GRIPNet: Gaussian Radial Intensity Prior Guided Architecture for Pulmonary Nodule Detection in CT

• Micro-nodules below 6 mm achieve only 65–75% sensitivity in routine reading, while conventional extractors also struggle with faint-margin ground-glass opacities.Source: §I · p. 1
• Gaussian fitting shows peak intensity at the nodule center with radial attenuation, but square convolutions are mismatched to these gradients, particularly for small nodules.Source: §I · p. 1, Figure 1 · p. 1
• GRIPNet maps measurable intensity properties to pinwheel convolutions, dual-frequency processing, dilated masked attention, and adaptive loss on a YOLOv11 backbone.Source: §I · p. 1
• 89.2% mAP@0.75 is reached on KanserSet at real-time throughput, with consistent improvement over strong and lung-nodule-specific baselines.Source: §I · pp. 1–2

• The protocol extracts concentric-annulus HU profiles around each bounding-box centroid, fits a Gaussian by nonlinear least squares, and estimates amplitude, spread, and R2.Source: §III · p. 2
• Mean radial R2 exceeds 0.86 in every benchmark stratum, and more than 89% of nodules exceed R2=0.70.Source: §III · p. 2
• The radial spread scales with lesion diameter, from about 3 pixels for sub-6 mm nodules to 12 pixels for nodules larger than 15 mm.Source: §III · p. 2
• The measured regularity is attributed to a dense central core and partial-volume averaging that produces values declining with distance.Source: §III · p. 2
• The prior motivates asymmetric operators for radial gradients and explicit frequency separation between the smooth Gaussian envelope and high-frequency boundary irregularities.Source: §III · p. 2

• GRIPNet implements four prior-derived modules on a YOLOv11 backbone with progressive downsampling and feature fusion at P3–P5.Source: §IV · p. 2
• Pinwheel Convolution uses four directionally padded asymmetric branches to capture radial gradients that standard 3 × 3 convolution may miss.Source: A. Pinwheel Convolution for Radial… · p. 2
• The branch outputs are concatenated and refined by a 2 × 2 convolution before PWConv is used at stride-2 downsampling stages.Source: A. Pinwheel Convolution for Radial… · p. 2
• The four branches reconstruct the radial field with 22% fewer parameters and a 177% larger receptive field than a 3 × 3 convolution.Source: A. Pinwheel Convolution for Radial… · p. 2

B. Dual-Frequency Feature Decomposition

• The high-frequency path targets spiculations, lobulations, and calcifications, while the low-frequency path represents the smooth Gaussian envelope.Source: B. Dual-Frequency Feature Decomposition · p. 2
• Table I reports radial-fit statistics across three benchmarks, including R2, mean spread, and the fraction of nodules with R2 > 0.70.Source: Table I · p. 3, B. Dual-Frequency Feature Decomposition · p. 3
• DualFreqC3k2 separates high-frequency morphology from low-frequency context at P4 and P5 within GRIPNet’s multi-scale architecture.Source: Figure 2 · p. 3, B. Dual-Frequency Feature Decomposition · p. 3

C. Dilated Masked Attention for Scale-Calibrated Fusion

• C2DTAB combines dilated grouped channel self-attention with masked-window self-attention that samples sparsely through even-coordinate positions.This design models inter-feature dependencies while reducing dense-attention cost.Source: C. Dilated Masked Attention for… · pp. 3–4
• A 3 × 3 feed-forward window expands to 7 × 7 with dilation rate d=2, covering the 3σ range of 6 to 15 mm nodules.The module replaces C2PSA in the neck.Source: C. Dilated Masked Attention for… · p. 4
• The attention design aggregates peripheral context across the Gaussian envelope without incurring the quadratic cost of dense attention.Source: C. Dilated Masked Attention for… · p. 4

D. Scale-Adaptive Detection Heads

• At P3, Efficient Multi-scale Attention emphasizes micro-nodule boundary detail, whereas at P5 it prioritizes context separating large masses from confluent vessels.The module splits inputs into eight groups and preserves PWConv’s orthogonal gradient components.Source: D. Scale-Adaptive Detection Heads · p. 4
• Efficient Multi-scale Attention splits each input into eight groups processed by parallel spatial and convolutional pathways with softmax-normalized weights.A sigmoid gate combines the pathway outputs.Source: D. Scale-Adaptive Detection Heads · p. 4, Figure 4 · p. 4

E. Adaptive Loss with Dynamic Difficulty Tracking

• EWMASlide dynamically tracks prediction IoU with threshold µt and shifts sample emphasis toward challenging examples as training progresses.The loss uses an exponentially weighted moving average rather than a fixed difficulty threshold.Source: E. Adaptive Loss with Dynamic… · p. 4
• The WiseIoU regression penalty uses centroid distance, matching nodules whose Gaussian peak defines a natural center; the unified objective sets λcls=1.0 and λbox=0.05.Source: E. Adaptive Loss with Dynamic… · p. 4

