IG-Mamba: Isoline-Guided Evolutionary State Space Model for Physics-Informed Underwater Image Restoration

Underwater imagery is degraded by depth-dependent absorption and scattering, which often introduce color casts and contrast attenuation. Although recent Vision Mamba models provide efficient long-range dependency modeling, their conventional 2D scanning patterns are not explicitly designed to exploit the depth-correlated structure of underwater degradation and may therefore weaken geometry-aware feature dependencies. To address this limitation, we propose Isoline-Guided Evolutionary Mamba (IG-Mamba), a physics-inspired framework that uses a depth-correlated potential prior to organize state-space token propagation. Specifically, we introduce a Topology-Preserving Isoline Scanning mechanism. By leveraging a geometric prior, this mechanism quantizes the scene into discrete iso-potential strata to guide Mamba sequences along geometry-aware orders, thereby preserving local spatial topology while establishing depth-aware long-range dependencies. Furthermore, a Potential Field Evolution method is developed to mitigate the domain discrepancy between terrestrial geometric priors and underwater optical attenuation. Driven by the reconstruction objective, the network adaptively refines the raw geometric anchor into a restoration-oriented optical potential field via a learned residual map. Finally, features are modulated by a transmission-inspired gate motivated by the Jaffe-McGlamery transmission term, enabling spatially adaptive feature reweighting under scattering-dominant conditions. Extensive experiments demonstrate that IG-Mamba achieves strong performance across multiple benchmarks, offering a physics-grounded perspective for dependency modeling in underwater vision.