and different from the modern population. As well known, the face is essentially the most distinct feature used to identify individuals [14] and used as one of the main inputs in measuring anthropological variances among ethnic groups [15]. Compared to body features like body height, head and facial features are less affected by environmental factors and more significantly affected by genetic factors [16,17]. This, in turn, means head and facial features could be used as one of the main factors to identify one person or ethnic group and even used to analyze the relationship between different ethnic groups.
Based on these research results and facts, theoretically, if the terracotta warriors were supposed to be crafted based on real people, each face of them should have distinct features as real humans have. Therefore, the quantitative analysis of the warriors would have a great significance in understanding whether the warriors were crafted based on the real portraits of Qin people. The analysis of similarity/dissimilarity of the warriors with contemporary Chinese people could provide useful clues for further research on the relationship between the ancient Qin people and the contemporary Chinese ethnic people.
This paper focused on the quantitative analysis of the facial features of warriors and comparison with contemporary Chinese people. The structure of this paper is as follows. "Data collection and measurements" section is focused on data collection, including the collection of the terracotta warriors' heads as well as 3D model construction, the measurements of key head and face features, and the collection of the head and face feature data of contemporary Chinese people. "Methodology of data analysis" section describes the main analysis methods used in this study. "Results and statistical analyses"  section introduces the analysis results of sample data, including multidimensional scaling analysis (MDS) for examination of the variability of facial features, and analysis of variance (ANOVA) for detecting the resemblance to the modern Chinese population. Conclusion and discussion are included in "Conclusion and discussion" section. The overall workflow of the study process is illustrated in Fig. 3.

Data collection and measurements
To build a precise 3D model of each sample, 3D laser scanning technology is used to capture 3D point clouds in this study. 3D laser scanning technology and computer vision or photogrammetry technology are able to acquire high-precision 3D data in archaeological research and applications [12,18]. The technology provides new and unlimited access to fragile and valuable remains once 3D models are generated [19]. For instance, it contributes to the restoration of terracotta warriors in contactless virtual reality to reduce repeated contacts [20] or to the virtual color reconstruction of the Terracotta Army [21]. It also provides facial reconstructions as it was used for Robert the Bruce [22], or used to reveal otherwise hidden trauma such as in the examination of the Jericho skull [19].

3D data acquisition equipment
Considering the rich details of terracotta warriors and the need for data extraction accuracy, Faro arm platinum (Model 14000) was selected to scan the samples of terracotta warriors in this study, as its ideal scanning single point precision could reach up to 0.029 mm [23], which allows highly detailed feature capture of terracotta warriors. In this manner, each head model consists of 35 million 3D points on average, and the spatial resolution is high enough to support the needs of measurement in this study. The detectable minimum distance among points in the raw data on the nose area of a warrior is 0.032 mm, as shown in Fig. 4.
Following the 3D scanning process, post-processing software is needed to generate 3D models from point clouds. In this study, Geomagic 3D software (Geomagic Design X and Geomagic Wrap 2020) is adopted to build digital 3D models. In the meantime, it also provides efficient tools for measuring the head and facial features.
Statistical analysis software SPSS (official IBM SPSS Statistics) version 27 is selected for the qualitative data analysis. It is one of the most powerful tools for complex statistical data analysis in various kinds of research fields. In this study, SPSS is mainly used to implement the MDS, ANOVA, Cluster analysis.

Sample selection
As mentioned in "Introduction" section, the terracotta army is distributed into three pits and is comprised of an estimated 7000 warriors, approximately 6000 of which are located in Pit 1. Thus far, approximately about 1500 pieces have been unearthed [24]. The samples used in our  The excavation of Pit 1 was divided into 27 explorations, among which 6 areas were excavated and cleaned. The specific locations of the 6 excavated and cleaned areas are shown in Fig. 5, with numbers T1, T2, T10, T19, T20 and T23 [1].
Our 58 research samples were randomly selected from T19, T20, and T23, and the numbers of terracotta warriors arranged in the three areas were 218, 220 and 200. 20, 11 and 27 terracotta warriors were randomly selected respectively from the three areas respectively. The overall arrangement and sample locations are shown in Fig. 6.

