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We define LCL decompositions of the plane and investigate the advantages ofusing such decompositions in the context of digital topology. We show thatdiscretization schemes based on such decompositions associate, to each LCLtiling of the plane, the digital model preserving the local topologicalstructure of the object. We prove that for any LCL tiling of the plane, thedigital model is necessarily a digital 2-manifold. We show that elements of anLCL tiling can be of an arbitrary shape and size. This feature generates avariable density grid with a required resolution in any region of interest,which is extremely important in medicine. Finally, we describe a simplealgorithm, which allows transforming regions of interest produced by the imageacquisition process into digital spaces with topological features of theregions.

Variable density preserving topology grids and the digital models for the plane