Lattice Boltzmann Models for Anisotropic Diffusion of Images

The lattice Boltzmann method has attracted more and more attention as an alternative numerical scheme to traditional numerical methods for solving partial differential equations and modeling physical systems. The idea of the lattice Boltzmann method is to construct a simplified discrete microscopic dynamics to simulate the macroscopic model described by the partial differential equations. The use of the lattice Boltzmann method has allowed the study of a broad class of systems that would have been difficult by other means. The advantage of the lattice Boltzmann method is that it provides easily implemented fully parallel algorithms and the capability of handling complicated boundaries. In this paper, we present two lattice Boltzmann models for nonlinear anisotropic diffusion of images. We show that image feature selective diffusion (smoothing) can be achieved by making the relaxation parameter in the lattice Boltzmann equation be image feature and direction dependent. The models naturally lead to the numerical algorithms that are easy to implement. Experimental results on both synthetic and real images are described.