Automated prediction of hand–wrist maturation stage from lateral cephalometric and panoramic radiographs using a deep learning approach

Abstract

Objectives

This study aimed to predict hand–wrist developmental stages, the most reliable indicator of skeletal maturation, from panoramic radiographs (PRs) and lateral cephalometric radiographs (LCRs) using deep learning and to compare the two methods. The goal was to provide a rapid and objective method for growth assessment in orthodontic planning without additional radiation exposure.

Methods

A total of 3703 patients who underwent hand–wrist radiographs (HWRs), PRs, and LCRs prior to orthodontic treatment were retrospectively analyzed. HWRs were classified according to Björk's 9-stage system and reduced to 5- and 3-group schemes. YOLOv5 was used for automated reference point detection, and the extracted regions were classified using a multimodal deep learning framework. EfficientNet-B0 was used for 9-stage classification, and EfficientNet-B4 was used for 5- and 3-group classifications. Clinical variables (age, gender) were included, and hybrid loss strategies addressed class imbalance while preserving sequential stage relationships. Performance metrics included accuracy, recall, mAP@0.5, balanced accuracy, Cohen's Kappa coefficient, and detailed error analysis; 5-fold cross-validation and ensemble learning were used to improve robustness.

Results

YOLOv5 detected tooth roots in PRs (accuracy 92.5%, recall 93.3%, mAP@0.5 = 0.942) and cervical vertebrae in LCRs (accuracy 98.9%, recall 99.9%, mAP@0.5 = 0.995). In PRs, the standard accuracy in 9-, 5-, and 3-stage classifications was 0.3648, 0.5307, and 0.7520, respectively, while in LCRs, the standard accuracy in 9-, 5-, and 3-stage classifications was 0.4350, 0.6336, and 0.8975, respectively.

Conclusion

Deep learning can reliably automate skeletal maturation assessment across imaging methods and resolutions. Appropriately optimized models provide valuable decision support in orthodontic treatment, increasing efficiency and consistency.

Introduction

In orthodontics, understanding growth and development is of critical importance, as accurate determination of the growth stage in patients undergoing orthodontic treatment directly influences diagnosis, optimal timing, treatment outcomes, and retention protocols. Furthermore, it has been reported that initiating treatment during the appropriate growth period can accelerate tooth movement. Hand–wrist radiographs (HWRs) are widely accepted as a reference method for the assessment of skeletal maturation and growth stage. However, since obtaining HWRs exposes patients to additional radiation, alternative radiological methods have been proposed over time [1]. One of these methods involves predicting the pubertal growth spurt by evaluating cervical vertebral maturation (CVM) on lateral cephalometric radiographs (LCRs). This approach is based on the maturation stages of the second, third, and fourth cervical vertebrae [2]. Since LCRs are routinely acquired in orthodontic practice, the CVM method provides an opportunity to assess skeletal maturation without exposing patients to additional radiation. Nevertheless, concerns regarding the relatively low intra- and interobserver agreement of CVM stage assessment persist. In this context, artificial intelligence (AI)–based decision support systems may contribute to more objective, consistent, and reproducible skeletal maturation evaluation [3–5]. Another method involves evaluating the stages of tooth calcification on panoramic radiographs (PRs). While tooth development is not a direct measure of skeletal maturation, this method is an indirect biological marker [1, 6, 7].

AI is defined as the ability of a machine to simulate intelligent human behavior in order to perform complex tasks, such as problem-solving, object and word recognition, and decision-making [8]. In the field of oral and maxillofacial radiology, AI models have been utilized in numerous applications, including the classification of cysts and tumors [9], automatic localization of cephalometric landmarks [10], mandibular canal localization [11], assessment of anatomical structures [12], tooth identification [13], diagnosis of caries and periodontal diseases [14–16], and evaluation of bone density [17, 18]. AI-driven approaches have the potential to support clinical decision-making by facilitating efficient image analysis, reducing observer-dependent variability, and assisting diagnostic processes. Consequently, they have gained a prominent role in medical imaging [19].

In supervised deep learning models, predictions are based on radiographic patterns learned from reference labels rather than direct biological measurements. Accordingly, the present study investigates whether patterns observed on PRs and LCRs can be associated with hand–wrist maturation stages used as reference labels.

The study aimed to develop a rapid and objective decision-support approach for growth assessment in orthodontic treatment planning without the need for additional radiation exposure. To the authors’ knowledge, this is the first study of its kind in this field.

The hypothesis of this study was that the radiographic patterns observed in PRs and LCRs contain sufficient information for deep learning models to classify hand–wrist maturation stages with clinically acceptable performance, and that there would be differences in diagnostic performance between the two imaging methods.

