2.1 Lung nodule segmentation

Traditional segmentation approaches relied on region growing, watershed algorithms, and level set methods with limited success in handling complex nodule morphologies. Recent deep learning advances have shifted focus to convolutional neural networks (CNNs), with U-Net and its variants becoming dominant architectures for medical image segmentation [17]. The introduction of attention mechanisms has significantly improved segmentation performance, as demonstrated by Wang et al. [3] who developed a multilevel attention U-Net segmentation algorithm for lung cancer based on CT images.

Two-stage detection frameworks have gained prominence due to their superior accuracy in complex scenarios. Cui et al. [18] presented SF2T, leveraging Swin Transformer and two-stream networks for lung nodule detection, introducing attention-based feature fusion mechanisms. Similarly, Sumathi and Phamila [19] developed an efficient two-stage segmentation framework for chest X-ray images with U-Net model fusion, demonstrating the effectiveness of multi-stage approaches in medical imaging.

Recent developments have focused on multi-scale detection capabilities. Cai et al. [20] proposed MSDet with receptive field enhanced multiscale detection for tiny pulmonary nodules, addressing challenges in detecting small-scale nodules that are critical for early cancer diagnosis. Tang and Zhang [21] developed a multi-task model for simultaneous pulmonary nodule segmentation and classification, demonstrating the benefits of unified approaches.

The integration of advanced architectures has shown promising results. Wang et al. [22] introduced CPLOYO, a pulmonary nodule detection model with multi-scale feature fusion and nonlinear feature learning, focusing on multi-type nodule detection corresponding to various forms of lung cancer. These advances highlight the importance of sophisticated architectures in addressing the complexity of lung nodule segmentation.

2.2 Lung nodule classification

Classification approaches have evolved from handcrafted features to sophisticated deep learning models over the past decade. Murugan and Dhanasekaran [23] developed an automatic lung tumor volume estimation method using PSO-TSVM, implementing a two-stage framework called Suspicious Volumetric Tumor (SVT) segmentation. This work demonstrated the effectiveness of optimization-based approaches in lung tumor analysis.

Recent studies have emphasized the importance of lightweight architectures for practical deployment. Neelameghasri et al. [24] explored CNN models for lung cancer detection and classification, comparing single-stage and two-stage detectors. Jenipher and Radhika [25] proposed a lung tumor cell classification approach using lightweight MobileNetV2 and attention-based SCAM enhanced Faster R-CNN, demonstrating the potential for efficient mobile deployment.

Multi-scale and attention-based approaches have shown significant improvements in classification accuracy. Linginani and Lakshmi [26] developed an intelligent model for pulmonary emphysema detection using adaptive image segmentation and multi-dilated DenseNet with attention mechanism. Li et al. [27] constructed a multi-scale convolutional neural network with global channel spatial attention mechanisms for lung nodule detection, achieving improved performance through sophisticated attention strategies.

The integration of deformable attention mechanisms has emerged as a promising direction. Liu and Ao [28] presented a deformable attention mechanism-based YOLOv7 structure for lung nodule detection, outperforming traditional two-stage Faster R-CNN approaches. These developments highlight the evolution toward more sophisticated attention mechanisms in lung nodule analysis.

2.3 Attention mechanisms in medical imaging

Attention mechanisms have gained popularity for focusing on relevant image regions in medical applications, with transformer-based approaches showing particular promise. Ramezani [29] developed a transformer-based CT anomaly detection and auto-segmentation approach for sparse lung nodules, implementing a novel two-stage approach using bounding box embeddings as attention cues.

Dual-attention architectures have demonstrated superior performance in medical imaging tasks. Zamanidoost et al. [30] proposed DA OMS-CNN with dual-attention and 3D Swin Transformer for early-stage lung cancer detection, highlighting the effectiveness of attention mechanisms in improving lung nodule detection accuracy. The integration of multiple attention types has proven beneficial for complex medical imaging scenarios.

Recent work has explored the application of attention mechanisms in federated learning scenarios. Lee et al. [6] developed federated online learning with filters for lung nodule segmentation in low-dose computed tomography images, implementing a Precision Nodule Filter with a structured two-stage framework. This work demonstrates the feasibility of attention-based approaches in distributed learning environments.

Vision transformer architectures have emerged as powerful alternatives to traditional CNNs. Mannepalli et al. [31] presented GSC-DVIT, a vision transformer-based deep learning model for lung cancer classification in CT images, demonstrating competitive performance with traditional approaches. The success of transformer architectures has motivated their adoption in various medical imaging applications.

2.4 Federated learning in healthcare

Federated learning has emerged as a promising paradigm for collaborative machine learning while preserving data privacy in healthcare applications. The challenge of handling distributed datasets while maintaining model performance has been addressed through various optimization strategies and communication-efficient protocols.

Metaheuristic approaches have been explored for enhancing federated learning performance. Kaulgud and Saundattikar [32] investigated metaheuristics and deep learning in lung nodule detection and classification, proposing optimization strategies for distributed learning scenarios. These approaches demonstrate the potential for improving federated learning efficiency through advanced optimization techniques.

Comparative studies have highlighted the importance of selecting appropriate architectures for federated medical imaging. Aishwarya and Asuntha [33] conducted a comprehensive survey on lung nodules applying machine learning and deep learning techniques, emphasizing the critical role of segmentation and classification methods in federated scenarios. Their work provides valuable insights into the selection criteria for federated medical AI systems.

Recent advances have focused on integrated approaches combining multiple AI techniques. Karimullah et al. [34] developed an integrated method for detecting lung cancer via CT scanning through optimization, deep learning, and IoT data transmission, achieving enhanced accuracy in tumor classification and localization. This work demonstrates the potential for comprehensive federated healthcare solutions.

2.5 State-of-the-art review and surveys

Comprehensive reviews have provided valuable insights into the current state and future directions of lung nodule analysis. Wang et al. [35] conducted a thorough review of pulmonary nodule segmentation using deep learning, analyzing fine two-stage frameworks and their effectiveness in medical imagery classification. Their survey highlights the importance of sophisticated segmentation approaches for accurate lung cancer diagnosis.

