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Geometric-to-Semantic Spherical Transfer Learning for Cortical Sulci Labeling
Saeb Tounsi, Joël Chavas, Pietro Gori, Vincent Frouin, Denis Rivière, Jean-François Mangin
TL;DR
Cortical sulci vary markedly across people, while exhaustive surface labeling is difficult with limited annotations and models that cover only a small subset of structures. The paper transfers locally learned geometric representations into a semantic labeling framework, which achieves the highest held-out mean Dice and shows its largest error reductions on variable, tertiary sulci.
Problem
Sulci vary substantially across individuals, while existing surface models often label only a subset and typically rely on much larger annotated cohorts than the 62-subject expert setting.
Source: §1 · p. 2Method
The framework pretrains a spherical encoder on unlabeled UK Biobank surfaces and uses a soft-initialized Topological Prior Injector to integrate sulcal lines into downstream labeling.
Source: §1 · p. 2, §2.2 · p. 4Results
The framework achieves the highest held-out mean Dice (0.77 ± 0.03), with the largest error reductions concentrated on small, highly variable sulci.
Source: §4 · pp. 6, 8Takeaways & Limitations
Localized geometric priors are presented as fundamental for surface-native neuroanatomy, with the largest identification-error reductions on highly variable, tertiary sulci.
Source: §5 · p. 9
Abstract
from arXiv · showhide
Deep learning on cortical surfaces faces a dilemma: capturing the complex topology of over 60 nomenclature-dependent sulci per hemisphere requires high-capacity models, yet the extreme scarcity of expert annotations ($N=62$ subjects) inevitably causes overfitting. Standard supervised approaches fail to generalize in this data-scarce regime, particularly for variable and small sulci where topological ambiguity is high. To overcome this limitation, we introduce a Geometric-to-Semantic Spherical Transfer Learning framework. First, we leverage massive unlabeled data (UK Biobank, $\approx$30,000 subjects) to pre-train a spherical encoder using a locally-optimized strategy. By relying solely on continuous surface features (curvature and depth), the relevance of this pre-training is confirmed by the model's ability to detect localized and rare topological traits, such as sulcal interruptions. The downstream labeling task, however, introduces extracted sulcal fundi (lines) as an explicit semantic input. To bridge this dimensional domain gap (from purely geometric to semantic) without causing catastrophic forgetting, these anatomical lines are integrated into the pre-trained backbone via a soft-initialized Topological Prior Injector. Our experiments demonstrate that this approach outperforms fully supervised baselines trained from scratch, achieving a mean Dice of 0.77. Crucially, a local analysis reveals that the self-supervised geometric priors yield the largest performance gains on variable and tertiary sulci (up to 14.8%), confirming that learning the cortex shape is highly beneficial for identifying its rarest parts.
1 Introduction
Cortical sulci vary substantially across individuals, and exhaustive surface labeling remains difficult because existing approaches often cover only a few sulci or require far more annotations than expert-driven datasets provide. The paper proposes spherical transfer learning to bring locally learned geometric features into comprehensive sulcal labeling.
1 Introduction
- Sulci vary substantially between individuals in morphology, location, length, and depth, yet they are important landmarks for brain mapping.Accurate identification is relevant to neurodevelopmental trajectories and functional-area localization.Source: §1 · pp. 1–2
- Earlier volumetric methods modeled fold topology from voxel-space skeletons, but volumetric representations can struggle to capture intrinsic cortical topology.Sulcal labeling has served both brain alignment and detailed morphometric studies, with the latter requiring high topological precision.Source: §1 · p. 2
- Cortical surface representations enable curvature and sulcal depth analysis on native geometry, supporting precise topographical labeling.The field shifted from volumetric approaches toward triangular-mesh representations for characterizing morphology and aligning anatomy.Source: §1 · p. 2
- Surface-based models still face limited sulcal coverage and high data demands, while foundation models lack native support for cortical surface topology.The target setting has 62 annotated subjects, compared with cohorts exceeding 1,400 used for robust performance in prior work.Source: §1 · p. 2
- The framework combines UK Biobank self-supervised pre-training with a soft-initialized Topological Prior Injector for exhaustive labeling in a 62-subject regime.Its surface-native pipeline projects expert volumetric knowledge onto the spherical mesh.Source: §1 · pp. 2–3, Figure 1 · p. 3
2 Proposed Methodology
The methodology prepares surface-native sulcal labels, learns localized spherical representations from unlabeled data, and transfers those representations into a semantic labeling model. A soft-initialized injector adapts the pretrained encoder to the downstream input while retaining its geometric features.
