This study selected a total of 3,790 panoramic dental radiographs (orthopantomograms) from children and adolescents aged 5–23 years who visited the Department of Dentistry at the Affiliated People's Hospital of the Medical University between June 2021 and December 2024. Among them, 1,693 were male, and 2,097 were female.

All imaging data used in this study were obtained through retrospective analysis and were not associated with any commercial interests. During the research process, the images were anonymized, with only gender, imaging date, and birthdate recorded to ensure the protection of personal privacy. According to the current Ethical Review Measures for Biomedical Research Involving Humans, this study is exempt from the requirement of obtaining informed consent.

Inclusion Criteria: (1) The sample consists of Han Chinese individuals who were born and have lived long-term in the North China region to ensure consistency in regional and ethnic characteristics. (2) The collected panoramic images must be clear and free of blurring, with the width difference between the left and right first permanent molar crowns not exceeding 20% to ensure measurement accuracy. (3) The sample must have a complete dentition with normal dental growth and development, without cavities, periodontal disease, dental trauma, or congenital or acquired tooth loss.

Exclusion Criteria: (1) Diseases affecting normal jawbone development, such as temporomandibular joint ankylosis, cleft lip and palate, jaw deformities, or jaw tumors. (2) History of maxillofacial trauma. (3) Previous orthodontic treatment. (4) Abnormal development of the third molar, such as short roots, malformed roots, or impacted third molars. (5) Individuals with chronic diseases, systemic conditions, genetic disorders, or abnormal physical development.

The distribution of gender characteristics and age characteristics of the samples involved in this study are shown in Tables 1, 2, respectively.

In the sample of this study, males accounted for 44.67% and females accounted for 55.33%, indicating a relatively balanced gender ratio with little deviation. However, considering the significant differences in tooth age development between genders, gender factors have a strong impact on tooth age estimation. Therefore, when constructing a dental age prediction model, it is necessary to perform gender stratified analysis on the samples to improve the model's prediction accuracy and generalization ability.

The age distribution of the sample shows a clear concentration trend, especially during the tooth replacement period (6–12 years old), with a sample proportion of as high as 60.26% in this age group. At this stage, the mineralization, eruption, and root development characteristics of teeth are relatively active and significant, which is a critical period for tooth age assessment research. In contrast, the proportion of samples in the age groups of under 5 years old (4.46%) and 18 years old and above (11.06%) is relatively low, which may be related to the lower frequency of individual visits or atypical and unrepresentative dental development characteristics in these stages.

To maximize the use of image information from panoramic radiographs, irrelevant elements were first removed prior to analysis, ensuring that the images processed by the convolutional neural networks (CNNs) contained only the dental arch region, as illustrated in Figure 1.

The fully automated dental age estimation method involves the following steps: First, OpenCV image processing tools were used to locate and label the oral region in the radiographs (13). Second, various convolutional neural network models were employed to train on the panoramic dental images for age prediction. Finally, the trained CNN models were evaluated on a test set to assess their performance and to perform dental age estimation, as shown in the Figure 2.

Automatic dental age estimation is a fine-grained visual regression task, made particularly challenging by the subtle inherent differences between individual teeth. Unlike traditional regression problems, this task requires precise recognition of fine visual cues. Motivated by the hypothesis that incorporating segmentation tasks can enhance regression performance, this study first compared various tooth segmentation methods and ultimately employed the U-Net architecture for tooth segmentation (14). Using the U-Net model, segmentation masks were automatically generated for the teeth in panoramic radiographs. These masks were then manually reviewed to ensure that they accurately captured the complete tooth regions, as shown in Figure 3. After verifying the masks, various deep learning models were applied to perform age prediction based on the segmented images. The models used include LeNet-5, AlexNet, VGG-16, ResNet-50, Swin Transformer, and ConvNeXt (15).

The following subsection will introduce the specific architectures of these neural network models.

To expand the dataset and enhance model robustness, data augmentation techniques such as image rotation and flipping were applied to the original images. Before validation, this study applied data augmentation techniques (horizontal flip, vertical flip, rotation, and Gaussian blur.) to expand the original set of 3,790 images to 18,950 images (22, 23). These augmented images were then split into training, validation, and test sets in a 7:2:1 ratio. As a result, the dataset contained 13,265 training images, 3,790 test images, and 1,895 validation images. All experiments were conducted on a workstation equipped with an NVIDIA RTX 3090 (32GB) GPU running CUDA 11.4. The models were developed using Python 3.11 and PyTorch v1.12.1.

To prevent data leakage, all augmented versions of a given original image were grouped and assigned to the same dataset split. Stratification and splitting were performed prior to data augmentation, ensuring no overlap of source images across training, validation, and test sets. Additionally, when applicable, splits were made at the patient level to avoid intra-subject information leakage.

