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Convex Combination Star Shape Prior for Data-driven Image Semantic Segmentation
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Proposes a convex combination star (CCS) shape prior with a smooth shape field, unrolls its dual algorithm into a sigmoid/softmax-like network module, and plugs it into SAM and SAM2 for medical and remote sensing segmentation.
Problem
Multi-center star shape priors induce non-smooth shape fields that cause instability when used in backpropagation for data-driven segmentation networks.
Approach
Replace the non-smooth multi-center min with a log-sum-exp smoothed min to define a convex-combination star shape with a smooth field; the dual algorithm of the resulting variational model unrolls into a CCS-Sigmoid module that replaces the standard sigmoid output in SAM-type decoders.
Key results
- On Kvasir, SAM with CCS module reaches 86.91 DICE vs 84.82 for fine-tuned SAM.
- On WHU Building, SAM2 with CCS loss reaches 93.26 DICE vs 92.33 for fine-tuned SAM2.
- CCS module adds negligible cost on SAM2: FLOPs 651.34G to 651.38G, FPS 16.55 to 14.42.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add CCS shape loss | SAM ViT-B · ISIC 2018 test | DICE: 88.81 -> 89.43 | Helped |
| add CCS module | SAM ViT-B · ISIC 2018 test | DICE: 88.81 -> 89.67 | Helped |
| add CCS shape loss | SAM2 Hiera-Base · Refuge test | DICE: 79.05 -> 81.63 | Helped |
| add CCS module | SAM2 Hiera-Base · Refuge test | DICE: 79.05 -> 81.15 | Helped |
| add CCS shape loss | SAM ViT-B · Kvasir test | DICE: 84.82 -> 85.30 | Helped |
| add CCS module | SAM ViT-B · Kvasir test | DICE: 84.82 -> 86.91 | Helped |
| add CCS shape loss | SAM2 Hiera-Base · WHU Building test | DICE: 92.33 -> 93.26 | Helped |
| add CCS module | SAM2 Hiera-Base · WHU Building test | DICE: 92.33 -> 93.32 | Helped |
| set CCS layer count to 5 instead of 10 (ablation) | SAM + CCS module · ISIC 2018 | DICE: 89.67 -> 89.31 | Hurt |
| set CCS layer count to 20 instead of 10 (ablation) | SAM + CCS module · ISIC 2018 | DICE: 89.67 -> 89.14 | Hurt |
| set CCS layer count to 30 instead of 10 (ablation) | SAM + CCS module · ISIC 2018 | DICE: 89.67 -> 89.08 | Hurt |
| use CCS post-processing instead of the integrated module (ablation) | SAM2 + CCS module · Refuge | DICE: 81.15 -> 79.11 | Hurt |
Limitations
- Theoretical guarantee of CCS property only holds as epsilon tends to 0; not proven for finite epsilon.
- Ground-truth-derived shape field requires center point sampling heuristics (30 boundary points or morphological extraction).
Experimental setup
Datasets: ISIC 2018 Refuge Kvasir WHU Building
Benchmarks: ISIC 2018 Refuge Kvasir WHU Building
Metrics: DICE IOU ACC FPS FLOPs
Baselines: SAM fine-tuned SAM2 fine-tuned
Builds on: SAM SAM2 star shape constraint (Veksler) multi-center star shape (Gulshan et al.) LoRA
Closest papers by meaning
- Hedgehog Shape Priors for Multi-Object Segmentation (CVPR 2016 · similarity 0.84)
- Convexity Shape Constraints for Image Segmentation (CVPR 2016 · similarity 0.84)
- D-Convexity: A Unified Differentiable Convex Shape Prior via Quasi-Concavity for Data-driven Image Segmentation (CVPR 2026 · similarity 0.84)
- Delving Into Shape-Aware Zero-Shot Semantic Segmentation (CVPR 2023 · similarity 0.83)
- SAM-CP: Marrying SAM with Composable Prompts for Versatile Segmentation (ICLR 2025 · similarity 0.80)
- Uncertainty-aware Fine-tuning of Segmentation Foundation Models (NeurIPS 2024 · similarity 0.80)
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