Introduction

Identification of the deceased is necessary for criminal, social, humanitarian, ethical, and civil purposes1. However, the identification of unknown individuals, especially those who have undergone decomposition or burning, is a global challenge2. There are number of markers responsible for the identification of the individual such as DNA profile, personal belongings, various morphological and dental features of the deceased, ante-mortem records etc. Among the various biological markers used for human identification, the face or facial profile plays a pivotal role. Forensic anthropologists contribute significantly to this process through a specialized field of forensic anthropology known as forensic facial reconstruction, which involves recreating facial features from human remains3,4.

Anthropometric measurements of the face provide quantitative assessment of various dimensions of the human face. The measurements involve determined distances between specific landmarks on the face. Such anthropometric data can be used to create a two-dimensional as well as three-dimensional representation of an unknown individual’s face5. Such techniques prove particularly valuable in forensic investigations involving mass disasters or cases where the face is unidentifiable due to severe burns or decomposition6. Conventional identification methods, such as DNA analysis and fingerprinting, may not always be appropriate in such situations7. For example, in wartime scenarios, remains are frequently severely mutilated and commingled, compounded by the destruction of personal belongings and records, leaving investigators with few traditional methods of identification. Consequently, forensic experts must rely on alternative techniques to establish identity8. Skeletal remains, including long bones, the skull, bone fragments, the jaw, and teeth, may aid in identification process9.

Reconstructing the facial profile in such conditions becomes a primary objective, with the jaw and teeth emerging as critical anatomical structures for estimating facial dimensions. Their significance in forensic identification is further reinforced by INTERPOL’s recommendation to prioritize dental records for disaster victim identification due to the resilience, uniqueness, and forensic applicability of teeth10,11,12,13,14.

Numerous studies have shown how important dental characteristics are for identifying individuals. For instance, the accuracy of age estimation using the pulp-tooth area ratio was examined by Scendoni et al.15. Their analysis of 96 digital periapical X-ray pictures of the maxillary and mandibular canines revealed no statistically significant differences and excellent agreement. In addition to estimating age, dental characteristics have been used successfully to determine sex16, stature17, and facial identification18. The significance of dental analysis in forensic reconstructions has also been highlighted by the numerous studies that have discovered correlations between dental dimensions and facial anthropometric parameters19,20,21.

All of the conventional methods used by various researchers are time-consuming and require expert knowledge; however, once the machine has been trained on the artificial intelligence (machine learning) principle of predictive analysis, this process can be automated and more convenient to use in real-time forensic scenarios in future.

Artificial intelligence and its subsets, machine learning and deep learning, are emerging as transformative tools in forensic research and casework especially in facial recognition technologies (FRTs). Various studies show the current state of AI in forensic science, especially in the field of presented research. For instance, Hargreaves et al.22 utilized 665 head CT scans to train Convolutional Neural Network (CNN) model to automated facial reconstruction. Their results demonstrated that jaw and muscle structures could be reconstructed with high accuracy, given their strong anatomical correlation with the underlying skull. Similarly, a Niño-Sandoval et al.23 tried to predict mandibular measurements from craniofacial landmarks by using artificial neural network (ANNs) and Support vector regression (SVR). The result of the study showed that mandibular shape can be reliably predicted from cranio-maxillary measurements using AI models. Collectively, such studies emphasize that AI has capability to infer one set of anatomical features from another, therefore, forming a scientific foundation for the present research.

Moreover, due to the presence of the strong allometric relationship between jaw and dental structures and overall facial morphology24, the present study aims to employ various machine learning (ML) models to predict specific horizontal facial dimensions using parameters derived from the teeth and jaw. It is hypothesized that these anatomical dimensions exhibit proportionate correlations, thereby facilitating accurate predictive modelling. The proposed ML models can be used in forensic examinations especially in the practical and real situations, where teeth and jaw parameters potentially predict the dimensions of face which may ultimately help in the facial identification.

Methods

The study participants

After receiving approval from Panjab University Institutional Ethics Committee vide reference no. PUIEC-II-240928-161, dated 28.09.2024, a total of 422 participants (201 males and 221 females) were enrolled for the present study. All methods were performed in accordance with the relevant guidelines and regulations. Specifically, the population was sourced from district Shimla of the Himachal Pradesh State of north India, with the age range between 18 and 40 years using snowball and convenient sampling. The number of participants was calculated using Cochran’s method of sample size calculation for large population25. With this method, the minimum sample size was considered to be 384; therefore, for the present study, 422 participants were taken.