During model evaluation, this study calculated Accuracy, Mean Absolute Error (MAE), and the Coefficient of Determination (R²). By comparing the performance metrics of different models, the most optimal model for dental age estimation was selected. The calculation formulas for different performance metrics are shown in Equations 1–3:(1)MAE=1n∑i=1n|−y^i|(2)R2=1−1n∑i=1n(yi−y^i)2/∑i=1n(yi−y¯)2(3)Accuracy=TPTP+FPIn the above formula, yi is the true age of the i-th sample, y^i is the predicted age of the i-th sample, yi is the average of the true ages of the samples, and n is the sample size. TP is the correct sample for prediction (the residual between the predicted value and the true value within 1 year old). FP is the wrong sample for prediction. This research discretized continuous age values into 1-year bins to assess performance from a clinically relevant perspective. In dental age estimation, a prediction within ±1 year of the actual age is generally acceptable in practice. Therefore, we defined predictions within this range as “correct” and used this criterion to calculate an accuracy metric.

By analyzing the data samples collected in this study, we observed a class imbalance phenomenon, with most samples concentrated in the 6–18 age range. Therefore, when designing the loss functions for the various network models, it is important to consider not only model performance but also the issue of class imbalance. In this study, we followed approaches reported in the literature and adopted the balanced MSE loss as the loss function for all network models. The formula for the loss function is shown in Equation 4.(4)L=1N∑i=1N(yi−y^i)2⋅wiHere, wi represents the weight assigned to each class, which is used to suppress the influence of dominant classes and increase the relative importance of minority classes. Specifically, wi is defined as the inverse of the frequency fi of the class to which sample iii belongs, i.e., wi=1/fi.

Hyperparameters are parameters that must be set before training a deep learning model. They control the model's architecture and learning process, such as the learning rate, optimizer, and weight decay. In this study, the optimal hyperparameters for each network model are listed in Table 3.

Tooth segmentation can significantly enhance the accuracy and robustness of dental age estimation by isolating individual teeth or tooth structures—from irrelevant background information. In this study, incorporating a segmentation step prior to age estimation helped the model learn more discriminative patterns, ultimately contributing to improved regression performance. This study first compared various tooth segmentation methods, including dice coefficients, segmentation time. The performance of different segmentation methods in tooth segmentation as shown in Table 4.

The DICE coefficient is an indicator used to measure the effectiveness of image segmentation, with higher values indicating better segmentation performance. As seen in Table 4, U-Net performs significantly better than the other methods in terms of segmentation quality. Although its segmentation time is slightly longer (4.93 s), overall, it provides the best performance. Therefore, this research ultimately employed the U-Net architecture for tooth segmentation due to its effectiveness and robustness.

To evaluate the effectiveness of convolutional neural networks (CNNs) in dental age estimation, the study first compared the performance of different CNN architectures based on various metrics, as shown in Table 5.

Table 5 shows the performance metrics of six different network models in the dental age estimation task, including Mean Absolute Error, Coefficient of Determination, and Accuracy. Lower MAE values, higher R² values, and higher accuracy indicate better model performance (24).

The loss function curve is a vital tool for monitoring the training dynamics of deep learning models (25). It illustrates how the loss value changes over training epochs, enabling researchers to determine whether the model is converging, overfitting, or underfitting.

In this study, we compared the loss curves of multiple convolutional neural network architectures throughout the training process, as shown in Figure 4. By observing the trend and stability of these curves, we can assess each model's learning efficiency and generalization capability. A well-performing model typically demonstrates a smooth and steadily declining loss curve on the training set, accompanied by a similarly stable or slightly fluctuating validation loss curve.

Figure 4A shows the loss function curve of the LeNet-5 model during training. Both the training loss and validation loss exhibit a sharp decline during the initial 1–2 epochs, dropping rapidly from a high starting point of approximately 60–70 down to a range of 10–15. However, after this initial descent, the loss values do not continue to decrease significantly. Figure 4B illustrates the loss function curve of the AlexNet model. As shown in the figure, the validation loss initially decreases in tandem with the training loss and reaches a relatively low point around epochs 2–3. Afterward, it experiences slight fluctuations but gradually stabilizes at a level close to the training loss. This suggests that no significant overfitting or divergence occurred in the later stages of training, indicating relatively stable learning behavior. Figure 4C displays the loss curve of VGG-16. In this case, the training loss remains slightly lower than the validation loss throughout the training process. However, the gap between the two curves is not substantial, suggesting that VGG-16 maintains a balanced generalization ability. This implies that the model does not suffer from pronounced overfitting or instability during training, and it performs consistently across both training and validation datasets. Figure 4D shows the loss trajectory of ResNet-50. During the early training phase, both the training and validation losses drop rapidly from an initial high value (approximately 4.75) to a range between 2.5 and 3.0. This indicates that the model quickly learns low-level or general image features. In the later training stages, the training loss remains slightly lower than the validation loss, but the margin is narrow, which reflects good model fitting and generalization performance on both datasets. Figure 4E presents the loss curve of the Swin Transformer model. Compared to other deep networks such as ResNet-50, the Swin Transformer exhibits a relatively high validation loss throughout training and fails to converge to a lower and stable value. This trend suggests that the model faces challenges in learning effectively from the current dataset, potentially due to the limited sample size, insufficient tuning, or the architecture being less compatible with the specific characteristics of panoramic dental images. Figure 4F illustrates the loss curve of ConvNeXt. In this case, the training loss consistently stays slightly below the validation loss, with no pronounced divergence. This pattern indicates that the model does not exhibit severe overfitting or underfitting in the later training epochs. The overall trend suggests that ConvNeXt achieves a well-balanced fit between the training and validation sets, demonstrating strong learning stability and generalization capability.