Materials and methods

Research design and ethics committee approval

This research was designed as a retrospective development and internal validation study of a deep learning model. The study aimed to create an automated decision-support approach for growth assessment in orthodontic treatment planning using routinely acquired LCRs and PRs. The research protocol was prepared in accordance with the principles of the Helsinki Declaration and approved by the Health Sciences Research Ethics Committee (2026/16). All radiographic data used in the study were processed by completely removing personal identifying information (name, protocol number, etc.) to protect patient privacy. Furthermore, the study was reported in accordance with the Checklist for Artificial Intelligence in Medical Imaging guidelines.

Dataset creation and characteristics

Previously acquired pretreatment HWRs, LCRs, and PRs of patients who applied to the Faculty of Dentistry between 2009 and 2025 were retrospectively retrieved from the institutional radiographic archives and reviewed for eligibility. The dataset was constructed from these archived radiographs.

Inclusion and exclusion criteria

Inclusion criteria were defined as individuals being under 18 years of age and the PRs, LCRs, and HWRs having sufficient diagnostic quality and having all three radiographs obtained within the same week as part of the routine pretreatment orthodontic records. Exclusion criteria were a history of trauma in the craniofacial region before PR was taken, having undergone orthodontic treatment, the presence of trauma affecting the hand–wrist or cervical region, the presence of serious craniofacial anomalies, structural defects or loss in cervical vertebrae or tooth roots, and the presence of metal artifacts or motion blur in the images.

Data distribution

Considering the inclusion and exclusion criteria, a total of 3703 individuals with an average age of 157.4 months were included in the study: 1721 women with an average age of 152.6 months and 1982 men with an average age of 161.6 months. (The ages of the included individuals were recorded in months for greater reliability.)

A total of 11 109 HWRs, LCRs, and PRs from 3703 different individuals were included in the study. HWRs were used in hand–wrist staging, while PRs and LCRs were used to predict the wrist maturation stage using deep learning methods. HWRs were obtained in anteroposterior projection using a Planmeca Proline XC device by the same radiology technician, in accordance with standard positioning rules. LCRs were taken with the same device. With metal accessories removed, patients were positioned upright with the midsagittal plane perpendicular to the floor and the Frankfurt horizontal plane parallel to the floor. Images were obtained with cephalostat stabilization to maintain a natural head position and centric occlusion. PRs were obtained using Orthopantomograph OP200 D and Planmeca Proline XC devices according to standard protocol, ensuring the appropriate head position and removing metal accessories; exposure parameters were automatically adjusted according to the patient. Chronological age was calculated in months based on the panoramic imaging date. Low-dose protocols were used in all imaging according to the ALADA principle.

PRs and LCRs were classified into nine classes according to Björk's classification [20] of HWRs taken in the week they were shot:

• PP2: The epiphysis and diaphysis of the second proximal phalanx are equal in width.

• MP3: The epiphysis and diaphysis of the third middle phalanx are equal in width.

• PISI/H1/R: The pisiform bone begins to appear; the hook of the hamate becomes more distinct; epiphysis–diaphysis equality is observed in the radius.

• S-H2: The sesamoid bone becomes visible; the hook of the hamate is clearly distinguishable.

• MP3 CAP: The epiphysis of the third middle phalanx begins to cap the diaphysis.

• DP3U: Fusion of the epiphysis and diaphysis of the third distal phalanx has occurred.

• PP3U: Fusion of the epiphysis and diaphysis of the third proximal phalanx has occurred.

• MP3U: Fusion of the epiphysis and diaphysis of the third middle phalanx has occurred.

• RU: Fusion of the epiphysis and diaphysis of the radius has occurred.

Classifications were performed by one researcher. All data were checked and validated by a second researcher to minimize potential errors in the evaluation process. To assess intraobserver agreement, samples representing 20% of the dataset were reclassified by the same researcher 2 months after the initial evaluation. The agreement between the two resulting evaluations was analyzed using the weighted Cohen's Kappa (κ) test, given the ordinal categorical nature of the data.

To see if high accuracy can be achieved by reducing the number of classes in the deep learning method, Björk's 9-stage phase [20] was later reduced to 5- and 3-group classifications [21]. Previous studies have stated that reducing from 9 stages to 5 stages does not lead to significant data loss. The 5-group classification is as follows:

• Group A: PP2, MP3, and PISI/H1/R stages

• Group B: S-H2 stage

• Group C: MP3 CAP stage

• Group D: DP3U and PP3U stages

• Group E: MP3U and RU stages

When Björk's [20] 9 stages are reduced to 3 groups, these 3 stages are classified as pregrowth peak (Group 1), growth peak (Group 2), and postgrowth peak (Group 3) periods (Table 3). This classification method was previously used by Tentaş et al. [22] (prepeak, peak, and postpeak). The 3-group classification is as follows:

Table 3.

Classification-based performance distribution in panoramic radiographs.