Dental casts, anthropometric facial measurements and photographs of the participants were obtained with their informed consent. The informed consent was obtained from all the participants of the study. The parallelism of the participant’s Frankfort horizontal plane and the allocation at a standardized position to the floor were verified26. Different anthropometric measurements of the face were taken using spreading and sliding callipers (Fig. 1). The facial measurements analysed in present study are Minimum frontal width (Ft-Ft), Maximum facial width or Bizygomatic width (Zy-Zy), Mandibular width (Go-Go), Inner-canthal distance (Ic-Ic), Outer –canthal distance (Oc-Oc), Nasal width (Al-Al), Inter-commissural distance (Ch-Ch), Interpupillary distance (Pu-Pu)27,28 (Fig. 1) and teeth and jaw measurements employed in the study are dental dimensions of maxillary and mandibular set of teeth i.e. crown diameter, combined width of incisor (CWCI), inter-incisor distance (I-I D), inter-canine distance (I-C D), inter-premolar distance (I-P D), inter-molar distance (I-M D)29,30,31,32 (Fig. 2). The dental cast of each participant was prepared using dental tray, Alginate material for making the mould and dental stone was poured for making the cast33. Furthermore, dental measurements were taken on the prepared dental cast of maxillary and mandibular set of teeth by using dial calliper (Fig. 2). Tables 1 and 2 show detailed description of all the anthropometric measurements employed in the study. The obtained measurements were entered in a data sheet for the pre-processing step, which prepares the data for the supervised machine learning models.

Model construction

The following supervised regression-based predictive machine learning algorithms for present study were used: Support Vector Regression (SVR), Random Forest Regression (RFR), Decision Tree Regression (DTR) and Linear Regression (LR)34. The Grid Search method was employed to optimise the model’s performance and determine the best hyperparameter combination. This method involves systematically evaluating the predefined combinations of hyperparameters that influence the performance of a model. The validation performance of each model was calculated using a 10-fold cross validation in a combination of Grid Search method. The ‘scikit-learn’ library functions and other libraries such as Pandas, Matplotlib, NumPy in the Python programming language have been used for the analysis.

Background of machine learning models

Four different algorithms were used in the present study to achieve the best results. These algorithms provide wide range of categories, including kernel-based regression and in contrast linear regression, in order to find out non-linear as well as linear relationship between the independent and dependent variables.

i) Support vector regression

Support vector Regression (SVR) works in the similar principal like support vector machine (SVM) for regression tasks or to predict continuous-valued functio35. The goal of the SVR is to identify the support vectors, place the hyperplane and defined the margin. The mathematical equation for the SVR hyperplane is:

$$\text{f(x)}\,=\,\text{w.x} + \text{b}.$$

where:

  1. -

    w: the weight vector that defines the orientation of the hyperplane.

  2. -

    x: The input features.

  3. -

    b: The bias terms that adjust the hyperplane position.

ii) Decision tree regression

A machine learning method called decision tree regression (DTR) predicts continuous numerical values using a structure like a tree36,37. Each feature represented as leaf node and the output of the leaf node is the mean or median of target value, and this is how decision tree predicts the target output on the basis of input features.

$$\:\text{L}\left(\text{y},\text{f}\left(\text{x}\right)\right)={\sum\:}_{i=1}^{n}{\left({\text{y}}_{i}-\text{f}\left({\text{x}}_{i}\right)\right)}^{2}$$

where:

  1. -

    y: vector of target values.

  2. -

    f(x): predicted value of x.

  3. -

    n: number of training examples.

iii) Random forest regression

Random forest regression (RFR) is an ensemble supervised machine learning model which forms by the combination of decision trees for regression tasks36,37. It contains combination of decision tree and the output of the final model is the combination of the results given by all the decision trees. The mathematical equation for random forest regression is:

(x).

$$\:\text{f}\left(\text{x}\right)=\text{(}\frac{1}{N})\:*{\sum\:}_{i=0}^{n}{T}_{j}$$

where:

  1. -

    f(x): predicted value.

  2. -

    Tj(x): prediction of jth decision tree.

  3. -

    N: total number of decision trees.

iv) Linear regression

This is one of the simplest algorithms of machine learning which finds the correlation between the dependent and independent variables. The linear regression uses a best-fit straight line through a collection of data points to determine a linear connection between a dependent variable and one or more independent variables38.

                                                                  y = β1 (x1) + β2 (x2) +…. + βn (xn).

where:

  1. -

    y: predicted value.

  2. -

    β1: weight 1.

