RSADAF: a Rayleigh scattering-adaptive anisotropic diffusion filter for underwater image restoration in marine ecosystems

Underwater ecosystems play a crucial role in maintaining marine biodiversity and global environmental sustainability. However, underwater monitoring and imaging is a highly challenging area of image processing, where images are severely degraded by haze, wavelength-dependent light absorption, color distortion, scattering, and noise, affecting marine monitoring, object detection, underwater navigation, and limited assessment of coral reefs, marine organisms, benthic habitats, and water quality. The conventional anisotropic diffusion filters do not effectively suppress noise and often fail to adequately preserve image edges and structural details. The manual selection of conductance parameters done in existing methods does not adequately account for the physical degradation mechanisms present in underwater environments. To address these limitations, a new framework, known as Rayleigh scattering-adapted diffusion anisotropic filter (RSADAF), has been proposed, which is a wavelength-aware physics-based diffusion framework that integrates a second-order partial differential equation (PDE) diffusion with the atmospheric scattering model (ASM) and Rayleigh scattering law. The adaptive conductance gradient parameter has been derived from ambient light estimation, and the dominant wavelength of the images has been derived from the CIE 1931 chromaticity model, giving spatial variation of diffusion and reducing local degradations. The second-order PDE formulation (two-stencil approach) preserves the structural information and mitigates staircase artifacts commonly observed in conventional diffusion schemes. Experimental evaluation on the EUVP and UIEB benchmark datasets demonstrates that the proposed approach achieves superior enhancement performance in terms of both full-reference and no-reference image quality metrics. The CIE 1931 wavelength-aware framework achieved a PSNR of 42.85 dB, SSIM of 0.967, UCIQE of 0.341, and BRISQUE of 21.99, outperforming conventional anisotropic diffusion and related enhancement methods. Visual results further confirm improved color restoration, contrast enhancement, edge preservation, and texture retention, offering an interpretable, computationally efficient, and physically meaningful alternative solution for underwater imaging applications.