To evaluate the distribution of prediction errors and the reliability of the regression model, this study employed two key diagnostic tools: the Standardized Residual Histogram (SRH) and the normal P–P plot of standardized residuals (26).

The standardized residual histogram visualizes the distribution of residuals. A bell-shaped, symmetric histogram indicates that residuals are approximately normally distributed, which supports one of the core assumptions in linear regression models. A skewed or multimodal distribution, however, might suggest model misspecification, outliers, or non-linearity in the data.

The normal probability–probability (P–P) plot of standardized residuals further tests the normality assumption by plotting the cumulative distribution of the observed standardized residuals against a theoretical normal distribution. If the residuals are normally distributed, the points on the P–P plot should fall closely along the 45-degree reference line.

The Standardized Residual Histogram and Normal P-P Plot of Standardized Residual for different models are shown in the Figure 5.

As shown in Figure 5, the residuals from all deep learning models approximately follow a normal distribution. This is evidenced by the standardized residual histograms, which exhibit a bell-shaped curve, and the normal P-P plots, in which most of the data points lie close to the diagonal reference line. These visual assessments suggest that the residuals satisfy the assumption of normality. Furthermore, based on the residual statistics, although a few outliers are observed, the overall standard deviation of the residuals remains relatively small. This implies that prediction errors are generally limited in magnitude, and the deep learning models are not significantly biased. Taken together, the conformity of the residuals to a normal distribution, the low dispersion, and the limited number of outliers validate the appropriateness and robustness of the deep learning models for dental age estimation tasks. These results support the conclusion that the models exhibit good predictive performance and reliability on the given dataset.

The optimal age estimation models for the total sample, as well as for the female and male subgroups, were identified. The performance evaluation across different age ranges is detailed in Tables 5–7. The residual value in the Tables 6–8 is the residual between the true value and the predicted value.

According to Tables 6–8, it is evident that the optimal age estimation models demonstrate varying levels of accuracy across different age groups. The models exhibit relatively high accuracy in the adolescent population aged between 5.00 and 15.99 years, with the mean absolute error approaching approximately 1 year. However, for individuals aged 16 years and above, the accuracy of age estimation gradually declines. Specifically, the MAE values for the total sample in the 4.00–11.99 age group are all under 1 year, indicating strong performance. Similarly, the MAE values for the female subgroup in the 6.00–9.99 and 11.00–11.99 age intervals are below 1 year. In the male subgroup, the model achieved an MAE close to 1 year across the 5.00–15.99 age range.

These findings suggest that combining machine learning techniques with Demirjian's method yields promising results in estimating dental age among children and adolescents in North China—especially during early and middle childhood, where predictive performance is particularly robust. However, the model's performance significantly declines when applied to individuals over the age of 16.

Based on clinical observations and a review of relevant literature, this performance trend can be attributed to the developmental characteristics of the dentition. The age ranges from 6 to 15 represents a crucial period for dental development, during which the permanent dentition undergoes active eruption and replacement. During this stage, the morphological differentiation of tooth crowns and the calcification of roots follow a relatively consistent and predictable pattern. Imaging features such as dentin deposition and root canal closure undergo continuous and discernible changes, which are well-suited for quantitative feature extraction by machine learning algorithms.

In contrast, after the age of 15, tooth development slows, and growth patterns become increasingly influenced by individual variation, hormonal fluctuations during and after puberty, as well as environmental and pathological factors. These elements introduce greater heterogeneity and irregularity in dental development, making it more challenging for algorithms to learn stable predictive patterns. Consequently, the model's performance in older adolescents and adults is less reliable.

To visually demonstrate the effect, features with shapes of (416, 416, 32) were extracted from the ResNet-50 and ConvNeXt for visualization. The visualization results are shown in Figure 6.

In Figure 6, the left column (A) displays the original panoramic dental images, the column (B) presents the corresponding model-generated attention heatmaps of ResNet-50 and the column (C) presents the attention heatmaps of ConvNeXt. The patients in the first to fourth rows are aged 8, 11, 15, and 20, respectively. As illustrated in Figure 6, the model primarily focuses on the dental arch, capturing key features such as apical closure and occlusal surface wear. In children's patients, particularly those under the age of 10, the ResNet-50 pays closer attention to areas of permanent tooth eruption, root development, and deciduous tooth resorption. Observing from column C, the ConvNeXt focuses on the left posterior teeth and anterior mandible. These visualization results highlight the deep learning models strong biological interpretability and its ability to effectively distinguish age-related dental characteristics.