  3. -

    β2: weight 2.

  4. -

    βn: weight at nth number.

  5. -

    x1: Feature 1.

  6. -

    x2: Feature 2.

  7. -

    xn: nth feature.

Hyperparameters for machine learning models

The hyperparameters of each algorithm are shown in the Table 3. These are the hyperparameters that are best tuned after Grid search method to achieve the best performance of the algorithms.

Table 1 Description of anthropometric measurements of face employed in the study (taken directly on the face of participants using spreading and sliding callipers).
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Table 2 Description of anthropometric measurements of teeth and jaw employed in the study (taken on dental cast using a dial calliper).
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Table 3 Tuned hyperparameters of the machine learning (ML) models.
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Data pre-processing or data cleaning

Data pre-processing is a technique for converting the raw dataset into a clean dataset to avoid biasness in the predictions. It involves the process such as checking and removing missing values, normalizing and scales the data, eliminates duplicate values and handling the outlier. The present dataset for the study is a type of primary dataset, therefore the chances of missing and duplicate values are less. However, the data was normalized using standardization technique before training and testing the models using Scikit library. After the cleaning of dataset, the dataset was split into training and testing set with the ratio of 80:20, respectively. This division of dataset was performed using the ‘train_test_split’ function from the ‘sklearn.model_selection’ library.

Evaluation methods of predictive models

Various evaluation criteria were used to assess the performance of each predictive model. The general parameters for evaluating the performance of regression-based models are Mean Square Error (MSE), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE)39,40 along with the accuracy in percentage.

Results

The ML models were trained on teeth and jaw measurements (independent variables or features) to predict the facial measurements (dependent variables or targets). Each model is predicting multiple targets (measurements of face) from the similar features (measurements of teeth), which shows multi-target regression approach. After getting the tuned hyperparameters using Grid search methods, the performance of model was evaluated.

Evaluating the performance of ML models

The results show that models are predicting the facial dimensions with very less error and hence more accuracy. The MSE, RMSE, MAE and the accuracy of the model are shown in Table 4. Nasal width (Al-Al), Inter-pupillary distance (Pu-Pu), Inner-canthi distance (Ic-Ic), outer canthi distance (Oc-Oc) and Inter-commissural distance (Ch-Ch) show a small error of prediction (Fig. 1). A small error of prediction means better accuracy and reliability of the model.

Fig. 1
Fig. 1
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Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE) depicting the performance of each model; Support Vector Regression (SVR), Random Forest Regression (RFR), Decision Tree Regression (DTR) and Linear Regression (LR), for the prediction of facial measurement targets; Minimum frontal width (Ft-Ft), Maximum facial width (Zy-Zy), Mandibular width (Go-Go), Inner-canthal distance (Ic-Ic), Outer –canthal distance (Oc-Oc), Nasal width (Al-Al), Inter-commissural distance (Ch-Ch), Interpupillary distance (Pu-Pu).

Table 4 Evaluating the performance of ML models for predicting the facial dimensions from teeth measurements.
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Comparative analysis of ML models

Figure 2 presents a comparative analysis of four predictive models; (SVR), (RFR), (DTR), and (LR)—in estimating facial dimensions. Among these models, LR and SVR exhibit the best performance, achieving cumulative prediction errors below 0.60. RFR follows with a satisfactory performance, recording a cumulative error of approximately 0.70. In contrast, DTR demonstrates the poorest predictive accuracy, with a cumulative error exceeding 0.80.

Fig. 2
Fig. 2
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Illustrating the comparison among the performances of ML models employed in the study; Support Vector Regression (SVR), Random Forest Regression (RFR), Decision Tree Regression (DTR) and Linear Regression (LR).

Feature importance for the prediction of facial measurements

It is crucial to identify which parameters—maxillary or mandibular—contribute more significantly to the prediction of facial dimensions. Figure 3 indicates that for all the machine learning models, the maxillary parameters play a more dominant role in prediction compared to the mandibular measurements. Among the maxillary parameters, the maxillary inter-molar distance (Max. I-M D) has the greatest predictive influence, followed by the maxillary inter-canine distance (Max. I-C D) and the maxillary inter-premolar distance (Max. I-P D). In contrast, among the mandibular parameters, the crown diameter of the first right molar (Man. Crown Diameter) shows the highest contribution to prediction, followed by the mandibular inter-molar distance (Man. I-M D) and the mandibular dental arch length (Man. DAL).

Fig. 3
Fig. 3
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Illustration of the importance of features (dental measurements) and their influence on the prediction of facial dimensions.

