Cellular automata labeling of connected components in n-dimensional binary lattices

Abstract

A new cellular automata-based algorithm for labeling of connected components in n-dimensional binary lattices, for $$n \ge 2$$nź2, is proposed. The algorithm for 3D binary images was implemented in NetLogo and MatLab programming environments. The algorithm is local and can be efficiently implemented on data-flow parallel platforms with an average asymptotic complexity of $$\mathcal{O}(L)$$O(L) on $$L^n $$Ln binary lattices. However, some worst-case arrangements of the n-dimensional lattice cells could require $$\mathcal{O}(L^{n})$$O(Ln) calculation steps.