Adaptive Finite Difference Image Fusion (AFDIF): A Novel PDE‐Based Approach

ABSTRACT This paper introduces the adaptive finite difference image fusion (AFDIF) method, a novel partial differential equation (PDE)‐based framework for enhancing multimodal image fusion. By employing adaptive grid refinement and stability‐optimized finite difference discretization derived from a variational energy functional, AFDIF dynamically adjusts to local gradients, addressing limitations in fixed‐grid PDE methods and improving feature preservation with 15% higher peak signal‐to‐noise ratio (PSNR), structural similarity index (SSIM) > 0.86, visual information fidelity (VIF) > 0.9, and gradient‐based fusion metric > 0.7. Unlike established works, AFDIF fills recent knowledge gaps such as real‐time scalability and hybrid deep learning integration through computational complexity and comparisons with deep learning methods. Experiments on public datasets and a proprietary dataset of 10 local medical pairs demonstrate superiority over baselines, validated by fivefold cross‐validation, statistical ‐tests ( ), sensitivity analysis, and graphical validations. Key contributions include enhanced stability, real‐time potential in diagnostics and remote sensing, and future deep learning‐PDE hybrids. Its significance is as follows: advances computational imaging by bridging traditional and modern techniques.