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