Lattice Boltzmann Method & Mathematical Morphology

This paper suggests to build a direct link between the mathematical morphology and the Lattice Boltzmann Method (LBM) which leads to the LB3M (Lattice Boltzmann Method & Mathematical Morphology). To do so, a proof of the equivalence between the equations in the method and the definitions of morphological dilation and erosion in grey level is established. Thanks to the LB3M, the image processing and the physical simulation are embedded in the same formalism. In order to illustrate the efficiency of the suggested method, the elementary operations are applied to the Lena's image, then an example of bone growth is studied.