Geometric-Structural Dual-Guided Network

• The paper introduces GSD-Net, a framework that leverages geometric and structural cues to robustly segment medical images despite annotation noise.
• It employs a Geometric Distance-Aware module, a Structure-Guided Label Refinement module, and a Knowledge Transfer module to address both simulated and real-world label inconsistencies.
• Comprehensive evaluations across diverse datasets show significant Dice score improvements, validating its effectiveness and efficiency in handling noisy annotations.

Geometric-Structural Dual-Guided Network (GSD-Net) is a noise-robust medical image segmentation framework introduced in “From Noisy Labels to Intrinsic Structure: A Geometric-Structural Dual-Guided Framework for Noise-Robust Medical Image Segmentation” (Wang et al., 2 Sep 2025). It is designed for the setting in which convolutional neural networks depend on large-scale, high-quality annotations, yet medical segmentation labels are often noisy because of subjectivity, coarse delineations, low contrast, modality-specific artifacts, and ambiguous boundaries. GSD-Net integrates geometric and structural cues through a Geometric Distance-Aware module, a Structure-Guided Label Refinement module, and a Knowledge Transfer module, with the stated aim of improving robustness against both simulated label noise and real-world multi-expert inconsistency in medical image segmentation (Wang et al., 2 Sep 2025).

1. Problem setting and noise model

Medical image annotation is costly and time-consuming, and even expert-labeled datasets inevitably contain noise arising from subjectivity and coarse delineations. The problem is particularly acute in segmentation because the noise is spatially localized and structure-dependent, especially near boundaries, rather than behaving like instance-level label noise in classification. The reported sources of ambiguity include CT motion, MRI Rician noise and inhomogeneity, ultrasound speckle and shadowing, and generally ambiguous boundaries in low-contrast images (Wang et al., 2 Sep 2025).

The framework is explicitly motivated by three simulated noise types and by real-world multi-expert variability. The simulated types are foreground-reducing noise (SR), foreground-expanding noise (SE), and morphology-based dilation/erosion (SDE). SR simulates under-annotation through Markov-based boundary perturbations that distort contours inward and reduce foreground extent; SE simulates over-annotation through similar perturbations biasing outward and expanding foreground extent; SDE applies uniform morphological operations and is described as less realistic because of its uniformity across the mask. The Markov-based perturbations follow Yao et al. (2023) and are intended to capture irregular boundary errors rather than uniform deformation.

For real-world noise, LIDC and MMIS-2024 are treated as multi-rater datasets in which one expert label per image is sampled during training. This “Sample” setting is used to reflect inter-observer subjectivity and inconsistency and to mimic realistic data collection without aggregating to consensus. A plausible implication is that GSD-Net is targeted less at adversarial corruption than at annotation uncertainty concentrated around anatomical or lesion boundaries.

2. Architectural organization and training-time design

GSD-Net uses U-Net for 2D tasks and 3D U-Net for BraTS2020, and the proposed modules are placed at training time around the segmentation models rather than altering backbone parameters or the segmentation head (Wang et al., 2 Sep 2025). The central training configuration is a dual-model co-regularization scheme with two segmentation networks, $f_{\theta_1}$ and $f_{\theta_2}$, trained jointly under weak augmentations. Predictions are co-regularized through symmetric KL divergence and filtered by small-loss selection to form a reliable clean pixel subset.

The three core modules are functionally distinct. The Geometric Distance-Aware (GDA) module computes a distance-to-boundary weighting map from the noisy annotation $nGT$ and uses it to upweight pixels far from likely-noisy boundaries while downweighting near-boundary pixels. The Structure-Guided Label Refinement (SGLR) module generates pseudo-labels by stochastically fusing the two networks’ soft predictions and imposing SLIC superpixel structural priors, thereby filling the complement of the clean subset that would otherwise be discarded by small-loss selection. The Knowledge Transfer (KT) module performs cross-image regional mixing through random masks that swap local foreground or background patches between paired images, with losses computed on the mixed samples using CE, Dice, and a weighted symmetric KL term.

The resulting data flow is staged. Each input $x$ is weakly augmented to $x' = A(x)$; both models predict on $x$ and $x'$; supervised CE losses to $nGT$ and symmetric KL consistency are computed; small-loss selection retains $\mathbb{D}^{clean}$; GDA computes geometric weights from $nGT$ and the epoch index; SGLR fuses predictions with a random $f_{\theta_2}$0 and SLIC superpixels to generate pseudo-labels $f_{\theta_2}$1 for pixels not in $f_{\theta_2}$2; KT forms mixed images and corresponding labels and weights; and the total loss updates both networks. This suggests a forward-collaborative training pipeline in which supervision is first filtered, then reweighted, then structurally repaired, and finally diversified through regional transfer.

3. Mathematical formulation

The formulation uses $f_{\theta_2}$3, or $f_{\theta_2}$4 for volumetric data, with noisy annotations $f_{\theta_2}$5, pixel index set $f_{\theta_2}$6, and selected clean subset $f_{\theta_2}$7 (Wang et al., 2 Sep 2025). Weak augmentation is denoted by $f_{\theta_2}$8. The two predictions are $f_{\theta_2}$9 and $nGT$0.