Definition of terracotta warriors' key facial features
To obtain quantitatively the variation of facial features of terracotta warriors, the anthropometric method is adopted to measure the physical dimensions of each warrior in this study. Due to the quantitatively and objectively descriptive ability and objectivity anthropometric method, many researchers used it for the analysis of humanoid sculpture relics based in archaeology [25][26][27][28].
The head and facial features in anthropometry are based on five measurement dimensions, including height, length, breadth, angle, circumference and radian, all further subdivided into 54 features. These characteristics and indices are clearly defined in the Anthropometric Manual [29] and are specifically described in Chinese national and international standards related to anthropometry [30]. Because of the decorative parts of warriors' heads such as the bun and the crown as shown in Fig. 7, some head features are unavailable such as the head circumference, maximum head breadth and maximum head length.
Each defined feature and index can describe a characteristic or variation among faces. However, they vary due to descriptive ability and possible errors by operators. According to the study [31,32], 14 selected facial landmarks used for measuring facial features can be used to create a dense corresponding mesh to capture   Fig. 8. Thus, we can use fewer features to capture the main facial variance and reduce the noise in recognizing and measuring facial shapes.
Another important factor in the key feature selection considered in this study is the limitation of accessible historical data on facial features of modern populations used for comparison with terracotta warriors.
Considering these two main factors, it is unnecessary or impossible to use all features described above in this study. As a result, 8 key features and 2 indices were selected and used for measuring and comparing the facial features of warriors and modern populations, as illustrated in Fig. 9. Comparing Figs. 8 and 9, we can see that the 8 key features basically cover the landmark points selected in the study [31,32].
The definitions of the 8 key features in Fig. 9 above are described as follows [33][34][35].   In addition, the morphological facial index and nasal index can be calculated, which are mainly used to judge the width of the face and nose of terracotta warriors.

Morphological facial index = (morphological facial
length/bizygomatic breadth) * 100, reflecting the width and narrowness of the face; the larger the value, the narrower the face. 2. Nasal index = (nose breadth/nose height) * 100, reflecting the width of the nose. The larger the value is, the wider the nose.

Measurement of terracotta warriors' heads and facial features
The traditional measurement of head and facial features is to directly measure the head and face of a real person using various tools, such as bending foot gauges and straight foot gauges [36]. The accuracy of measurement is approximately 0.1 mm. However, there exists the risk of damage to cultural relics in the traditional manual measurement method. The measurement of head and facial features on the high-precision 3D model of terracotta warriors could be automatically extracted by an algorithm or manually measured by computer aiding software. These feature points include corner points (ectocanthions, cheilions), inflection points (sellions, gnathions, zygions, alares, subnasales) and lip midpoint (labrale superius, labrale inferius).
Taking the head of a terracotta warrior, number G9-10 as an example, we described the process of measuring the 8 head and facial features. Figure 10 illustrates a schematic diagram of measuring each feature: (a) biocular breadth, (b) interocular breadth, (c) morphological facial length, (d) bizygomatic breadth, (E) nose breadth, (f ) nose height, (g) height of mucons lips, (h) mouth breadth.

Head and face data collection from contemporary Chinese population
To compare the heads and faces of warriors and those of contemporary population, the head and face data of 29 ethnic groups were collected from of the past studies. The associated geographical distribution is illustrated in Fig. 11. The mean values of the 8 key facial features are listed in Table 1. These ethnic groups cover most regions of China, accounting for 2/3 of ethnically Chinese population which can be used to comprehensively analyze the distant and near relationship between terracotta warriors and the modern Chinese population.

Methodology of data analysis
In this paper, a quantitative and more precise analysis is conducted to assess the facial variability of the terracotta warriors with 3D laser scanning technology and statistical methods. Furthermore, in order to examine the similarities and dissimilarities of the key head and facial features between terracotta warriors and contemporary

Normality test of samples
Statistically, the normality test is to check if the distribution of samples used in this study conforms to a normal distribution. There exist more than 40 test methods available in the statistical literature. The Kolmogorov-Smirnov test (K-S test) is used in this study due to the fact that it has more general use in different areas and data analysis than other tests.
The Kolmogorov-Smirnov (K-S) test is a nonparametric hypothesis and distribution-free test in which there is no assumption about the distribution of data [64]. Therefore, it is a more universal test method without restriction on the size of the sample and is widely supported by statistical software such as SPSS (Statistical Package for the Social Sciences) and SAS (Statistical Analysis Software) [65]. However, it is noted that there is a restriction when the original K-S test is applied to the normality test in which the parameters of the hypothesized distribution are supposed to be known completely. Therefore, in this study, a modification of the K-S test, the Lilliefors test, is adopted, in which the parameters are allowed to be estimated based on the sample [66]. This test is performed based on the formula below.
where S n (X) is the sample cumulative distribution function and F* (X) is the cumulative normal distribution function with µ = X, the sample mean and s2, the sample variance, defined with denominator n − 1.

Clustering analysis
The method of cluster analysis is often used in the classification of races in anthropology [67][68][69]. The purpose of cluster analysis is to divide objects into several clusters based on their similarity so that objects in the same cluster are highly correlated, while objects in different clusters are low correlated [70]. The specific step includes calculating the distance between characteristic values between two clusters, merging the two clusters with the smallest distance into a new cluster, and taking Then, the process is repeated until all clusters are merged into one and the clustering ends [71].
Euclidean distance is commonly used in clustering calculations to measure the distance of individuals in space. The larger the distance is, the greater the gap; otherwise, it will be closer. The calculation formula is as follows (2): Finally, to verify the statistical significance of cluster analysis, ANOVA was conducted on the head and facial features of terracotta warriors and 29 modern ethnic groups to infer the probability of difference or to compare whether the difference between the two variables was significant. If the p value in the test result is less than 0.05, it means that there is a significant difference between the two groups. In contrast, the larger the p value is, the smaller the difference [72].

