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Debled proposed an efficient algorithm for the recognition of rectangular digital planes pieces. However, uses, in some cases called strongly exterior cases, some validity criteria which are only sufficient but not necessary. In this paper we give necessary and sufficient conditions (including strongly exterior cases) to recognize pieces of digital planes. We build up a simplified form of Debled's algorithm. Furthermore, our approach is independent from the rectangular form of pieces considered by Debled.

A Simplified Recognition Algorithm of Digital Planes Pieces