Model	Class/group	Precision	Recall	F1 score	Number of samples (n)
9-Stage	PP2	0.50	0.56	0.53	25
	MP3	0.00	0.00	0.00	22
	PISI	0.53	0.55	0.54	67
	S	0.26	0.09	0.13	91
	MP3 CAP	0.23	0.41	0.30	68
	DP3U	0.14	0.26	0.18	39
	PP3U	0.11	0.05	0.07	38
	MP3U	0.35	0.38	0.37	60
	RU	0.74	0.72	0.73	78
	Weighted average	0.36	0.36	0.35	488
5-Group	Group A	0.87	0.68	0.76	114
	Group B	0.42	0.20	0.27	92
	Group C	0.23	0.41	0.30	68
	Group D	0.33	0.47	0.39	76
	Group E	0.78	0.72	0.75	138
	Weighted average	0.59	0.53	0.54	488
3-Group	Group 1	0.84	0.78	0.81	206
	Group 2	0.35	0.28	0.31	68
	Group 3	0.77	0.87	0.82	214
	Weighted average	0.74	0.75	0.74	488

• Group 1: Includes PP2, MP3, PISI/H1/R, and S-H2 stages

• Group 2: Includes MP3 CAP stage

• Group 3: Includes DP3U, PP3U, MP3U, and RU stages

Automated landmark detection and image preprocessing

A subset of 200 reference radiographs was randomly selected to establish a robust training set. We manually annotated the anatomical regions of interest (ROIs) using LabelImg software to generate bounding boxes in XML format. In LCRs, separate classes were defined for the C2, C3, and C4 cervical vertebrae (Fig. 1). We prioritized these landmarks because CVM stages are highly reliable indicators of skeletal maturity and correlate with mandibular growth spurts [23].

Figure 1.

Manual annotation of cervical vertebrae (C2, C3, and C4) on a lateral cephalometric radiograph.

In PRs, the mandibular left canine, first premolar, and the second and third molars were localized (Fig. 2). To prevent label overlap, the second and third molars were grouped within a single bounding box. While the feature extraction was informed by the Demirjian method [24], we deliberately focused on teeth with gradual developmental trajectories (canines and molars) to enhance the model's sensitivity to age-specific patterns [25].

Figure 2.

Manual annotation of mandibular left canine, first premolar, and grouped second/third molars on a panoramic radiograph.

The YOLOv5 architecture was implemented to automate the localization of diagnostic landmarks. While newer iterations of the YOLO family exist, we selected the v5 model due to its extensive validation in medical imaging literature, superior stability, and optimal balance between inference speed and localization precision [26, 27]. This architecture has consistently demonstrated high performance in detecting complex anatomical structures in dental and skeletal radiographs, providing a robust foundation for subsequent classification [28]. Specifically, we deployed the YOLOv5l (large) architecture, initializing the model with pretrained weights from the COCO dataset, followed by fine-tuning on our radiographic dataset to overcome the challenges associated with limited annotated medical data. The pipeline was designed to automatically isolate the cervical vertebrae and specific dental regions, effectively eliminating irrelevant craniofacial background noise.

To mitigate the risk of overfitting and improve the model's generalization capacity, advanced augmentation strategies integrated within YOLOv5 were applied. The Mosaic technique was utilized to combine four training images at random scales, while MixUp augmentation was employed to blend images and labels, increasing resilience to class transition uncertainties. Additionally, random photometric distortions (HSV space) and perspective transformations were incorporated to maximize the model's tolerance to radiographic noise and anatomical variations.

Training was conducted at a resolution of 640 × 640 pixels for a maximum of 1000 epochs. To prevent overfitting and ensure optimal convergence, we utilized an early stopping mechanism that terminated the process if no improvement was observed in the validation loss. For optimization, the stochastic gradient descent algorithm was selected, while the complete intersection over union loss function was used for bounding box regression.

Following the training and deployment of this automated landmark detection pipeline, we established strict quality control criteria for the final dataset. Successful automated detection and extraction of all necessary anatomical patches were required for a given patient. Due to the inherent structural complexity, overlapping shadows, and morphological variations present in PRs, the algorithm experienced a higher rejection rate (i.e. failure to locate all required patches) compared with LCRs, which present a more standardized anatomical view. Consequently, images with incomplete patch extractions were automatically excluded to prevent feeding noisy or incomplete data into the subsequent classification models. This technical preprocessing step directly led to the observed variance in the final sample sizes between the panoramic and cephalometric datasets.

ROI localization performance and patch generation

The performance of the YOLOv5 model in detecting anatomical ROIs was evaluated using a comprehensive suite of metrics to ensure both spatial precision and classification reliability. We utilized the intersection over union metric to validate detections, setting a threshold of 0.50 to categorize predictions as true positive or false positive [29]. To provide a rigorous assessment, we analyzed the model through precision and recall values, which collectively measured its ability to minimize false identifications while ensuring no critical anatomical structures were missed. The primary benchmark for overall proficiency was the mean average precision (mAP@0.5), representing the area under the precision–recall curve across all targeted classes. Achieving a mAP@0.5 exceeding 0.95 confirmed the model's high accuracy in both precise localization and correct identification of vertebrae and dental landmarks.

