Computing the fundamental group in digital spaces
As its analogue in the continuous framework, the digital fundamental group represents major information on the topology of discrete objects. However, the fundamental group is abstract information and cannot directly be encoded in a computer by only using its definition. A classical mathematical way to encode a discrete group is to find a 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.
graphs pattern recognition digital topology homotopy