Recent survey work by Cai et al. [36] focused on medical AI for early detection of lung cancer, providing comprehensive coverage of pulmonary nodule detection, segmentation, and classification approaches. The survey emphasizes the integration of 3D coordinate attention and edge detection techniques, demonstrating the evolution toward more sophisticated analytical frameworks.

These comprehensive reviews highlight the rapid advancement in lung nodule analysis techniques and the growing importance of attention mechanisms, multi-stage frameworks, and federated learning approaches. The convergence of these technologies presents opportunities for developing more robust, accurate, and privacy-preserving medical AI systems.

3.1 Framework overview

The proposed AGA-Net framework consists of two interconnected stages designed to operate efficiently in federated learning environments. As shown in Fig 1, the first stage employs the Geometric-Constrained Attention Module (GCAM) to produce precise nodule boundaries, while the second stage utilizes the Multi-Scale Uncertainty Quantification Network (MUQ-Net) for malignancy prediction with confidence estimation. The framework is specifically designed to handle the challenges of distributed healthcare IoT systems while maintaining high accuracy and clinical interpretability.

The overall architecture integrates privacy-preserving mechanisms with advanced deep learning techniques to enable secure and accurate lung nodule analysis across multiple healthcare institutions. The framework incorporates differential privacy guarantees and secure aggregation protocols to ensure patient data protection during the federated training process.

3.2 Geometric-constrained attention module (GCAM)

The GCAM module is designed to leverage the approximately spherical nature of lung nodules while adapting to the constraints of federated learning environments. For a given feature map , the geometric attention is computed through a multi-step process that incorporates spatial, channel, and geometric constraints.

The spatial attention component identifies regions of interest based on spatial relationships:

(1)

where GAP and GMP represent global average pooling and global max pooling operations, respectively, and denotes the sigmoid activation function.

The channel attention mechanism emphasizes important feature channels:

(2)

The geometric attention component incorporates spherical constraints specific to lung nodules:

(3)

where represents the geometric constraint function:

(4)

Here, is the Euclidean distance from the estimated nodule center to position (i,j,k), and is an adaptive radius parameter learned during training:

(5)

where represents the predicted nodule radius distribution, and , , are learnable parameters. calculation: where is the volume of the initial segmentation mask from the backbone network, assuming spherical nodule approximation. Alternative approach: Add explicit radius prediction head: where are segmentation features and are learnable parameters.

Computation of : The adaptive radius in Eq. (5) is calculated based on the predicted nodule radius distribution rpred. The parameters , , and are learnable and are optimized during training via backpropagation, allowing the model to dynamically adapt to nodules of varying sizes.

Intuition: – controls the influence of the mean predicted radius across all nodules. - adjusts for variations by incorporating the standard deviation of . - acts as a bias term for numerical stability. Thus, automatically adapts to different nodule sizes across datasets, improving segmentation accuracy for heterogeneous lung nodule distributions.

Computation of : The predicted nodule radius is obtained from the segmentation mask volume |S| assuming spherical approximation:

(6)

Additionally, we implement a learnable radius prediction head to refine from network features:

(7)

where are segmentation features and are learnable parameters.

3.3 Nodule center point estimation

The geometric constraint function in Equation 4 requires accurate estimation of the nodule center point. The center estimation is performed through a multi-step process that combines initial segmentation predictions with geometric analysis:

(8)

where represents the set of voxel coordinates in the initial segmentation mask obtained from the backbone network.

However, for more robust center estimation, especially in cases with irregular nodule shapes or partial volume effects, we employ a weighted centroid calculation:

(9)

where represents the entire volume of interest, and the weight is computed as:

(10)

Here, is the segmentation probability at position (i,j,k) from the initial network prediction, represents the gradient magnitude, and is an empirically determined parameter that controls the influence of edge regions.

Note: The parameter is a fixed hyperparameter controlling the influence of edge regions during weighted centroid calculation. Its value is set empirically to based on cross-validation experiments.

The distance calculation in the geometric constraint function then becomes:

(11)

This weighted centroid approach provides more stable center estimation by reducing the influence of boundary artifacts and partial volume effects that are common in medical imaging. The gradient-based weighting ensures that the center calculation prioritizes regions with high confidence and low edge activity, leading to more accurate geometric constraints.

(12)

where is computed using Equations 9–11.

The complete attention mechanism combines spatial, channel, and geometric attention through an adaptive fusion strategy:

(13)

where , , are learnable weight parameters that adapt based on the local data characteristics in federated settings.

To ensure privacy preservation in federated learning, the geometric constraints are computed locally at each client, and only the aggregated attention weights are shared during the federated optimization process:

(14)

where K is the number of participating clients, is the number of samples at client k, and is the total number of samples.

3.4 Multi-scale uncertainty quantification network (MUQ-Net)

The MUQ-Net employs Monte Carlo Dropout and deep ensembles to quantify prediction uncertainty while maintaining computational efficiency in federated environments. As illustrated in Fig 2, the network processes multi-scale features extracted from the segmented nodules.

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Fig 2. Architecture of the multi-scale uncertainty quantification network (MUQ-Net) showing the ensemble approach with Monte Carlo Dropout for uncertainty estimation.

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For a given segmented nodule N, the network processes multi-scale features through parallel pathways:

(15)

where represents features at scale i, computed using different receptive field sizes.

Each feature scale is processed through a dedicated branch with dropout layers:

(16)

where is the dropout probability for scale i.

The uncertainty-aware prediction is computed using Monte Carlo sampling:

(17)

where T is the number of Monte Carlo samples, is the network function, and represents random dropout masks.

The predictive uncertainty is estimated using the variance of predictions:

(18)

The heteroscedastic uncertainty loss captures both aleatoric and epistemic uncertainty by predicting the variance alongside the mean:

(19)

where represents the predicted variance for sample i, learned jointly with the classification output.

where represents the predicted variance for sample i.

The ensemble prediction combines multiple models trained with different initializations:

(20)

where M is the number of ensemble members.

3.5 Federated learning algorithm

Algorithm 1 presents the complete federated learning procedure for training the AGA-Net framework across distributed healthcare institutions while preserving patient privacy.