Following the detection phase, an automated pipeline was implemented to crop specific anatomical patches for each patient based on the coordinates generated by YOLOv5. To ensure consistency across the dataset and optimize gradient flow, all extracted patches were resized to a fixed resolution of 224 × 224 pixels and subjected to standard normalization procedures. Furthermore, to enhance the model's robustness against variations in image quality and inherent distortions in PRs, we strategically integrated Gaussian blur and random affine transformations into the preprocessing workflow. This standardized data formed the input for the subsequent deep learning-based maturation classification network.

Multimodal hybrid architecture and training strategy

The standardized anatomical patches were processed using a multimodal deep learning framework designed to integrate both morphological and clinical features. We selected the EfficientNet family as the core backbone for visual feature extraction due to its optimal balance between parameter efficiency and accuracy [30]. The architecture was adapted based on task complexity, utilizing EfficientNet-B4 for the 3- and 5-group models and EfficientNet-B0 for the 9-stage model to mitigate overfitting. Rather than stacking the three distinct patches into a multichannel input, a Siamese-style “Shared Weights” architecture was implemented. Each of the three anatomical patches was processed independently through the same EfficientNet backbone. This unified weight mechanism forces the network to learn generalized radiological patterns across all vertebrae, preventing overfitting while significantly reducing the computational footprint.

In addition to visual data, clinical parameters including age and sex were processed through a specialized subnetwork termed “Meta-Net.” Sex data was binary encoded, while age was normalized on a 240-month developmental scale. These clinical vectors ($F_m$) were then integrated with the visual feature vectors ($F_v$) via a feature fusion layer (concatenation), resulting in a high-dimensional hybrid vector ($F_{\mathrm{fusion}}$) that accounts for both anatomical structures and biological growth expectations (Fig. 3).

Figure 3.

The fusion architecture illustrating the construction of the unified hybrid vector $F_{\mathrm{fusion}}$ by combining visual features extracted from multiple anatomical patches using EfficientNet-B4 with clinical features generated by Meta-Net. Visual and clinical information are integrated into a single representation through a concatenation layer.

Training was conducted in the Google Colab Pro environment using NVIDIA GPU accelerators. To ensure gradient stability and diagnostic precision, a weighted random sampler was implemented at the data-loader level to maintain minibatch equilibrium, ensuring that rare skeletal stages (e.g. extreme developmental phases with a weight coefficient of ≈3.5) were not neglected. The Adam optimizer was utilized for gradient-based optimization, with learning rates finely tuned at $1\times {10}^{-4}$ for LCR models and $5\times {10}^{-5}$ for PR models to achieve stable convergence.

Given that standard loss functions often fall short in modeling the hierarchical relationships and class imbalances inherent in biological datasets, we developed a specialized hybrid loss strategy:

• Weighted focal loss and label smoothing: To prioritize underrepresented stages and prevent the model from ignoring rare phases, weighted focal loss was applied. Additionally, acknowledging that skeletal maturation stages are not bounded by discrete biological limits, label smoothing ($\epsilon =0.1$) was integrated to prevent overconfident predictions at transitionary boundaries, thereby enhancing generalization [31].

• Hybrid ordinal loss: In the 9-stage models, to preserve the ordinal relationship (Stage 1 → Stage 9), we implemented a hybrid loss function ($L_{\mathrm{total}}$) that combines categorical classification with spatial distance error. The total loss is calculated as follows:

  $$L_{\mathrm{total}}=L_{\mathrm{CrossEntropy}}+\lambda \times L_{\mathrm{MSE}}$$

where $L_{\mathrm{CrossEntropy}}$ ensures accurate categorical classification and $L_{\mathrm{MSE}}$ (mean squared error) penalizes the distance between the predicted and actual maturation stages. The term λ serves as a scaling factor to balance the contribution of the ordinal penalty. This approach ensures that the model's predictions remain consistent with medical logic and the chronological progression of growth [32].

Model validation and statistical analysis

To analyze the diagnostic success and clinical reliability of the developed models from a multidimensional perspective, a comprehensive evaluation protocol was adopted. To eliminate the potentially misleading effects of class imbalance, we prioritized balanced accuracy, which is calculated as the arithmetic mean of class-specific recall values over standard accuracy. This approach ensures that majority classes do not dominate the performance scores, reflecting the model's true proficiency across all maturation stages. Additionally, Cohen's κ was utilized to measure the agreement between the model's predictions and expert labels, providing a reliability index adjusted for chance.

To enhance the stability of the final test results and minimize individual model variance, an ensemble learning strategy was implemented. During the 5-fold cross-validation process, probability vectors generated by five independent models were integrated using probability-based averaging. The maturation stage with the highest aggregated confidence score was then reported as the final consensus prediction. This ensemble approach significantly improved the robustness of the system against outlier variations in radiographic data.

