Computing the Fundamental Group in Digital Space

Abstract : As its analogue in the continuous framework, the digital fundamental group represents a major information on the topology of discrete objects. However, the fundamental group is an abstract information and cannot directly be encoded in a computer using its definition. A classical mathematical way to encode a discrete group is to find a \emph{presentation} of this group. In this paper, we construct a presentation for the fundamental group of an arbitrary graph, and a finite presentation (hence encodable in the memory of a computer) of any subset of Z^3. This presentation can be computed by an efficient algorithm.
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Rémy Malgouyres. Computing the Fundamental Group in Digital Space. International Journal on Pattern Recognition and Artificial Intelligence (IJPRAI), 2001, 15 (7), pp.1075--1088. ⟨10.1142/S0218001401001325⟩. ⟨hal-01319678⟩

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