Algorithm 1 Federated AGA-Net Training Algorithm

Require: Number of clients K, rounds R, local epochs E, Client datasets

Ensure: Global model parameters

1:  Initialize global model parameters

2:  for round r = 1 to R do

3:   Select subset of clients

4:   for each client in parallel do

5:    

6:    for epoch e = 1 to E do

7:     for batch B in do

8:      Compute GCAM attention weights

9:      Forward pass through segmentation network

10:     Compute segmentation loss

11:     Forward pass through MUQ-Net

12:     Compute classification loss

13:     Compute uncertainty loss

14:     

15:     Update local parameters:

16:    end for

17:   end for

18:   Apply differential privacy:

19:  end for

20:  Aggregate updates:

21: end for

22: return

The algorithm incorporates differential privacy through the addition of calibrated noise to the local model updates before aggregation. The noise variance is determined based on the desired privacy budget and sensitivity analysis of the model parameters.

3.6 Loss function design

The total loss function combines segmentation, classification, and uncertainty objectives with adaptive weighting based on federated learning dynamics:

(21)

The segmentation loss includes Dice and focal components to handle class imbalance:

(22)

where the Dice coefficient is computed as:

(23)

and the focal loss addresses class imbalance:

(24)

The classification loss employs cross-entropy with label smoothing:

(25)

where and are empirically determined weights that balance the contribution of both uncertainty estimation approaches. The heteroscedastic component focuses on learning appropriate uncertainty estimates during training, while the calibration component ensures that the predicted probabilities align with actual accuracy rates. parameter type: is a hyperparameter that is empirically determined through validation experiments, not learned during training.

Usage: Controls the influence of edge regions in weighted centroid calculation via where larger values reduce edge penalty.

The calibration uncertainty loss encourages well-calibrated predictions by penalizing overconfident incorrect predictions. It also calculates the uncertainty loss encourages calibrated predictions

(26)

where is the predicted probability and is the target probability.

3.7 Privacy-preserving mechanisms

To ensure patient data protection in federated learning scenarios, we implement several privacy-preserving mechanisms. Differential privacy is achieved through the addition of calibrated Gaussian noise to gradient updates:

(27)

where the noise variance is determined by the privacy budget:

(28)

Secure aggregation protocols ensure that individual client updates remain private during the aggregation process. The server only receives encrypted aggregated updates without access to individual client data.

3.8 Adaptive loss weight adjustment strategy

The loss weighting parameters in Equation 21 require careful adjustment to balance the contributions of different loss components throughout the federated training process. The adjustment strategy is based on the relative convergence rates and magnitude differences between loss terms:

(29)

where t represents the current training iteration, and each is dynamically adjusted based on loss magnitude and convergence behavior.

Calculation of : The federated regularization loss is defined as:

(30)

where controls client drift regularization, and weights the effect of differential privacy noise.

Calculation of : The derivative in Eq. 31 is approximated using a finite-difference method:

(31)

where iterations by default. This formulation smooths loss changes and ensures stable adaptive weighting during federated training.

The adaptive weighting scheme follows these principles:

1. Magnitude Normalization: The base weights are adjusted to account for the natural magnitude differences between loss terms: (32)
   where is an exponential moving average with decay factor , and are the initial weights: , , , .
2. Convergence-Based Adjustment: Weights are modified based on the convergence rate of each loss component: (33)
   where is a sensitivity parameter, and represents the gradient of loss i with respect to training iterations, approximated using finite differences over a sliding window of 10 iterations.
3. Federated-Specific Adjustment: The federated loss weight receives additional adjustment based on client heterogeneity: (34)
   where is a heterogeneity sensitivity parameter, and represents the variance of local losses across participating clients in the current round.

Algorithm 2 Enhanced Federated AGA-Net Training with Adaptive Loss Weighting

Require: Number of clients K, rounds R, local epochs E, Client datasets , Initial loss weights

Ensure: Global model parameters

1:  Initialize global model parameters

2:  Initialize loss history buffers for

3:  for round r = 1 to R do

4:   Select subset of clients

5:   Initialize client loss collection

6:   for each client in parallel do

7:   

8:    for epoch e = 1 to E do

9:     for batch B in do

10:     Compute GCAM attention weights

11:     Forward pass through segmentation network

12:     Compute segmentation loss

13:     Forward pass through MUQ-Net

14:     Compute classification loss

15:     Compute uncertainty loss

16:     Compute federated loss

17:     Update loss histories:

18:     Compute adaptive weights using Equations 32–34

19:     

20:     Update local parameters:

21:    end for

22:   end for

23:   

24:   Apply differential privacy:

25:  end for

26:  Compute client loss variance:

27:  Update using Equation 34

28:  Aggregate updates:

20: end for

30: return ▷ Final optimized global model after R rounds

Note: The expression refers to the final optimized global model parameters obtained after R communication rounds and is not set to zero.

The rationale for this adaptive weighting strategy is based on several key observations from federated medical imaging training:

1. Loss Scale Imbalance: Segmentation losses (Dice + Focal) typically have magnitudes in the range [0.1, 2.0], while classification losses range [0.01, 0.5], and uncertainty losses range [0.001, 0.1]. Without magnitude normalization, the segmentation loss would dominate training.
2. Convergence Rate Differences: Classification losses typically converge faster than segmentation losses in medical imaging tasks. The convergence-based adjustment ensures that slower-converging components receive appropriate emphasis throughout training.
3. Federated Heterogeneity Impact: Higher client heterogeneity requires stronger regularization through increased federated loss weighting to prevent client drift and maintain global model coherence.
4. Training Phase Adaptation: Early training phases benefit from higher segmentation emphasis for feature learning, while later phases require balanced weighting for fine-tuning. The adaptive scheme naturally transitions between these phases based on loss behavior.

Table 1 shows the evolution of loss weights throughout training under different federated scenarios:

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Table 1. Evolution of loss weights throughout federated training.

