Lattice Boltzmann model for diffusion equation with reduced truncation errors: Applications to Gaussian filtering and image processing

Abstract

Several image processing approaches require blurring an image using the Gaussian filter. In the present study the filtering method based on a novel four-velocity lattice Boltzmann model with non-local collision kernel is proposed. By applying the Chapman–Enskog expansion up to super-Burnett terms it is shown that the present scheme is equivalent to the diffusion equation with relatively small hyper-viscous defects (truncation errors). Compared to the conventional lattice Boltzmann model the proposed scheme has a small computational overhead but significantly improves accuracy due to the reduced hyper-viscosity. To validate the model the following test problems are considered: diffusion in time of a Gaussian bell, sinusoidal wave, image filtering, feature detection with the application of the modified SIFT method. The numerical experiments indicate that the novel model gives more precise results than the standard lattice Boltzmann model for non-small values of diffusion coefficient and in several cases its computational cost is competitive with OpenCV blurring techniques. In addition, the model can be efficiently used in feature detection algorithms like SIFT.