Recognition of salt-marsh fairy circles in conventional optical satellite imagery: A generalizable framework with multiple machine learning models and imbalanced Bayesian probability updating

Salt-marsh Fairy circles (FC) are enigmatic, quasi-circular structures linked to interacting biogeophysical processes, yet they remain difficult to detect and quantify at scale from conventional RGB imagery. Limited labeled data, transient and variable FC appearance, and severe class-imbalance make single-model machine learning (ML) unreliable for quantitative monitoring. We propose a framework for automatic FC recognition and enumeration on 3-band imagery. A zero-shot foundation model (SAM) segments images into instance-level blocks. Novel distribution-pattern and geometric features, class-equalized losses, weighted resampling, and augmentation are applied within deep-learning (U-Net, Attention-U-Net, Swin-Unet) and ensemble-learning (Random Forest, XGBoost) models. The key innovation is an imbalance-aware Bayesian method that fuses pixel-wise probabilities across models; a counting algorithm then tallies FC instances. We evaluate eight pan-sharpened scenes covering four sites along China's coast. No individual ML model or standard Bayesian fusion is fully satisfactory. The imbalance-aware Bayesian method improves over the best single model: tight scheme: κ rises from 0.69 to 0.76, F1-score from 70.9% to 75.8% (Class 1) and from 63.5% to 68.2% (Class 2), and AUC from 84.8% to 93.1% and from 78.5% to 84.8%; loose scheme: κ increases from 0.74 to 0.79, AUC from 85.1% to 90.3%, F1-score from 74.3% to 78.6%. The counting algorithm achieves RMSE 1.62 and MAPE 0.33% over 1,135 instances, outperforming DBSCAN. A 22-month case study on Chongming Island captures marsh expansion and dieback dynamics through shifts between FC classes. Our framework delivers reliable FC recognition and enumeration on a small dataset with severe class-imbalance, generalizing across salt-marsh types.