(untitled) (European Journal of Pure and Applied Mathematics, 2025)
This paper presents a novel image inpainting algorithm based on the Lattice Boltzmann Method (LBM), inspired by the vorticity-stream formulation of the Navier-Stokes equations. The proposed method, employing D2Q5 and D2Q9 lattice models, effectively reconstructs missing or damaged image regions by propagating smoothness information along isophote directions. Experimental evaluations demonstrate that LBM achieves superior results in terms of PSNR, SSIM, and reduced CPU time compared to classical inpainting techniques, such as Total Variation (TV) regularisation and the Bertalmio-Sapiro-Caselles-Ballaster (BSCB) algorithm. The method’s efficiency in handling complex boundary conditions and preserving image details highlights its robustness for advanced image restoration tasks.