Enhancing image quality through fractional PDEs: A novel approach to image osmosis

Shadow removal remains a critical challenge in image processing, hindering accurate analysis and interpretation. This paper introduces a novel shadow removal model underpinned by an anisotropic osmotic partial differential equation (PDE). Our approach incorporates a spatial fractional operator to capture long-range dependencies and a drift vector field to steer the diffusion process effectively. This synergistic combination enables the model to balance local and global image features while preserving fine details and intricate textures. We rigorously analyze the properties of the proposed model and provide a robust numerical discretization scheme based on the finite difference method. Numerical experiments demonstrate the superior performance of our approach compared to classical integer-order models, showcasing significant improvements in image quality across various applications. This work opens new avenues for advanced image processing techniques, driven by the rich properties of fractional PDEs.