Facial reconstruction in practical situations

An additional experiment was conducted using the trained Linear Regression (LR) model to evaluate its predictive capability on an unseen dataset. The teeth and jaw measurements of an unknown individual were provided to the trained model, which then predicted the corresponding facial dimensions. The prediction was exclusively performed using the LR model due to its superior performance compared to other models in this study. A comparison between the actual facial measurements and the predicted values is presented in Table 5. The predicted landmarks show minimal deviation from the actual landmarks, demonstrating the high accuracy and reliability of the model in prediction of facial dimensions (Fig. 4).

Fig. 4
Fig. 4
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Experiment of LR model showing the deviation in facial dimensions from the actual dimensions of face: (A) depicting the placement of actual landmarks with actual measurements of face; (B) depicting the placement of predicted landmarks and predicted measurements of face.

Table 5 Experiment on linear regression (LR) model by comparing actual facial measurements with predicted facial measurements showing error of prediction.
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Furthermore, the model accurately predicted five key facial measurements—nasal width (Al-Al), inter-pupillary distance (Pu-Pu), inner canthi distance (Ic-Ic), outer canthi distance (Oc-Oc), and inter-commissural distance (Ch-Ch)—with a small prediction error, indicating high precision. Notably, all these measurements are located around the mid-sagittal plane (Fig. 4). These parameters may serve as valuable markers for aligning the mid-sagittal plane in practical forensic facial reconstruction scenarios.

Discussion

Facial reconstruction has always been one of the final steps in identifying human remains. Teeth, on the other hand, are resilient enough41 to withstand harsh conditions such as decomposition and disaster; thus, measurements of the teeth and jaw can be used to predict facial dimensions, which can then be used for facial reconstruction. In the current study, teeth and jaw measurements (Fig. 5) predict facial measurements (Fig. 6) with a smaller error and higher accuracy. The findings show that the five dimensions of the face were predicted with a small error, including nasal width. This emphasises the importance of teeth and jaw for nose reconstruction. For instance, Singh and Purkait42 predicted different parts of the soft nose based on the bony structure of the nose on the skull. They stated that minor differences in the shape and size of the nose can alter the overall appearance of the face. They discovered a significant relationship between the bony and soft tissues of the nose especially the nasal width i.e. Alare-Alare distance42. In the current study, all five measurements predicted with a small error and are located near the mid-sagittal plane of the face. These measurements can be used to predict the alignment of the mid-sagittal plane, which is considered an important part of forensic facial reconstruction. Furthermore, it can be useful for dental treatments such as orthodontic treatments, prosthetic designing to adjust the alignment of teeth by correlating the mid-sagittal plane with tooth dimensions, as this is the main plane for symmetry of the face21,43.

Fig. 5
Fig. 5
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Anthropometric measurements of teeth and jaw; Landmark abbreviation: CWCI- Combined width of central incisors; I-I D- Inter-incisor distance; I-C D- Inter-canine distance; I-P D- Inter-premolar distance; I-M D- Inter-molar distance; DAL- Dental arch length.

Fig. 6
Fig. 6
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Anthropometric measurements of face; landmarks abbreviations: ft – frontotemporal; Ic- Inner- Canthi; Oc- Outer- canthi; Pu- Pupil; Zy- Zygion; Al- Alare; Ch- Cheilion; Go- Gonion.

Nevertheless, numerous dental studies show a strong correlation between facial measurements and measurements of the teeth, dental arch, and jaw. For instance, Chunhabundit et al.20 demonstrate a significant correlation between facial measurements such as interpupillary width, inter lateral canthal width, inter commissural width, and bizygomatic width with dental measurements20. In addition, Pisulkar et al.19 also determines the correlation between the mesiodistal width of anterior maxillary teeth, intercanthal distance, inter-alar distance, and inter-commissural distance. The results show that the width of the maxillary anterior teeth and the inter-canthal gap showed a strong positive correlation; the inter-alar difference and the mesiodistal width of anterior teeth showed a moderately positive correlation; and the estimated inter-commissural width and the mesiodistal width of anterior teeth showed a strong positive correlation19. Additionally, Chitara and Krishan44 demonstrate how dental dimensions can be used to predict facial geometry and shape. Their results demonstrate the importance of these metrics in forensic facial reconstruction by showing a relationship between tooth measurements and the general form and structure of the face. Similarly, findings of the present study indicate the highest contribution of maxillary inter-molar distance in the prediction of facial measurements.