Statistical analysis of the data obtained in this study was performed using IBM SPSS Statistics software. Descriptive statistics were expressed as mean ± standard deviation for continuous variables and as number and percentage for categorical variables.

The homogeneity of radiograph distribution according to stages in all classification systems was evaluated with the univariate chi-square test. In addition, the homogeneity of the distribution of women and men within groups in each classification system was analyzed using the chi-square test by creating cross-tables.

The relationship between age and stages was examined with Spearman rank difference correlation analysis due to the ordinal structure of the stage variable. The direction and strength of the relationship were evaluated using the correlation coefficient (ρ). In all statistical analyses, a P value of <0.05 was considered statistically significant. In this study, six different scenarios with different class resolutions (9, 5, and 3 classes) were evaluated under the EfficientNet deep learning architecture. These scenarios are structurally different from each other not only in terms of model parameters but also in terms of target class spaces and clinical interpretation levels. This situation methodologically limits the direct comparison of performance metrics (accuracy, F1-score, sensitivity, etc.) within a single statistical framework. Furthermore, obtaining an independent and singular test set result for each scenario does not allow for the reliable application of parametric or nonparametric significance tests based on variance estimation. Therefore, instead of classical statistical significance tests, a comprehensive evaluation approach was adopted in this study, based on class-based performance distributions, balanced accuracy, Cohen's κ coefficient and tolerance accuracy measures, and detailed error analyses. Thus, the clinical applicability, decision consistency, and generalizability of the model were interpreted holistically through multidimensional performance indicators.

Results

Dataset and demographic distribution

The number of cases included in the study and their average ages are shown in Table 1. The number of PRs and LCRs included in the study is equal (3703 PRs, 3703 LCRs) (3149 training/confirmation, 554 tests in LCRs, 488 tests in PRs).

Table 1.

Number of cases included in the study and average ages.

Stage/group	Female n (%)	Male n (%)	Total n (%)	Age (months), mean ± SD
PP2	42 (19.6)	172 (80.4)	214 (100)	111.4 ± 20.2
MP3	45 (23.4)	147 (76.6)	192 (100)	126.4 ± 18.1
PİSİ/H1/R	220 (41.3)	313 (58.7)	533 (100)	130.7 ± 20.4
S-H2	283 (41.0)	407 (59.0)	690 (100)	151.5 ± 20.1
MP3 CAP	228 (45.3)	275 (54.7)	503 (100)	160.0 ± 18.8
DP3U	159 (56.0)	125 (44.0)	284 (100)	163.8 ± 17.6
PP3U	158 (55.2)	128 (44.8)	286 (100)	168.7 ± 15.3
MP3U	295 (65.6)	155 (34.4)	450 (100)	174.1 ± 16.8
RU	291 (52.8)	260 (47.2)	551 (100)	190.4 ± 17.1
Group A	307 (32.6)	632 (67.3)	939 (100)	125.4 ± 21.3
Group B	283 (41.0)	407 (59.0)	690 (100)	151.5 ± 20.1
Group C	228 (45.3)	275 (54.7)	503 (100)	160.0 ± 18.8
Group D	317 (55.6)	253 (44.4)	570 (100)	166.2 ± 16.7
Group E	586 (58.5)	415 (41.5)	1001 (100)	185.2 ± 20.0
Group 1	590 (36.2)	1039 (63.8)	1629 (100)	135.5 ± 24.5
Group 2	228 (45.3)	275 (54.7)	503 (100)	160.0 ± 18.8
Group 3	903 (57.5)	668 (42.5)	1571 (100)	178.4 ± 21.0

Intraobserver agreement in the classification of HWRs was evaluated using Cohen's κ and found to be very high (κ = 0.998). The homogeneity of the radiograph distribution according to stages in all three classification systems (9-stage, 5-stage, and 3-stage) was analyzed with the univariate chi-square test, and it was determined that the distribution was not homogeneous (P < 0.001). Similarly, it was determined that the male–female distribution was not homogeneous in all classifications (P < 0.001). The relationship between age and stages was examined with Spearman correlation analysis, and a statistically significant, positive, and strong relationship was found between age and stage (9-stage, ρ = 0.775; 5-stage, ρ = 0.754; 3-stage, ρ = 0.680; P < 0.001). Furthermore, it was observed that age increased significantly as the stages progressed (RU in the 9-point system, E in the 5-point system, Group 3 in the 3-point system).

Object detection (YOLOv5) model performance

When the performance of the developed object detection models was examined, the YOLOv5 model, used for detecting tooth roots in PRs, achieved 92.5% precision, 93.3% sensitivity (recall), and a score of 0.942 mAP@0.5 on the test dataset, while the YOLOv5m model, used for detecting cervical vertebrae in cephalometric images, achieved 98.9% precision, 99.9% sensitivity (recall), and a score of 0.995 mAP@0.5. This high success rate obtained in both modalities enabled the transfer of noise-free, accurately aligned, and standardized anatomical patches to the classification model, which is the next stage.