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This adaptive weighting strategy ensures optimal training dynamics while maintaining the flexibility to respond to different federated learning conditions and dataset characteristics. The approach has been validated across all three benchmark datasets with consistent improvements in convergence speed and final performance compared to fixed weighting schemes. Furthermore, The detailed definitions, symbols, and values of all parameters used in the proposed framework are summarized in Table A1 in S1 Appendix.

3.9 Experimental setup

This part elaborates the datasets details, implementation details, and metrics for evaluation the models.

3.9.1 Datasets and federated simulation.

We evaluate our method on three benchmark datasets configured for federated learning simulation. As detailed in Table 2, the datasets are partitioned across multiple simulated clients to reflect real-world federated scenarios.

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Table 2. Dataset specifications for federated learning evaluation.

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The LUNA16 dataset provides standardized annotations for nodule detection and segmentation with ground truth annotations from multiple radiologists. The LIDC-IDRI dataset includes detailed radiologist annotations with malignancy ratings, enabling comprehensive evaluation of classification performance. The NSCLC-Radiomics dataset provides clinical outcomes and survival data for validation of clinical utility.

Data heterogeneity is simulated by introducing non-IID distributions across clients based on institutional characteristics, imaging protocols, and patient demographics. The degree of non-IIDness is controlled using a Dirichlet distribution with concentration parameter , where smaller values indicate higher heterogeneity.

3.9.2 Implementation details.

The network was implemented using PyTorch with federated learning extensions through the FedML framework. Training was conducted on a cluster of NVIDIA A100 GPUs distributed across multiple nodes to simulate realistic federated scenarios. Table 3 summarizes the key hyperparameters used in our experiments.

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Table 3. Hyperparameter configuration.

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The federated learning process involves 100 global communication rounds with 5 local epochs per round. Client selection follows a random sampling strategy with 50% participation rate per round to simulate realistic federated scenarios where not all clients are available simultaneously.

3.9.3 Evaluation metrics.

Segmentation performance is evaluated using multiple complementary metrics to provide comprehensive assessment. The Dice Similarity Coefficient (DSC), defined as , measures volumetric overlap between the predicted segmentation P and ground truth G. The Intersection over Union (IoU), computed as , provides a stricter overlap measure. Boundary accuracy is assessed using the 95th percentile Hausdorff Distance (HD95) and Average Surface Distance (ASD), which quantify the maximum and mean surface distances between predicted and ground truth boundaries, respectively. Additionally, Sensitivity () and Specificity () are computed to evaluate the detection performance for nodule and background regions.

Classification performance is assessed using standard metrics along with uncertainty quantification measures. The Expected Calibration Error (ECE) evaluates the calibration quality of uncertainty estimates:

(35)

where represents the m-th confidence bin, is the accuracy within the bin, and is the average confidence.

4.1 Baseline methods

We compare our approach against several state-of-the-art methods adapted for federated learning scenarios. For segmentation, the baseline methods include U-Net, Attention U-Net, and nnU-Net, all configured for federated training. For classification, we evaluate against ResNet-50, DenseNet-121, and EfficientNet-B3 under identical federated settings. Additionally, three federated learning algorithms are compared: FedAvg, FedProx, and SCAFFOLD, to assess the effectiveness of our federated optimization strategy independently of the network architecture.

4.1.3 Evaluation of proposed model.

Before presenting our experimental results, Fig 3 illustrates the complexity of the LIDC-IDRI dataset used in our evaluation, showing the inherent challenges in lung nodule annotation that our uncertainty quantification approach addresses. Fig 4 shows the Comprehensive distribution analysis of the LIDC-IDRI dataset revealing key characteristics, Top row: Histogram distributions showing (left) the number of nodules per patient with most patients having 1–2 nodules, creating class imbalance challenges; (center) the number of images per nodule indicating high variability in nodule representation across CT slices; (right) the distribution of annotation masks per nodule demonstrating the multi-radiologist annotation protocol. Bottom row: Box plots providing statistical summaries of (left) images per nodule showing median values around 5–7 slices with significant outliers up to 50 + slices for large nodules; (center) masks per nodule confirming the consistent 4-radiologist annotation protocol; (right) the distribution of mask-to-image ratios concentrated around 4.0, indicating that most nodules receive annotations from all four radiologists. These distribution characteristics directly inform our federated learning client partitioning strategy and highlight the need for uncertainty quantification to handle inter-radiologist variability. The skewed distributions and presence of outliers justify our adaptive geometric attention approach and multi-scale uncertainty estimation framework.

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Fig 3. Sample LIDC-IDRI dataset images and corresponding annotation masks.

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Fig 4. Comprehensive distribution analysis of the LIDC-IDRI dataset revealing key characteristics that influence federated learning performance and uncertainty quantification requirements.

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4.2 Segmentation performance analysis

The segmentation results demonstrate the effectiveness of the geometric-constrained attention mechanism across all three datasets. As shown in Fig 5, the training convergence is stable across federated learning rounds with consistent improvement in segmentation accuracy.

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Fig 5. Training loss curves showing convergence behavior across federated learning rounds for segmentation and classification tasks.

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Table 4 presents comprehensive segmentation results across all datasets, demonstrating superior performance of our AGA-Net approach compared to baseline methods.

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Table 4. Comprehensive segmentation results comparison.

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The geometric constraints in GCAM provide significant improvements in boundary delineation, particularly for small nodules where traditional attention mechanisms often fail. Fig 6 illustrates the accuracy progression throughout the federated training process.

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Fig 6. Accuracy maps showing performance improvement across federated learning rounds for both segmentation and classification tasks.

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4.3 Classification and uncertainty quantification results

The classification results demonstrate the effectiveness of uncertainty quantification in providing reliable confidence estimates for clinical decision-making. Table 5 shows comprehensive classification performance with uncertainty metrics.

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Table 5. Classification results with uncertainty quantification.

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The uncertainty quantification capabilities of MUQ-Net provide significant improvements in calibration quality, as evidenced by the low Expected Calibration Error (ECE) values. Fig 7 presents the confusion matrices for all three datasets, demonstrating the balanced performance across malignant and benign classifications.

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Fig 7. Confusion matrices for malignancy classification across all three datasets showing balanced performance for both malignant and benign cases.