MDS analysis
Multidimensional scaling (MDS) is a visual representation of dissimilarities (or similarities) among objects. MDS is a multivariate data analysis technique that can represent higher-dimensional data in lower space and transform dissimilarity measurements into distances on a spatial map [73]. On the spatial map, the dissimilar objects are further apart, while similar objects are placed closer to each other. As such, MDS provides us with a spatial and intuitive data analysis method. Most MDS algorithms use Euclidean principles, where the distance (d ij ) between points i and j is defined as follows: where x i and x j represent the coordinates of points i and j on dimension a, respectively. MDS analysis can be found in most statistical software, such as SPSS or SAS. It has been widely applied      Table 4 Head index classification of terracotta warriors in many fields, such as biology, artificial intelligence, neural networks, image analysis, and ecology, even in psychological research [74]. In the field of archaeology and culture relics, MDS has provided intuitive, effective and valuable ways to analyze dissimilarities or similarities [75]. In this paper, MDS is applied in the analysis and spatialized representation of dissimilarities among facial features of the terracotta warriors.

Analysis of variance (ANOVA) is a statistical technique
that is used to determine if two or more groups are significantly different from each other. ANOVA checks the impact of one or more factors by comparing the means of different samples. It can reduce the compounded effect on the error rate of the result pairwise test like T-test method. ANOVA was developed by the English statistician Yates and Fisher [76] and has been applied in various fields for data analysis. It has been applied successfully to face recognition and classification [77,78]. In this paper, ANOVA is utilized to compare the differences among facial features of terracotta warriors and modern Chinese ethnic groups.

Measurement results
According to the measurement method described in "Definition of terracotta warriors' key facial features" section, the head and facial features of 58 terracotta warriors were measured. All measurement results are shown in   Table 3 indicate that 8 independent variables of facial features conform to a normal distribution.
The morphological facial and nasal indices of the sample data were also calculated, the sample number at different index intervals was counted (Table 4), and the quantity distribution charts were generated (Fig. 12). From the above data, it is interesting to note that most of the 58 samples are within the hyperleptoprosopy and mesorrhiny types. According to investigation results from Yu et al. [37], there are more males of northern Chinese Han individuals that belong to hyperleptoprosopy and mesorrhiny types than males of the southern Chinese Han ethnicity. This shows that the face form and nasal shape of terracotta warriors are closer to those of the northern Han population.
In order to assess the precision of measurement via 3D model in this study, a comparison was made with the traditional contact measurement method using a millimeter. Table 5 illustrates the measurement precision of interocular breadth based on the actual face of a terracotta warrior and based on its 3D model. The result shows that the precision of the 3D model measurement is 0.30 mm, while the precision of the traditional method is 0.79 mm. The contactless method can obtain more accurate measurement results than the traditional contact method. The main reason lies in the fact that he high-resolution/density 3D model could ensure that an operator positions at the same location at each time of measurement as possible as he can.

Variability of terracotta warriors' heads and faces
The MDS method was applied in analyzing the variability of 58 terracotta warrior samples randomly selected. The overall result is shown in Fig. 13. The label beside each dot represents the number of each terracotta warrior. The further the distance between the two dots is, the more different they are.
It can be observed from Fig. 13 that the distribution of dots is scattered and random, and no two dots are identical. This chart reveals that the fact the faces of warriors appear great variability of key facial features. Each terracotta warrior has distinct facial features, which seem like real humans. That means the MDS analysis result supports the theory that the warriors were based on a Fig. 13 Result of MDS analysis real army. Actually, this inference is also consistent with the funeral tradition and culture around Qin Dynasty. At that time, people viewed the afterlife as an extension of worldly life. Thereby, tomb builders always pursued to duplicate all aspects of the real world in the netherworld, including everything they needed [7]. Therefore, it is reasonable that Qin Shihuang, as the first China emperor who unified the vassal states, established the "real army" in his necropolis to protect himself in the afterlife. Besides thousands of warriors, almost five hundred weapons such as spears and swords, and more than ten thousand scattered arrowheads have been found in pit no. 1 [5]. Sima Qian, a Han Dynasty historian who lived about a century after the first emperor's time, also mentioned that the tomb of Qin Shihuang was intended to replicate the real world in his "Shiji" (Records of the Grand Historian). Therefore, theoretically, it is more reasonable that each life-sized terracotta soldier was modeled on an actual person.
However, some dots are noticed to be very close. For example, the group of red green or blue dots in Fig. 13 are closer than the others. This can be verified from the 3D head and face models of the warriors, as shown in Fig. 14, the faces in the same box look more alike. In Fig. 14, the face number under each face model, the first part such as "G11-51", "G8-25" represent the location of warriors in the Pit no. 1, the second part such "v10", "v54" represents the number used in Fig. 13. This situation is like the real world of human beings, on the contrary, it increases the realism of terracotta warriors.