Model performance in panoramic radiographs

For estimating the hand–wrist maturation stage based on PRs, the EfficientNet-B0 model was used in the 9-stage classification, while the multiview EfficientNet-B4 model was used in the 3- and 5-group classifications. The 9-stage model exhibited low standard accuracy (0.3648) and Cohen's κ (0.274) in the test set but achieved high accuracy with a ±1 class tolerance (0.7520), indicating that the model learned the sequential structure of the stages but showed limited performance in precise class differentiation. When examined on a stage basis, the RU stage showed high performance (precision 0.74; recall 0.72; F1 0.73), while the MP3 stage was not correctly identified by the model (precision, recall, F1 = 0). Overall, low-to-medium performance was observed in the other stages. In the 5-group classification, the model achieved a standard accuracy of 53.07% and an accuracy of 85.45% with a ±1 class tolerance, reliably tracking the growth trend. Group-based performance was high in Groups A and E (F1 = 0.76 and 0.75) and low in Groups B and C, and recall values were higher than precision in some groups. Weighted average results (precision = 0.59; recall = 0.53; F1 = 0.54) indicate that the model performed at a moderate level and reveal intergroup imbalance.

In the 3-group classification, the model exhibited a moderate level of agreement with 75.20% overall accuracy, 64.49% balanced accuracy, and Cohen's κ 0.587. While F1 scores were above 80% in Group 1 and Group 3, Group 2 F1 was limited to 0.31. This difference stems from Group 2 being a biological transition phase and the high uncertainties in PRs.

Tables 2 and 3 show the test set performance metrics and class-based distribution of the models; Figs. 4–6 show the confusion matrices in 9-stage and 5- and 3-group classifications.

Table 2.

Test set performance metrics in panoramic radiographs.

Model		Standard accuracy	Balanced accuracy	Cohen's κ value	±1 class tolerance accuracy
Panoramic radiograph	9-Stage	0.3648	0.3358	0.274	0.7520
	5-Group	0.5307	0.4965	0.4119	0.8545
	3-Group	0.7520	0.6449	0.5874	0.9344

Figure 4.

Confusion matrix of the 9-stage model in PRs. In the matrix, rows represent the actual classes, and columns represent the classes predicted by the model. Values on the diagonal indicate correctly classified examples, while values off the diagonal indicate incorrect classifications.

Figure 6.

Confusion matrix created for 3-group (Groups 1–3) classification in PRs. It shows the actual and predicted class distribution of the model. In the matrix, rows represent the actual classes, and columns represent the classes predicted by the model. Values on the diagonal indicate correctly classified examples, while values outside the diagonal indicate incorrect classifications (Group 1, X; Group 2, Y; and Group 3, Z are indicated).

Figure 5.

Confusion matrix created for 5-group (Groups A–E) classification in PRs. It shows the actual and predicted class distribution of the model. In the matrix, rows represent the actual classes, and columns represent the classes predicted by the model. Values on the diagonal indicate correctly classified samples, while values off the diagonal indicate incorrect classifications.

Model performance in lateral cephalometric radiographs

For estimating the hand–wrist maturation stage from LCRs, the EfficientNet-B0 model was used in a 9-stage system, and the multiview EfficientNet-B4 model was used in 3- and 5-group systems. In the 9-stage classification, a lighter model and ordinal loss function were applied to reduce class imbalance in the dataset and prevent overlearning. The model showed 43.50% accuracy, 42.04% balanced accuracy, and a κ value of 0.35 in the test set. The highest performance was observed in the RU stage (F1 = 0.74), while low performance and interference were observed in the S, DP3U, and MP3cap stages. Weighted average results (precision = 0.43; recall = 0.44; F1 = 0.42) reflect interclass imbalance and the difficulty of visual similarities. Ordinal loss significantly increased F1 scores in rare and challenging classes.

In 5-group classification, the model achieved 63.36% accuracy, 57.21% balanced accuracy, and 0.53 κ, successfully learning the sequential structure of growth with an accuracy of 93.3% with a tolerance of ±1 class. High F1 scores (0.80–0.84) were observed in Groups A and E, while medium–low performance was observed in Groups B, C, and D. Weighted average results (precision = 0.62; recall = 0.63; F1 = 0.62) indicate moderate performance and group-based imbalance.

In 3-group classification, dynamic threshold optimization and ensemble learning strategies were applied, and the model demonstrated high success with 89.75% accuracy, Cohen's κ of 0.828, and a weighted average F1 = 0.89. While F1 scores were 0.92–0.93 in Groups 1 and 3, recall was lower (0.56) in Group 2 during the transition phase. The ensemble method increased the reliability of the results by raising the average κ score of the individual models from 0.75 to 0.828.