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To further characterize the calibration quality of MUQ-Net, reliability diagrams and calibration curves are provided in Fig 8. These plots compare predicted confidence against observed accuracy across ten equal-width confidence bins for each dataset. MUQ-Net produces calibration curves that closely follow the diagonal identity line, confirming that predicted probabilities align well with empirical accuracy rates. Coverage analysis further shows that the 90% predictive interval achieves empirical coverage of 91.2%, 89.7%, and 90.5% on LUNA16, LIDC-IDRI, and NSCLC-Radiomics respectively, consistent with the low ECE values reported in Table 5. In contrast, baseline methods (ResNet-50, DenseNet-121, EfficientNet-B3) exhibit systematic overconfidence, manifesting as curves that fall below the diagonal. These visualizations confirm that the heteroscedastic loss and Monte Carlo Dropout in MUQ-Net yield well-calibrated uncertainty estimates suitable for clinical decision support.

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Fig 8. Reliability diagrams and 90% predictive interval coverage analysis for MUQ-Net compared against baseline methods.

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The ROC curves in Fig 9 illustrate the superior discriminative performance of our approach across all datasets, with particular improvements in the high-sensitivity region crucial for clinical applications. The ROC curves in Fig 9 illustrate the superior discriminative performance of our approach across all datasets, with particular improvements in the high-sensitivity region crucial for clinical applications.

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Fig 9. ROC curves comparing the proposed MUQ-Net with baseline methods across all three datasets, showing superior discriminative performance.

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4.4 Federated learning performance

The federated learning results demonstrate the effectiveness of our approach in distributed scenarios while maintaining privacy. Table 6 compares different federated learning algorithms with our AGA-Net framework.

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Table 6. Federated learning algorithm comparison across all datasets.

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Our federated implementation achieves faster convergence with fewer communication rounds while providing differential privacy guarantees. The communication efficiency is particularly important for real-world deployment where bandwidth and latency constraints exist.

4.5 Computational efficiency analysis

Table 7 presents a comprehensive analysis of computational requirements on the LUNA16 dataset, demonstrating the practical feasibility of our approach for deployment in resource-constrained healthcare IoT environments. Despite the additional complexity introduced by geometric constraints and uncertainty quantification, our method maintains reasonable computational requirements suitable for clinical deployment. Consistent efficiency trends were observed across LIDC-IDRI and NSCLC-Radiomics datasets, with inference times varying by no more than 10.7% and memory requirements by no more than 7.5% due to differences in input volume dimensions.

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Table 7. Computational efficiency analysis (LUNA16 dataset).

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Despite the additional complexity introduced by geometric constraints and uncertainty quantification, our method maintains reasonable computational requirements suitable for clinical deployment.

4.6 Ablation studies

Comprehensive ablation studies were conducted to evaluate the contribution of each component in our framework. Table 8 demonstrates the incremental improvements achieved by each module.

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Table 8. Comprehensive ablation study results.

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The ablation results clearly demonstrate that each component contributes meaningfully to the overall performance, with geometric constraints providing the most significant improvement in segmentation accuracy and uncertainty quantification most impacting calibration quality.

4.7 State-of-the-art comparison

Table 9 provides a comprehensive comparison with recent state-of-the-art methods in lung nodule analysis, demonstrating the superior performance of our approach across multiple metrics and highlighting the advantages of our integrated framework.

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Table 9. Comprehensive state-of-the-art comparison.

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Our approach represents the first comprehensive solution that simultaneously achieves high accuracy, uncertainty quantification, federated learning capabilities, privacy preservation, real-time performance, and clinical validation. This comprehensive integration addresses multiple critical requirements for next-generation medical AI systems, setting a new standard for lung nodule analysis in distributed healthcare environments.

4.8 Statistical significance analysis

To validate that performance improvements are statistically significant, we conduct paired Wilcoxon signed-rank tests and compute 95% bootstrap confidence intervals (1,000 resampling iterations, bias-corrected and accelerated method) across 5-fold cross-validation on all three datasets.

On LUNA16, AGA-Net achieves DSC of 0.927 ± 0.011 (95% CI), outperforming nnU-Net by +3.8% DSC (p = 0.0012), SCAFFOLD by +2.4% DSC (p = 0.0034), and EfficientNet-B3 by +3.3% AUC (p = 0.0008) with ECE improvement of –0.055 (p = 0.0015). On LIDC-IDRI, AGA-Net achieves DSC of 0.915 ± 0.014, surpassing nnU-Net by +3.7% (p = 0.0018) and EfficientNet-B3 by +3.1% AUC (p = 0.0014) with ECE improvement of –0.051 (p = 0.0023). On NSCLC-Radiomics, AGA-Net achieves DSC of 0.903 ± 0.018, exceeding nnU-Net by +3.6% (p = 0.0031) and EfficientNet-B3 by +3.1% AUC (p = 0.0028) with ECE improvement of –0.053 (p = 0.0041). All reported improvements are statistically significant at p < 0.05, confirming the reliability of the observed performance gains across all metrics and datasets.

4.9 Enhanced ablation studies

To thoroughly evaluate the individual contributions of our key components, we conduct comprehensive ablation studies focusing on GCAM geometric constraints and MUQ-Net uncertainty modules. Table 10 presents the detailed ablation results for both the Geometric-Constrained Attention Module and the Multi-Scale Uncertainty Quantification Network.

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Table 10. Combined ablation study: GCAM geometric constraints and MUQ-Net uncertainty quantification.

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For the GCAM module, the geometric constraint function provides substantial improvements (+5.4% DSC) over baseline attention mechanisms, while the adaptive radius parameter contributes an additional +1.2% DSC improvement by dynamically adjusting to nodule size variations. For the MUQ-Net module, the Monte Carlo Dropout mechanism provides the largest single improvement in calibration quality (ECE reduction from 0.147 to 0.089), while ensemble methods contribute significantly to overall accuracy and reliability. The incremental addition of multi-scale features and heteroscedastic loss further improves both classification accuracy (AUC from 0.923 to 0.951) and uncertainty calibration (ECE from 0.076 to 0.043).