The per-pixel supervised term is built from cross-entropy: $nGT$1 For the two-network setting, the supervised sum is

$nGT$2

Agreement is enforced through symmetric KL consistency: $nGT$3

Small-loss selection defines the clean subset by minimizing the combined supervised and consistency losses subject to a retention-rate schedule: $nGT$4

$nGT$5

Here $nGT$6 is set to the simulated noise rate for simulated datasets, and to $nGT$7 and $nGT$8 for LIDC and MMIS-2024 respectively, derived from $nGT$9 of foreground proportion.

The total objective is a direct sum,

$x$0

with no additional $x$1-weights in the reported formulation. The paper states that defaults yielded strong performance. A plausible implication is that the method emphasizes modular loss construction rather than careful balancing through extra hyperparameters.

4. Geometric and structural guidance

The GDA module uses a simple geometric cue: Euclidean distance to the annotation boundary $x$2, computed from the noisy label alone, without curvature, gradient, or skeletonization (Wang et al., 2 Sep 2025). Boundary pixels are defined by neighborhood disagreement,

$x$3

and the raw distance map is

$x$4

To avoid overemphasizing distant pixels, the distance is clipped and decayed with epoch: $x$5 with $x$6 for $x$7 images, $x$8 for $x$9, and $x' = A(x)$0. The weighted loss over clean pixels is

$x' = A(x)$1

The intended effect is to strengthen supervision in reliable interiors while suppressing contributions from boundary-adjacent pixels that are more susceptible to annotation errors.

The SGLR module provides structural guidance through stochastic dual-prediction fusion and SLIC superpixels. The fused soft prediction is

$x' = A(x)$2

SLIC is run as $x' = A(x)$3 with $x' = A(x)$4 and $x' = A(x)$5 for 2D data, defining superpixel regions $x' = A(x)$6. The method then assigns superpixel-consistent pseudo-labels through region-wise argmax. The paper explicitly notes that there is no explicit energy minimization or CRF; the regularization is imposed through superpixel-consistent argmax labeling guided by fused softmax. This is important because SGLR is a structural prior mechanism, not a post hoc graphical-model refinement stage.

The final pseudo-labels combine clean regions from $x' = A(x)$7 with SGLR-refined labels on the complement of the clean subset. In effect, small-loss selection identifies pixels that are likely trustworthy, and SGLR recovers supervision in regions that small-loss filtering would otherwise discard. This suggests that the structural prior is used not to replace noisy labels globally, but to selectively repair the supervision field where noise is most likely.

5. Knowledge transfer and optimization pipeline

The KT module is defined as a cross-image local region mixing strategy rather than teacher-student distillation or feature-level attention transfer (Wang et al., 2 Sep 2025). For two images $x' = A(x)$8 and $x' = A(x)$9 and binary masks $x$0 and $x$1, the mixed image, label, and geometric weight map are formed as

$x$2

$x$3

$x$4

Foreground or background regions are sampled probabilistically and swapped between random image pairs to enrich supervision diversity and improve sensitivity to local details.

Losses on transferred samples use CE and Dice with geometric weights. Dice is defined by

$x$5

The transferred-sample losses $x$6 are computed separately for the original and augmented pair sets, and weighted consistency on transferred samples is encoded in $x$7 through KL terms modulated by the mixed geometric weights. The overall optimization therefore couples standard supervised segmentation, agreement-based co-regularization, geometry-aware reweighting, structural pseudo-label refinement, and region-level transfer augmentation in a single end-to-end training loop.

The training algorithm is reported in textual form. Two networks are initialized; for each epoch $x$8, images are weakly augmented, forwarded through both models, and used to compute supervised CE and symmetric KL losses; $x$9 is selected via the small-loss criterion; GDA weights are computed from $x'$0 and the epoch index; SGLR runs SLIC and fuses predictions with random $x'$1 to obtain refined labels; KT samples paired images and performs masked swaps and corresponding loss computations; and finally $x'$2 and $x'$3 are optimized with $x'$4. In implementation, the framework uses PyTorch, SGD with learning rate $x'$5 and weight decay $x'$6, $x'$7 epochs, batch size $x'$8 for 2D U-Net, batch size $x'$9 for 3D U-Net, and NVIDIA RTX 4090 24 GB hardware.

6. Datasets, evaluation, and empirical behavior

The evaluation covers six publicly available datasets: Kvasir-SEG for endoscopy polyp segmentation, Shenzhen for X-ray lung segmentation, BU_SUC for ultrasound breast tumor segmentation, BraTS2020 for MRI glioma segmentation, LIDC for CT lung nodules with four annotators, and MMIS-2024 for multi-center MRI nasopharyngeal carcinoma segmentation with multi-expert annotation (Wang et al., 2 Sep 2025). For simulated noise, SDE uses uniform dilation or erosion of ground-truth masks, while SR and SE use Markov-based boundary perturbations to produce irregular boundary distortions that are stated to be more representative of clinician drawing variability than uniform morphology.