The customised ML models in the present study achieved 90–94% accuracy of prediction of facial dimensions from dental and jaw parameters. This promising range of accuracy make these models as reliable predictors in real world forensic applications. For instance, teeth and jaw measurements obtained during an investigation can be input in the model to generate corresponding facial measurements. These outputs of facial measurements can be utilized by forensic artists or facial reconstruction experts to reconstruct the face of an unidentified individual with greater precision. The maxillary dental parameters are more reliable and performed better in the facial reconstruction. Maxilla is also known as the immovable upper jaw and is considered as the most important part of the mid face and craniofacial skeleton. However, mandible is a lower jaw and a movable part of the facial skeleton45. Expressly, the maxilla has a close allometric relationship with other parts of the craniofacial skeleton however; the mandible forms the lower jaw and is a part of the lower face. Therefore, in the present study, the maxillary dental parameters performed well in the reconstruction of the facial dimensions and obtained greater accuracy of prediction.

It is also pertinent to mention here that out of all the maxillary and dental parameters, maxillary inter molar distance (Max. I-M D) is the best parameter for prediction in the present study. This may be attributed to the fact that it gives one of the largest width measurements of the dental arch/inner jaw and hence strongly correlated to the facial dimensions.

In addition to all this, ML models are getting popularity for their large range of accuracy and reliability for analysing the data sets. In present study, prominent models of ML were utilized which are performing well for the present task. For instance, a recent study by Ramachandran et al.46 employs the machine learning model to predict the width of maxillary central incisor from anthropological measurements of face. The inter commissural (ICW), inter alar (IAW), intermedial-canthus (MCW), inter lateral-canthus (LCW), and interpupillary (IPW) widths are used to determine the width of maxillary central incisors (CW). In their study, Random Forest model showed the best performance for all the cases, with an accuracy of 96% which represents the percentage of the correct predictions46. Similarly in the present study, LR and SVR are providing the most promising results. Hence, LR models also have been used to perform an experiment to predict facial dimensions from unknown measurements of teeth. LR might performing well in the present study to show the linear relationships between teeth/jaw measurements and facial measurements, while other models may perform well with non-linear datasets.

The findings of present study highlight the potential of using dental parameters for facial reconstruction, with minimal deviation of reconstructed landmarks from their actual anatomical positions (Fig. 4). In real-world forensic applications, minor differences in facial reconstructions are often unavoidable. Even in living humans, minor variations in facial contours can occur as a result of natural factors such as swelling or bloating. Similarly, when a forensic sketch artist creates a facial representation based on verbal descriptions, minor deviations from the actual facial features are common47. These subtle differences highlight the inherent complexities of accurately recreating facial features, whether through artistic interpretation or scientific methods. In addition, the deviation of predicted facial landmarks from the actual anatomical landmarks, demonstrating the feasibility of reconstructing facial structures based on dental measurements using AI models. This reconstructed facial representation can subsequently be utilized for identity verification by matching it against existing facial databases, following a methodology akin to Facial Recognition Technology48,49.

The promising results of present study underline the importance of teeth, dental arch and jaw dimensions in facial reconstruction, particular in scenarios such as mass disasters and disaster victim identification, where usually the dental remains are presented for forensic identification. However, a notable limitation of this study is the relatively small dataset used and confined geographical location. Future research should focus on training similar models on larger datasets and employing participants of wider age range and more diverse geographical locations to improve accuracy and reliability. With improved accuracy, these models have the potential to be directly implemented in the case work in field of forensic science, providing a reliable and efficient tool for identifying individuals in challenging situations.

Conclusion

This study suggests that machine learning models (SVR, RFR, DTR, and LR) can be used to predict facial dimensions based on measurements of the teeth, dental arch, and jawbone. The present approach can be combined with traditional methods of forensic facial reconstruction to improve precision and accuracy. The ML models provided facial dimensions with an accuracy range of 90–94% and at relatively low prediction error. Although, maxillary inter molar distance (Max. I-M D) is the best predictor; however, for calculation of the facial dimensions in real cases and practical scenarios, all the parameters evaluated in the present study should be taken into consideration. In future, similar models can be trained on large datasets to improve their real-time applicability in the field of forensic science. If teeth and jaw dimensions of an unknown individual are recovered from a crime scene, the trained model can predict the respective facial dimensions. These predictions can support forensic experts in reconstructing the individual’s face for identification purposes. Furthermore, our findings emphasize the importance of incorporating machine learning knowledge into forensic anthropological assessments in order to improve accuracy and reliability in a shorter amount of time for real time applications.