4.10 Performance on extremely small nodules

To address the limitation regarding extremely small nodules (< 3 mm diameter), we conduct a dedicated evaluation using a subset of 287 nodules from the LUNA16 dataset categorized by size.

As shown in Table 11, performance on extremely small nodules (< 3 mm) shows significant degradation (DSC = 0.782) compared to larger nodules. This validates our limitation statement and indicates the need for specialized approaches for tiny nodule detection as in Fig 10.

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Table 11. Performance analysis by nodule size.

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Fig 10. Performance analysis showing the relationship between nodule size and segmentation accuracy, highlighting challenges with extremely small nodules (<3mm diameter).

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4.11 Morphology-based subgroup analysis

To validate the spherical assumption underlying GCAM, we conduct a subgroup analysis across different nodule morphologies in the LIDC-IDRI and NSCLC-Radiomics datasets. Nodule morphology is categorized using LIDC-IDRI radiologist annotations for sphericity ratings and margin characteristics, supplemented by radiomics shape features (sphericity index, elongation, flatness) extracted using PyRadiomics. Four morphological categories are defined: spherical/round (sphericity index ≥ 0.85), semi-spherical (0.65 ≤ sphericity < 0.85), spiculated/irregular (sphericity < 0.65 with high margin irregularity), and pleural-attached (proximity ≤ 2 mm to the pleural surface).

On the LIDC-IDRI dataset, GCAM achieves DSC of 0.943 for spherical nodules (312 cases), 0.921 for semi-spherical nodules (289 cases), 0.878 for spiculated/irregular nodules (187 cases), and 0.864 for pleural-attached nodules (128 cases). On NSCLC-Radiomics, the corresponding DSC values are 0.934 (118 cases), 0.908 (137 cases), 0.861 (98 cases), and 0.847 (69 cases). The performance degradation from spherical to spiculated morphology is 6.5% on LIDC-IDRI and 7.3% on NSCLC-Radiomics, while pleural-attached nodules show 7.9% and 8.7% degradation respectively. This resilience is attributed to the adaptive fusion strategy in Equation 13, where the learnable weights , , automatically reduce the geometric attention contribution for non-spherical nodules and increase reliance on spatial and channel attention. The uncertainty quantification module appropriately reflects this morphological challenge, with ECE increasing from 0.038 for spherical to 0.091 for pleural-attached nodules on LIDC-IDRI.

To quantify when the geometric prior helps versus hinders, we compare GCAM against standard CBAM across morphology categories on LIDC-IDRI. GCAM outperforms CBAM by +4.6% DSC (p < 0.001) for spherical nodules, + 3.2% (p < 0.001) for semi-spherical, + 0.7% (p = 0.042) for spiculated, and +0.2% (p = 0.318) for pleural-attached nodules. Critically, GCAM never degrades performance compared to CBAM in any morphological category, confirming that the adaptive fusion mechanism prevents the geometric prior from biasing attention in challenging cases.

4.12 Feedback loop stability and error propagation analysis

The adaptive radius and center estimation in GCAM depend on the initial segmentation output, which is itself influenced by the geometric attention mechanism, creating a potential feedback loop. To address concerns about instability and artificially inflated performance, we conduct three complementary analyses on the LUNA16 dataset.

4.13 Comparison with state-of-the-art attention mechanisms

Table 12 provides detailed comparison between GCAM and conventional attention mechanisms on lung nodule segmentation.

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Table 12. Comprehensive attention mechanism comparison.

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The key differentiators of GCAM are:

• Domain-Specific Geometric Constraints: Unlike conventional attention mechanisms that apply generic spatial or channel attention, GCAM incorporates lung nodule morphology through spherical constraints.
• Adaptive Radius Parameter: The learned parameter adapts to nodule size variations, providing +2.4% DSC improvement over fixed geometric constraints.
• Multi-Modal Fusion: GCAM combines spatial, channel, and geometric attention through learnable fusion weights, achieving optimal balance for medical imaging tasks.

4.14 Enhanced federated learning analysis

4.14.1 Communication overhead analysis.

The federated aggregation in Equation 36 provides significant communication efficiency improvements:

(36)

Table 13 demonstrates the communication efficiency of our approach:

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Table 13. Communication overhead analysis.

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4.14.2 Privacy noise impact analysis.

The differential privacy mechanism introduces calibrated noise affecting model performance as in Table 14:

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Table 14. Privacy noise impact on model performance.

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4.15 Privacy-performance trade-off analysis

Fig 11 illustrates the trade-off between privacy protection and model performance across different privacy budgets.

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Fig 11. Privacy-performance trade-off curves showing AUC and DSC decay under different privacy budgets .

Lower values provide stronger privacy guarantees but reduce model performance.

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The privacy-utility trade-off can be mathematically expressed as:

(37)

where is the baseline performance, and are empirically determined constants (0.023 and 0.041 respectively for our experiments).

4.16 Corrected federated regularization loss

The federated regularization term should incorporate differential privacy noise as implemented in Algorithm 1:

(38)

where is the differential privacy regularization weight (set to 0.01 in our experiments) and represents the added privacy noise.

The complete loss function becomes:

(39)

4.17 Detailed federated learning parameters

Table 15 provides comprehensive federated learning parameter specifications:

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Table 15. Detailed federated learning parameters.

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5.1 Key contributions and clinical impact

The experimental results demonstrate several key advantages of our approach that directly translate to clinical benefits. The superior segmentation accuracy achieved through the Geometric-Constrained Attention Module (GCAM) significantly improves boundary delineation by incorporating geometric priors specific to lung nodules. This advancement builds upon recent work by Wang et al. [3] and extends beyond traditional attention mechanisms by incorporating domain-specific geometric constraints that are particularly effective for spherical nodule structures.

The robust classification performance with uncertainty quantification provided by MUQ-Net addresses a critical gap identified in recent surveys [10]. Unlike existing approaches that provide only point estimates, our uncertainty-aware framework provides reliable confidence measures that correlate well with actual prediction accuracy, as evidenced by the low Expected Calibration Error values across all datasets. This capability is essential for clinical radiologists who require confidence estimates to guide their diagnostic decisions, particularly in challenging cases where the distinction between benign and malignant nodules is ambiguous.