2.1 Data Preparation and Surface-Based Pipeline
- The pipeline extracts deep sulcal fundi from white-matter meshes and projects volumetric labels onto the lines using constrained geodesic Voronoi propagation.The propagation is limited by the white-matter mask and a 3.5 mm maximum geodesic distance.Source: §2.1 · p. 3
- Native meshes are parameterized onto an unaligned unit sphere and resampled to an order-6 icosahedron to preserve intrinsic folds.A conservative projection and morphology strategy is used to limit artificial gaps and local information loss.Source: §2.1 · pp. 3–4
2.2 Locally-Optimized Spherical Pre-training (SSL)
- A VGG-style spherical encoder is pretrained on 30,000 UK Biobank subjects with Barlow Twins, using rotations, vertex dropout, and patch masking as augmentations.The final convolutional output is flattened rather than globally averaged to retain spatial localization.Source: §2.2 · p. 4
- Frozen representations are probed on age and sex tasks and on central-sulcus interruption and paracingulate-sulcus presence.The interruption evaluation uses 207 cases and 207 controls; paracingulate labels are filtered to high-confidence predictions.Source: §2.2 · p. 4
2.3 Downstream Architecture: Transfer to the Hybrid U-Net
- The three-channel downstream input creates a mismatch with the two-channel pretrained encoder, so a 1 × 1 Topological Prior Injector projects it into the encoder’s input space.Soft initialization preserves the pretrained curvature and depth distribution initially, then allows gradual integration of sulcal-line information.Source: §2.3 · pp. 4–5
- A symmetric spherical decoder is grafted onto the pretrained encoder, with a lower encoder learning rate and skip connections carrying local features to dense labeling.Group Normalization accommodates small batch sizes.Source: §2.3 · p. 5
3 Experimental Setup and Evaluation Strategy
The evaluation compares the transfer framework with spherical, planar, and volumetric baselines on a held-out test set. Hyperparameters are selected using cross-validation confined to the development set.
3.1 Baselines and Comparative Models
- The 62-subject cohort is divided into a 40-subject development set for four-fold cross-validation and a 22-subject held-out test set.The held-out set is reserved for final statistical testing.Source: §3.1 · p. 5
- Baselines include a spherical U-Net trained from scratch, a 2D ResNet-18 U-Net, DINOv3 dense-prediction variants, and a 3D U-Net evaluated on the same dataset.The comparisons span spherical and planar surface-based approaches as well as a volumetric baseline.Source: §3.1 · pp. 5–6
3.2 Implementation Details and Hyperparameter Optimization
- Random search and four-fold cross-validation confined to the development set calibrate hyperparameters for pretraining and downstream fine-tuning.The implementation varies augmentation and optimization settings; projected 2D baselines use no rotational augmentation.Source: §3.2 · p. 6
4 Results
The transfer framework achieves the highest reported held-out mean Dice and remains more stable than the from-scratch model in the five-subject setting. Ablations and local error analysis associate the strongest gains with localized geometric pre-training, especially for small, variable sulci.
Evaluation metrics
- ESI weights labeling errors by sulcal length, while Elocal reaches 1 when a sulcus is completely hallucinated or missed.The paper cautions that ESI comparisons between 3D folds and 2D lines are irrelevant because their length definitions differ.Source: §4 · p. 6
Global performance
- On the held-out test set, the Spherical Transfer framework achieved the highest mean Dice, 0.77 ± 0.03, when trained on the maximum available split of N = 30 subjects.Source: §4 · p. 6
Data efficiency
- With five training subjects, the transfer model achieves ESI 0.24 ± 0.045 versus 0.32 ± 0.06 for the from-scratch baseline (p<0.01).All training configurations were evaluated on the same fixed test set of N=22 subjects.Source: Figure 2 · p. 7, §4 · p. 7
Ablation study
- The full transfer model reaches Dice 0.77 ± 0.03 and ESI 0.15 ± 0.02, significantly outperforming the from-scratch baseline (p < 0.01).A frozen locally optimized encoder scores Dice 0.71 ± 0.04, on par with the scratch baseline at 0.72 ± 0.05 (p>0.05); peak performance requires unfreezing and the soft-initialized TPI.Source: Table 1 · p. 7, §4 · pp. 7–8
Local error analysis
- −14.82% for Superior Postcentral, −13.94% for Rhinal, and −12.23% for Superior Precentral are the largest reported local error reductions, each significant at p<0.05.Fig. 3 maps local error variation against the from-scratch baseline; negative values indicate reductions.Source: Figure 3 · p. 8, §4 · p. 8
5 Conclusion
The framework separates geometric representation learning from semantic fine-tuning for exhaustive sulci identification in data-scarce settings. Its largest reported identification error reductions occur on highly variable, tertiary sulci; future work will scale localized pretext tasks to higher-capacity paradigms.
Conclusion
- The framework addresses exhaustive cortical sulci identification in data-scarce regimes by decoupling geometric representation learning from semantic fine-tuning.The conclusion attributes this approach to a locally optimized SSL prior and a soft-initialized TPI.Source: §5 · p. 8
- The largest identification error reductions occur on highly variable, tertiary sulci.Source: §5 · p. 9
- Future work will scale localized pretext tasks to higher-capacity paradigms to advance dense cortical mapping.Source: §5 · p. 9