Tables 4 and 5 show the test set performance metrics and class-based distribution of the models; Figs. 7–9 show the confusion matrices in 9-stage and 5- and 3-group classifications.

Table 4.

Test set performance metrics in lateral cephalometric radiographs.

Model		Standard accuracy	Balanced accuracy	Cohen's κ value	±1 class tolerance accuracy
Lateral Cephalometric Radiograph	9-Stage	0.4350	0.4204	0.3525	0.9170
	5-Group	0.6336	0.5721	0.5303	0.933
	3-Group	0.8975	0.8201	0828	0.9621

Table 5.

Classification-based performance distribution in lateral cephalometric radiographs.

Model	Class/group	Precision	Recall	F1 score	Number of samples (n)
9-Stage	PP2	0.50	0.44	0.47	32
	MP3	0.41	0.43	0.42	28
	Pisi	0.39	0.71	0.51	80
	S	0.33	0.21	0.26	103
	MP3 CAP	0.40	0.25	0.31	76
	DP3U	0.18	0.21	0.20	42
	PP3U	0.33	0.33	0.33	43
	MP3U	0.60	0.36	0.45	67
	RU	0.67	0.84	0.74	83
	Weighted average	0.43	0.44	0.42	554
5-Group	A	0.71	0.91	0.80	140
	B	0.55	0.34	0.42	103
	C	0.35	0.45	0.40	76
	D	0.45	0.31	0.36	85
	E	0.82	0.85	0.84	150
	Weighted average	0.62	0.63	0.62	554
3-Group	1	0.92	0.95	0.93	243
	2	0.79	0.56	0.66	75
	3	0.90	0.95	0.92	236
	Weighted average	0.89	0.90	0.89	554

Figure 7.

Confusion matrix created for 9-stage classification in LCRs. It shows the actual and predicted class distribution of the model. In the matrix, rows represent actual classes, and columns represent classes predicted by the model. Values on the diagonal indicate correctly classified samples, while values off the diagonal indicate incorrect classifications.

Figure 9.

Confusion matrix created for 3-group (Groups 1–3) classification in LCRs. It illustrates the actual and predicted class distribution of the model. In the matrix, rows represent the actual classes, and columns represent the classes predicted by the model. Values on the diagonal indicate correctly classified samples, while values off the diagonal indicate incorrect classifications (Group 1, X; Group 2, Y; Group 3, Z).

Figure 8.

Confusion matrix created for 5-group (Groups A–E) classification in LCRs. It illustrates the actual and predicted class distribution of the model. In the matrix, rows represent the actual classes, and columns represent the classes predicted by the model. Values on the diagonal indicate correctly classified examples, while values off the diagonal indicate incorrect classifications.

Discussion

In this study, an ensemble deep learning pipeline was evaluated for predicting skeletal maturation stages using PRs and LCRs across 9-stage, 5-group, and 3-group classification scenarios. To our knowledge, this is the first study in the literature to systematically compare PRs and LCRs for predicting hand–wrist maturation stages based on the Björk method [20] using a fully automated, multimodal AI framework.

From a clinical methodology perspective, while feature extraction from PRs was informed by the Demirjian method [24], our model deliberately prioritized specific teeth (mandibular canines, second premolars, second and third molars). As highlighted by Ferrillo et al. [25], these specific teeth exhibit longer, progressive developmental trajectories that correlate more strongly with chronological age. By excluding early-developing teeth, such as incisors and first molars, we minimized noncontributory anatomical variations, allowing the network to learn optimal age-specific patterns and enhancing the model's discriminative capacity.

A primary finding of this study is that model accuracy is inversely proportional to class resolution. The 3-group setup yielded the maximum performance, while the fine-grained 9-stage setup exhibited lower standard accuracy. However, this decline does not indicate algorithmic failure; rather, it reflects the inherent biological ambiguity of skeletal staging. Morphological differences between adjacent maturation stages are extremely subtle, and biological transitions lack discrete temporal boundaries, occasionally resulting in short developmental phases [20, 33]. Similar to Kim et al. [34] who reported substantial error clustering around neighboring classes, the high success of our models within a ±1 stage tolerance confirms that the challenge lies in the biological continuity of growth rather than methodological inadequacy.

When comparing imaging modalities, LCR models consistently demonstrated higher and more stable performance than PR models. This superiority is attributable to the standardized positioning and reduced anatomical superposition in lateral cephalometry, which preserves distinct morphological cues of the cervical vertebrae. Previous studies have validated the biological synchrony between CVM and hand–wrist skeletal age, emphasizing the diagnostic value of LCRs [35–37]. Notably, while Kim et al. [34] demonstrated the feasibility of AI for CVM assessment, their approach required manual landmarking of 13 anatomical points, introducing operator-dependent bias. In contrast, our end-to-end YOLOv5 and EfficientNet pipeline fully automates localization and feature extraction, eliminating subjectivity. Conversely, despite PRs containing less direct skeletal maturation cues, their relatively high success rate—especially under broader screening scenarios (3-group and 5-group)—demonstrates their significant potential for preliminary assessment without requiring additional radiation exposure. This aligns with recent reviews confirming the promising trajectory of deep learning in PR-based age estimation [38–40].