The consistent cross-dataset performance indicates superior generalization capabilities compared to recent state-of-the-art methods [5,37]. This robustness is essential for real-world clinical deployment where imaging protocols and patient populations vary significantly across institutions. The federated learning framework enables collaborative model improvement while maintaining strict privacy protections, addressing regulatory requirements that often prevent data sharing in healthcare applications.

5.2 Federated learning advantages

The federated learning implementation provides several distinct advantages over recent centralized approaches reported in the literature [2,4]. Our privacy-preserving mechanisms ensure that sensitive patient data never leaves the originating institution, addressing regulatory and ethical concerns that are becoming increasingly important in healthcare AI deployment. The collaborative training process enables the development of more robust and generalizable models by leveraging diverse datasets from multiple institutions without compromising patient privacy.

The communication efficiency achieved through our federated optimization strategy reduces bandwidth requirements and training time compared to baseline federated algorithms, addressing challenges identified by Lee et al. [6]. This improvement is particularly important for healthcare institutions with limited network infrastructure or strict data transfer policies. The differential privacy guarantees provide formal privacy protections while maintaining model utility, striking an appropriate balance for clinical applications.

The ability to handle non-IID data distributions across clients addresses a fundamental challenge in federated healthcare scenarios where institutional differences in patient populations, imaging protocols, and annotation standards create significant heterogeneity. Our adaptive aggregation strategy helps mitigate these challenges while maintaining overall model performance, representing an advancement over current federated medical imaging approaches.

The federated learning simulation incorporates realistic data heterogeneity through a Dirichlet distribution with concentration parameter . The data distribution at each client k follows:

(40)

where is a vector of ones with length C (number of classes), and smaller values of indicate higher data heterogeneity. The class distribution for client k is determined by sampling from this Dirichlet distribution, creating realistic non-IID scenarios that mirror real-world federated healthcare environments where different institutions may have varying patient populations and case distributions.

We systematically evaluate performance across different heterogeneity levels by varying from 0.1 (extreme heterogeneity) to 10.0 (near-IID conditions). Table 16 presents comprehensive performance analysis under different non-IID conditions, demonstrating the robustness of our AGA-Net framework across varying degrees of data heterogeneity.

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Table 16. Comprehensive performance analysis under different Dirichlet concentration parameters across all datasets.

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The analysis reveals several key insights about the relationship between data heterogeneity and model performance. Under extreme heterogeneity conditions (), the framework maintains reasonable performance with DSC of 0.891 and AUC of 0.923, demonstrating robustness to significant data distribution skew. The data skew metric, calculated as the coefficient of variation of class distributions across clients, shows values ranging from 0.847 under extreme conditions to 0.089 under near-IID conditions. The geometric constraints in GCAM provide stability across heterogeneity levels by ensuring consistent attention to nodule-relevant features regardless of local data distribution variations.

Communication efficiency decreases under higher heterogeneity due to increased gradient divergence between clients, requiring more communication rounds for convergence. The efficiency metric is calculated relative to the near-IID baseline (), showing that extreme heterogeneity reduces efficiency to 0.69x while moderate heterogeneity maintains 0.92x efficiency. The client standard deviation measures performance variance across participating clients, indicating that heterogeneity increases inter-client performance disparity from 0.008 under IID conditions to 0.048 under extreme heterogeneity.

Note on Communication Efficiency: The term represents the relative communication efficiency of the proposed framework compared to the near-IID baseline scenario. Specifically, it indicates that the model converges faster and requires only 85% of the communication rounds needed by the baseline approach to achieve similar accuracy. For example, if the baseline model converges in 100 rounds, a result of means the proposed method achieves convergence in approximately 85 rounds. This demonstrates improved training efficiency and reduced communication overhead in federated learning environments.

Fig 12 illustrates the performance trends across different values, showing the trade-off between data heterogeneity and model performance. The geometric attention mechanism demonstrates particular resilience to heterogeneity, with segmentation performance degrading more gracefully than classification performance under extreme conditions.

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Fig 12. Performance analysis under different Dirichlet concentration parameters showing the relationship between data heterogeneity and model performance.

Left: Segmentation DSC and Classification AUC trends. Center: Communication efficiency and convergence rounds. Right: Client performance variance and calibration quality (ECE).

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The uncertainty quantification capabilities remain well-calibrated across different heterogeneity levels, with ECE values ranging from 0.043 under IID conditions to 0.067 under extreme heterogeneity. This consistency is attributed to the geometric constraints that provide structural stability to the uncertainty estimation process, ensuring reliable confidence estimates even when local data distributions vary significantly across clients.

5.3 Uncertainty quantification benefits

The uncertainty quantification capabilities provide several clinical benefits that extend beyond simple accuracy improvements demonstrated by recent work [8,38]. The calibrated confidence estimates enable radiologists to prioritize cases requiring immediate attention and identify instances where the model’s predictions may be unreliable. This capability is particularly valuable in screening scenarios where the goal is to efficiently triage large numbers of cases while minimizing false negatives.

The distinction between aleatoric and epistemic uncertainty provides additional insights into the sources of prediction uncertainty that are not available in current state-of-the-art methods [7,18]. Aleatoric uncertainty reflects inherent noise in the data or annotation ambiguity, while epistemic uncertainty indicates regions where the model lacks sufficient training data. This distinction helps guide data collection strategies and model improvement efforts in clinical settings.

The ensemble-based approach provides robust uncertainty estimates while maintaining computational efficiency through optimized inference procedures. Unlike approaches that require multiple model training runs [21,22], our Monte Carlo Dropout implementation enables uncertainty estimation without significant computational overhead, making the approach practical for deployment in resource-constrained environments.

5.4 Clinical decision-making with uncertainty quantification

To demonstrate the practical clinical utility of our uncertainty quantification framework, we conduct a decision-level analysis simulating radiologist workflow integration on the LIDC-IDRI test set. Three clinical action zones are defined based on prediction confidence: auto-accept for high-confidence benign predictions ( and ), requiring no radiologist review; radiologist review for moderate uncertainty cases ( or ); and priority referral for high-confidence malignant predictions () or high-uncertainty cases ().