The primary metric is Dice coefficient. For simulated noise experiments, results are reported as mean $nGT$0 std across trials, with the final 10 epochs averaged. Under SR simulated noise, the reported improvements over the best competing method are $nGT$1 on Kvasir, $nGT$2 on Shenzhen, $nGT$3 on BU_SUC, and $nGT$4 on BraTS2020. The full simulated-noise Dice results for GSD-Net are:

• Kvasir: $nGT$5 (SR), $nGT$6 (SE), $nGT$7 (SDE)
• Shenzhen: $nGT$8 (SR), $nGT$9 (SE), $\mathbb{D}^{clean}$0 (SDE)
• BU_SUC: $\mathbb{D}^{clean}$1 (SR), $\mathbb{D}^{clean}$2 (SE), $\mathbb{D}^{clean}$3 (SDE)
• BraTS2020: $\mathbb{D}^{clean}$4 (SR), $\mathbb{D}^{clean}$5 (SE), $\mathbb{D}^{clean}$6 (SDE)

On the multi-expert datasets, the reported mean Dice is $\mathbb{D}^{clean}$7 for LIDC and $\mathbb{D}^{clean}$8 for MMIS-2024 under the “Sample, 100% images” setting. The paper states that GSD-Net outperforms multi-rater baselines such as D-Persona under comparable or higher annotation-cost settings.

The ablation study on Kvasir isolates the contribution of each module. Baseline JoCoR yields $\mathbb{D}^{clean}$9 (SR), $nGT$0 (SE), and $nGT$1 (SDE). Adding GDA gives $nGT$2, $nGT$3, and $nGT$4; adding label refinement gives $nGT$5, $nGT$6, and $nGT$7; adding SGLR gives $nGT$8, $nGT$9, and $f_{\theta_2}$00; adding KT gives $f_{\theta_2}$01, $f_{\theta_2}$02, and $f_{\theta_2}$03; and the full configuration, GDA+SGLR+KT, yields $f_{\theta_2}$04, $f_{\theta_2}$05, and $f_{\theta_2}$06. The qualitative interpretation given in the paper is that the modules are complementary, with visualizations showing improved adherence to true boundaries, preservation of fine structures, and progressively improved focus on lesion boundaries and anatomically meaningful regions in Grad-CAM outputs.

7. Efficiency, robustness, limitations, and reproducibility

The framework’s parameter count and FLOPs are reported as unchanged relative to the chosen backbones, because the added components operate at the training-loss level and through pre-processing or post-processing steps such as distance transforms, SLIC, and mask mixing (Wang et al., 2 Sep 2025). GDA adds a distance transform from $f_{\theta_2}$07 and per-pixel reweighting with negligible memory overhead for a single weight map. SGLR adds SLIC superpixel computation and argmax aggregation, with modest CPU or GPU overhead depending on implementation. KT adds region mixing and extra forwards on mixed samples, but remains within typical training bounds. The paper does not report precise training or inference time, or memory footprints, and states only that the empirical overhead is modest and does not hinder convergence.

The robustness analysis emphasizes boundary noise sensitivity and small structures. GDA suppresses potentially mislabeled boundary pixels early in training under SR, SE, and SDE. Superpixel-guided refinement helps recover supervision in small or low-contrast regions that may be mistakenly filtered by small-loss selection. Calibration metrics are not reported, but the paper notes that Grad-CAM visuals show improved structural focus, fewer spurious contours, and better local-detail sensitivity. At the same time, failure cases and trade-offs are acknowledged: if $f_{\theta_2}$08 boundaries are severely corrupted, the initial GDA weights may misguide loss reweighting; excessively aggressive superpixel parameters could over-smooth fine boundary details.

The reported limitations are specific. Current evaluation focuses on binary tasks, and multi-class noise simulation is described as harder because of inter-class overlaps. Robustness under extreme noise, defined as more than $f_{\theta_2}$09 of pixels corrupted near boundaries, may be limited; stronger structural models or anatomical priors such as topology constraints or CRFs are suggested as possible extensions. Modality generalization is described as strong across endoscopy, X-ray, ultrasound, MRI, and CT, but further multi-center clinical validation is stated to be warranted.

Reproducibility information is comparatively detailed. The code is available at the reported repository, the implementation uses U-Net or 3D U-Net with standard channels, SGD with learning rate $f_{\theta_2}$10 and weight decay $f_{\theta_2}$11, batch sizes $f_{\theta_2}$12 and $f_{\theta_2}$13 for 2D and 3D settings, GDA thresholds $f_{\theta_2}$14 for $f_{\theta_2}$15 and $f_{\theta_2}$16 for $f_{\theta_2}$17, SGLR with SLIC($f_{\theta_2}$18, $f_{\theta_2}$19) and $f_{\theta_2}$20, and KT with random region masks sampling foreground or background proportional to target area. Seeds are not explicitly reported; to mitigate variance, the paper averages across the final 10 epochs for simulated-noise experiments.