Variation of heads and faces between terracotta warriors and modern ethnic groups
The differences between the terracotta warriors and modern ethnic groups by size of facial features were examined. First, the 8 head and facial features were sorted according to their values. According to the sorting results (Fig. 15), 6 of the 8 facial features were neither at the maximum nor at the minimum, which falls into the range of the facial features of the 29 ethnic groups. The 6 facial features include morphological facial length, bizygomatic breadth, nose height, the height of mucons lips, mouth breadth and biocular breadth. However, it should be noted that one of the very interesting points is that nose breadth and eye breadth (interocular) are beyond the range of facial feature values of contemporary Chinese ethnic groups. Table 6 lists the statistical mean and standard deviation of key facial features of terracotta warriors and 29 modern Chinese ethnic groups.
This indicates that 75% (6/8 = 0.75) of the terracotta warriors overlapped the range of the head and facial feature values of modern multiethnic groups. Therefore, there was little difference in the head and face features between the terracotta warriors and modern multiethnic groups. The key features of the terracotta warriors highly resemble those of modern Chinese populations. Terracotta warriors seem like one of Chinese ethnic groups.

Clustering analysis results based on Euclidean distance
According to the above Euclidean distance cluster analysis formula, the Euclidean distance between the terracotta warriors and other ethnic groups is shown in Table 7. Then, cluster analysis was performed based on distance values, and the cluster graph was generated by SPSS. The results are shown in Fig. 16.
From the results of cluster analysis, we can see that these ethnic groups are divided into three main groups (Fig. 16). The terracotta warriors belong to Group 2, which has ethnic groups such as N4-Mongolian, N16-Jingpo, N19-Xibo, N21-Naxi, N28-Korean, N13-Daur, N12-Kazakh, N22-Uygur, N20-Tajik, and N11-Tibetan. Among them, nine (N4-Mongolian, N16-Jingpo, N19-Xibo, N21-Naxi, N13-Daur, N12-Kazakh, N22-Uygur, N20-Tajik, and N11-Tibetan) belong to western ethnic groups, which indicates that the relationship between the terracotta warriors and these ethnic groups is closer. According to the comparison of the D ij values, the terracotta warriors are close to N4-Mongolian ( D ij = 16.347) in facial features, followed by N16-Jingpo ( D ij = 16.418) and N19-Xibo ( D ij = 16.452). Further ANOVA implementation results (Table 8 and Fig. 17) also reveal that the faces of terracotta warriors resemble the modern Chinese population in six key facial parameters. In particular, the terracotta warrior's facial features resemble modern Chinese populations in morphological facial length, nose height, height of mucons lips much more than in other key features. Only in nose breadth and eye breadth (interocular) was there a statistically significant difference among all 29 ethnic groups, and the mean value exceeded all 29 ethnic groups. One of the possible reasons for this difference might be the procedure of producing terracotta warriors when they were made at high temperatures. Another possible reason is the face evolution of human beings caused by climate change and dietary changes [79,80]. Further reasons need to be revealed with more archeological material and analysis.

Conclusion and discussion
The striking realism of terracotta warriors has led to hypothesize or believe that they were based on real soldiers who served in the emperor's army. But few researchers examined quantitatively in statistical methods the     Chinese ethnic groups reveals that the facial features of terracotta warriors are more alike to those of northern and western Chinese populations. That means we could view the warriors as 3D portraits of Qin People. Therefore, the analysis results of similarities/differences could provide a further clue to explore the relationship between Qin people and contemporary Chinese people. For example, it could be used as clues to explore which Chinese ethnic groups could originate from Qin people, or where the Qin people migrated later. However, there are still some challenges that need further research. The terracotta warriors were actually a  kind of art, after all, made from clay and had been buried underground for over 2200 years. It is still unclear how they were deformed during the production procedure and the long time of being buried underground. This might lead that the measurement results of facial features are not the real values when. terracotta warriors were shaped originally from clay. In this research, this kind of effect is not yet considered in the measurement result. It could cause statistically significant differences between the warriors and the contemporary Chinese population. However, the difference might be caused by the possible variation of facial features contemporary Chinese population due to climate change and dietary changes. Therefore, there are still more facts behind the realism of terracotta warriors to be revealed with more archaeological material and analysis.