Deep spatial-spectral difference network with heterogeneous feature mutual learning for sea fog detection

Multispectral remote sensing image-based sea fog detection (SFD) is both important and challenging. Deep learning methods for SFD have become mainstream due to their powerful nonlinear learning capabilities and flexibility. However, existing methods have not fully utilized the physical difference priors in multispectral images (MSI) for SFD, making it difficult to skillfully capture the shape and appearance characteristics of sea fog, thus leading to uncertainties in SFD. We propose the spatial-spectral difference network (S2DNet), a deep encoding-decoding framework that merges inter-spectral and intra-spectral heterogeneous difference features. Specifically, inspired by physics-based difference threshold methods, we developed a physics-inspired inter-spectral difference module (PIDM) that combines feature-level difference with deep neural networks to capture the shape characteristics of sea fog. We designed the intra-spectral difference module (ISDM) using difference convolution to represent sea fog's fine-grained and dynamic appearance information. Furthermore, inspired by multi-view learning, we propose heterogeneous feature mutual learning (HFML) that seeks robust representations by focusing on semantically invariant aspects within heterogeneous difference features, adapting to the dynamic nature of sea fog. HFML is achieved through global feature mutual learning using an adversarial procedure and local feature mutual learning supported by a novel information-theoretic objective function that links maximizing statistical correlation with expectation maximization. Experiments on two SFD datasets show that integrating physical difference priors into deep learning improves SFD. In both continuous temporal and high spatial resolution SFD tasks, S2DNet outperforms existing advanced deep learning methods. Moreover, S2DNet demonstrates stronger robustness under degraded remote sensing image conditions, highlighting its potential usefulness and practicality in real-world applications.