On Gaps in Digital Objects

Different formulae were proposed in the literature for the number of gaps in digital objects. We give several new formulae for the number of 0-gaps in 2D, based on the known connection between the number of 0-gaps and the Euler characteristic of 2D digital objects. We also present two new, short and intuitive proofs of one of the two known equivalent formulae for the number of \((n-2)\)-gaps in nD digital objects.