Datasets and implementation

• The evaluation uses KanserSet, LUNA16, and Lung-PET-CT-Dx, covering lesions, radiologist-annotated nodules, and four histological subtypes.Training uses PyTorch 2.1.0 on an NVIDIA RTX 4090 with SGD and cosine annealing.Source: A. Datasets and Implementation · p. 4
• Augmentation preserves the radial prior through rotation, scaling, flipping, scanner-related brightness shifts, contrast scaling, and mild Gaussian noise.Mosaic augmentation is excluded because it creates anatomically impossible layouts and disrupts contextual reasoning.Source: A. Datasets and Implementation · pp. 4–5

Benchmark comparison

• GRIPNet reaches the highest mAP@0.5 on all three benchmarks, scoring 95.3% on KanserSet and 97.9% on Lung-PET-CT-Dx.It also leads all six metrics on LUNA16.Source: B. Comparison with State-of-the-Art · p. 5, Table II · p. 5
• At mAP@0.75, GRIPNet reaches 89.2% on KanserSet while every other method remains below 79%.This is the clearest separation from the compared detectors.Source: B. Comparison with State-of-the-Art · p. 5, Table II · p. 5
• GRIPNet trails YOLOv8 in KanserSet recall, 89.9% versus 92.5%, while providing higher-IoU localization precision for measuring nodule extent.The comparison describes this as a trade-off between recall and localization precision.Source: B. Comparison with State-of-the-Art · p. 5
• MSDet is the strongest competitor on KanserSet and Lung-PET-CT-Dx, but GRIPNet leads it by 2.2 and 1.7 points of mAP@0.5.On LUNA16, GRIPNet leads MSDet and improved YOLOv11 by 1.1 points of mAP@0.5 while achieving 87.8% recall.Source: B. Comparison with State-of-the-Art · p. 5

Component ablation

• The EWMASlide curriculum and WiseIoU center penalty together raise full-model mAP@0.75 to 89.2%, whereas omitting the curriculum reduces it to 67.8%.The ablation attributes the localization gain to their combination rather than to the center penalty alone.Source: C. Ablation Study · p. 5, Table III · p. 6
• PWConv produces the sharpest single ablation gain, lifting mAP@0.5 to 92.0% on KanserSet.The sequential ablation also reports 92.9% for the EMA-augmented baseline and intermediate changes from DualFreqC3k2 and C2DTAB.Source: C. Ablation Study · p. 5, Table III · p. 6

Efficiency

• The prior-guided model increases parameters from 2.58 M to 4.94 M and GFLOPs from 6.3 to 8.5 versus YOLOv11.These added costs correspond to mAP@0.5 gains of 1.9 to 7.4 points.Source: D. Computational Efficiency · p. 6, Table IV · p. 6
• Throughput remains above real time at 230 to 309 FPS across the three benchmarks despite the added model complexity.Table IV reports FPS and mAP@0.5 in KanserSet / LUNA16 / Lung-PET-CT-Dx order.Source: D. Computational Efficiency · p. 6, Table IV · p. 6

Training behavior

• Training stabilizes in about 100 epochs on KanserSet, roughly 266 epochs on LUNA16, and near epoch 200 on Lung-PET-CT-Dx.The early oscillation is attributed to the adaptive threshold shifting during optimization.Source: E. Training Dynamics · p. 6

• The detector preserves tight boxes for faint sub-centimeter lesions, pleural or vessel-adjacent nodules, and four histological subtypes across the benchmarks.The reported behavior is attributed to WiseIoU center anchoring and dilated masked attention constrained to the Gaussian decay envelope.Source: F. Qualitative Analysis · p. 6, §VI · pp. 6–7
• GRIPNet’s feature maps progress from radial rim activation at P3, through a peri-nodular 3σ ring at P4, to bronchial and vascular context at P5 across all three datasets.P4 separates smooth interior structure from sharp spiculation and lobulation detail.Source: §VI · p. 6, G. Feature Map Analysis · p. 6, Figure 7 · p. 7
• Representative detections are shown across the three benchmarks under diverse imaging conditions, complementing the feature-map progression and localization analysis.Source: Figure 6 · p. 7
• The mAP@0.75 increase from 84.1% to 89.2% occurs only when EWMASlide and the center penalty act together, while neither component alone exceeds 80%.This ablation links high-IoU localization to jointly learning sample difficulty and center position.Source: §VI · p. 7
• GRIPNet’s 2D isotropic assumption can fail for strongly anisotropic nodules, and its KanserSet recall remains slightly below YOLOv8 despite high-IoU precision.The authors identify an ellipsoidal volumetric prior and a gentler difficulty schedule as possible next steps.Source: §VI · pp. 7–8

• GRIPNet reaches mAP@0.5 values of 95.3%, 91.6% and 97.9% on KanserSet, LUNA16 and Lung-PET-CT-Dx, respectively.The detector maps radial gradients, frequency structure, decay extent and lesion conspicuity to corresponding architectural or training components.Source: §VII · p. 8