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

Hybrid Lattice Boltzmann Model for Nonlinear Diffusion and Image Denoising

“…The previous study [23] shows that the LB model with non-local collision term (6) has significantly smaller hyper-viscous errors than the scheme with the local collision step (5). This means that the model ( 6) has better accuracy than (5) in the case of non-small time step and diffusion coefficient.…”

“…Using Chapman-Enskog expansion, it has been shown that the LB model with the collision term in the form ( 5) reproduces the Perona-Malik equation [27], where D " 2c 2 5 pτ ´∆t{2q. The second considered model has a non-local collision term [23]:…”

“…A fourth-order accurate MRT scheme has been proposed recently [21,22], but this model operates in one spatial dimension. On the other hand, in several spatial dimensions, hyper-viscosity reduction can be achieved only for special values of diffusion coefficient, and in some cases, single-relaxation-time models show better precision than two-relaxation-time models [23].…”

“…LB models simulating anisotropic diffusion equations can be used for the smoothing and segmentation of two-dimensional and three-dimensional medical images [32][33][34][35]. A four-velocity LB model with a non-local collision step has been applied for the development of Gaussian pyramids and feature detection [23].…”