The work on digitizing subspaces of the 2-D Euclidean space with a certain digital approach is an important discipline in both digital geometry and topology. The present work considers Marcus-Wyse topological approach which was established for studying 2-D digital spaces, ℤ 2 . We introduce the digital singular homology groups of MA-spaces (M-topological space with an M-adjacency), and we compute singular homology groups of some certain MA-spaces, we give a formula for singular homology groups

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... f 2-D simple closed MA-curves, and an algorithm for determining homology groups of an arbitrary MA-space.