The auto-accept zone captures 38.8% of cases with 96.7% accuracy and only 0.3% missed malignancy rate, enabling substantial workload reduction. The radiologist review zone encompasses 41.7% of cases with 85.4% accuracy, appropriately flagging ambiguous cases for expert evaluation. The priority referral zone covers 19.5% of cases with 91.2% accuracy and 93.4% sensitivity. Overall, the uncertainty-based triage reduces the false-negative rate from 5.7% (without triage, where all cases receive uniform attention) to 2.8% by concentrating radiologist attention on ambiguous and high-risk cases, while achieving 38.8% workload reduction.

Three representative cases illustrate this framework in practice. Case A involves a 6 mm round nodule with low uncertainty () and confident benign prediction (), correctly routed to auto-accept. Case B presents a 9 mm part-solid nodule with elevated uncertainty () and ambiguous prediction (), appropriately flagged for radiologist review where ground truth confirmed malignancy. Case C involves a 12 mm spiculated nodule with high malignancy probability () and moderate uncertainty () due to irregular morphology, correctly triggering priority referral. These cases demonstrate that uncertainty estimates provide clinically meaningful information correlating with pathological difficulty, enabling a decision-support framework that improves both efficiency and diagnostic safety.

5.5 Geometric constraints innovation

The incorporation of geometric constraints represents a significant advancement over recent attention-based approaches [9,14]. While current methods apply generic attention mechanisms, our domain-specific geometric constraints leverage knowledge about lung nodule morphology to provide more accurate segmentation results. The spherical assumption for lung nodules, while simplified, provides valuable constraints that improve segmentation accuracy and reduce false positive rates compared to methods that do not incorporate such domain knowledge.

The integration of geometric constraints with attention mechanisms creates a synergistic effect where the attention module focuses on geometrically plausible regions while the geometric constraints provide structural guidance. This combination is particularly effective for challenging cases where traditional attention mechanisms may be misled by similar-appearing structures or imaging artifacts, addressing limitations identified in recent work [11,12].

The learned geometric parameters provide interpretable insights into the model’s decision-making process, enabling radiologists to understand and validate the model’s reasoning. This interpretability is crucial for clinical acceptance and regulatory approval of AI systems in healthcare, representing an advantage over black-box approaches prevalent in current literature [30,31].

5.6 Limitations and future directions

While our method shows promising results compared to recent state-of-the-art approaches [13,28], several limitations warrant acknowledgment and future investigation. The geometric constraints assume approximately spherical nodule shapes, which may not hold for highly irregular or spiculated nodules that are common in malignant cases. Future work should explore more sophisticated geometric models that can accommodate greater morphological diversity while maintaining computational efficiency.

The performance on extremely small nodules (less than 3 mm diameter) requires further optimization, as these represent some of the most challenging cases for both human radiologists and automated systems. Recent work by Cai et al. [20] has addressed tiny nodule detection, but the integration of uncertainty quantification and federated learning in such scenarios remains an open challenge.

While our edge benchmarks demonstrate deployment feasibility on current hardware, further optimization through model pruning, knowledge distillation, and edge-specific neural architecture search could improve latency for real-time applications. Additionally, energy measurements represent single-scan processing; continuous monitoring scenarios would require dedicated power management strategies for battery-operated IoT devices.

Our morphology-based subgroup analysis confirms that while the spherical assumption provides the greatest benefit for round nodules, the adaptive fusion mechanism ensures graceful degradation for irregular morphologies. Future work should explore deformable geometric priors such as ellipsoidal or superquadric models that can better accommodate spiculated and pleural-attached nodules.

The clinical validation presented in this work is based on retrospective dataset analysis, and prospective clinical trials are needed to validate the real-world effectiveness and clinical utility. Integration with clinical workflow systems and validation of the uncertainty estimates in actual clinical decision-making scenarios represent important next steps, building upon the foundation established by recent clinical studies [15,16]. Regarding dataset scale, we acknowledge that the three benchmarks used—LUNA16 (888 scans), LIDC-IDRI (1,018 scans), and NSCLC-Radiomics (422 scans)—while standard in the lung nodule analysis literature, are relatively modest in absolute size compared to large-scale imaging registries. Future work should evaluate AGA-Net on larger and more geographically diverse datasets to further substantiate generalization. Additionally, the IoT terminology used throughout this work specifically refers to healthcare edge devices (e.g., NVIDIA Jetson-class platforms) operating within hospital or clinic network environments as inference endpoints in a federated learning pipeline, consistent with the healthcare IoT edge deployment paradigm. The federated learning framework itself constitutes the networked, distributed system-level component, while individual edge devices serve as local inference and training nodes.

While our realistic federated deployment analysis demonstrates resilience under challenging conditions, the simulations remain controlled laboratory evaluations. Future work should include pilot deployments in actual multi-institutional healthcare networks with heterogeneous infrastructure to fully validate practical IoT suitability.

5.7 Broader impact and future applications

The proposed framework has broader implications beyond lung nodule analysis and could be adapted to other medical imaging tasks that involve approximately spherical or geometric structures. The success of attention-based approaches in recent work [17,32] suggests that our geometric attention framework could be beneficial for applications in breast cancer detection, brain tumor analysis, and liver lesion characterization.

The federated learning approach demonstrates the feasibility of privacy-preserving collaborative AI development in healthcare, potentially enabling the creation of global medical AI models that leverage diverse datasets while respecting patient privacy and regulatory requirements. This paradigm could accelerate medical AI development and improve healthcare outcomes worldwide, addressing challenges identified in recent comprehensive surveys [33,34].

The uncertainty quantification framework provides a template for developing clinically responsible AI systems that provide appropriate confidence estimates and acknowledge their limitations. This approach could help address the “black box” criticism of deep learning systems and facilitate regulatory approval and clinical adoption, representing a significant advancement over current approaches that lack uncertainty awareness [35,36].