Beaufort-geometry ordinal learning for cross-domain sea-state image classification

Abstract

Visual sea-state perception is a fundamental capability for intelligent maritime systems. However, most deep image classifiers treat Beaufort-scale recognition as a nominal multi-class problem. This formulation overlooks the ordered structure of the Beaufort scale and the distinction between adjacent errors and distant displacements. This study proposes a Beaufort-geometry ordinal cumulative distribution framework for cross-domain sea-state image classification. The method embeds Beaufort states into an ordered geometric label space and optimizes cumulative probability consistency across Beaufort boundaries. It matches predicted and target cumulative distributions, penalizing probability mass transported across multiple sea-state levels. The framework is evaluated using eight domain-separated protocols covering in-domain recognition, shipborne cross-domain transfer and external-domain transfer to MU-SSiD. The comparison includes six public-backbone baselines: ResNet-101, MobileNetV2, ViT-B/32, DeiT-III, Swin-T and XCiT-S. Four additional Beaufort-aware ordinal objectives are included for family-level ablation. Across the eight protocols, the proposed method achieves the highest mean ordinal consistency score of 0.898, exceeding all evaluated baselines and ordinal-loss variants. Sample-level and error-distance analyses show that it converts selected severe Beaufort displacements into exact or adjacent predictions. It also improves local ordinal consistency under shipborne cross-domain transfer and suppresses selected high-state false predictions in external low-state cases. These results show that incorporating Beaufort geometry into cumulative distribution learning supports ordinally consistent visual sea-state recognition under domain shift.