Methodologically, the integration of chronological age and sex via the “Meta-Net” was crucial. As Kim et al. [34] reported, supplementing visual features with clinical metadata significantly reduces mean absolute errors in bone age prediction. Furthermore, the robust object detection achieved by our YOLOv5 models (mAP@0.5 > 0.94 for both modalities) and the classification efficiency of the EfficientNet backbone parallel the high performance of these architectures in other complex medical domains, ranging from automated tooth detection [28, 41] to broader pathological screenings [42–46]. However, unlike binary pathology detection, fine-grained skeletal maturation poses a highly complex ordinal classification challenge. This underscores the necessity of the hybrid ordinal loss strategy and ensemble learning approach utilized in this study, which successfully reduced individual model variance and stabilized predictions against outlier radiographic data, corroborating the findings of Cunha et al. [47].

While advanced algorithmic strategies such as weighted focal loss and sampling balancing were effectively employed to mitigate the effects of class imbalance, it must be acknowledged that these techniques cannot entirely eliminate the inherent biases associated with imbalanced biological datasets. Skeletal maturation is fundamentally a continuous biological process. Converting this fluid continuum into rigid categorical stages inevitably introduces label uncertainty, particularly in transitional developmental phases that are naturally less frequent and biologically ambiguous. Consequently, the reduced predictive performance observed in these intermediate stages should not be interpreted purely as algorithmic insufficiency. Rather, it largely reflects the intrinsic limitations of categorizing a continuous biological phenomenon and the inherent subjectivity of the human reference classifications used for supervised deep learning training.

Beyond these inherent biological and conceptual challenges, the present study carries certain design limitations. The retrospective, single-center nature of the dataset and inherent class imbalances representing extreme developmental stages limit the immediate generalizability of the models. Furthermore, PRs and LCRs inherently provide indirect assessments compared with the gold standard HWRs. Future multicenter studies utilizing larger, ethnically diverse datasets and exploring model explainability (e.g. Grad-CAM) are recommended to further validate these automated systems for routine orthodontic decision support.

Limitations include the study being single centered, some classes in the dataset showing a relatively uneven distribution, and the reference labeling being based on expert opinion. In future studies, it may be possible to develop more accurate and generalizable systems using larger, multicenter datasets and multimodal approaches.

Although the 3-group classification models achieved higher predictive performance, this improvement may partially reflect the reduced complexity of the classification task rather than a true increase in diagnostic capability. Therefore, these findings should be interpreted with caution, as reducing the number of maturation stages may result in a loss of biological and clinical detail.

A limitation of the present study is that the deep learning models were trained using hand–wrist maturation stages as reference labels. Consequently, the models learned image patterns associated with these predefined stages rather than directly measuring skeletal maturation itself. Therefore, the reported performance should be interpreted as agreement with the reference classification system rather than as a direct biological validation of skeletal maturity.

Conclusion

This study has shown promising results in automating skeletal developmental staging under different classification resolutions and imaging modalities using deep learning–based models.

The study has once again emphasized that the standard “Accuracy” metric alone can be misleading in such clinical applications and that the use of metrics, such as balanced accuracy and Cohen’s κ, which fairly reflect the effects of class imbalance, is critical.

The main limitation in model performance stems from the inherent difficulties of the problem, rather than from the inadequacy of the algorithm. High interstage visual similarity and biological ambiguity, particularly observed in intermediate and transitional phases, constitute a natural classification limit for both human experts and AI models. The main reason for the performance degradation is these morphological overlaps. Deep learning models, developed with the right strategies and class resolution appropriate to clinical needs, have the potential to be a valuable decision support tool in orthodontic treatment planning, saving clinicians time and increasing decision consistency.

Author contributions

Merve Edik (Conceptualization, Methodology, Visualization, Writing—original draft, Writing—review & editing [equal], Data curation, Investigation, Project administration, Resources, Validation [lead]), Fatma Çelebi (Conceptualization, Formal analysis, Supervision [supporting], Investigation, Methodology, Project administration, Validation, Visualization, Writing—original draft [equal], Resources, Software, Writing—review & editing [lead]), and Meryem Etöz (Project administration, Supervision, Validation, Writing—review & editing [supporting])

Funding

The open access publication charge for this article was funded by the Scientific and Technological Research Council of Turkey (TÜBİTAK) through the Turkish Institutions (TÜBİTAK affiliated) Open Access Agreement.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Ethics approval and consent to participate

Approval for the study was obtained from Erciyes University Health Sciences Research Ethics Committee (Decision No.: 2026/16).