Presentation of the Fundamental Group in Digital Surfaces

Rémy Malgouyres (1)

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes

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 deeni-tion. A classical mathematical way to encode a discrete group is to nd a presentation of this group. In this paper, we construct a presentation for the fundamental group of any subset of a digital surface. This presentation can be computed by an eecient algorithm.

Mots clés: Pattern Recognition; Digital topology; Homotopy; Surfaces

Domaines: Traitement des images [eess.IV]

Rémy Malgouyres. Presentation of the Fundamental Group in Digital Surfaces. 8th International Conference on Discrete Geometry for Computer Imagery (DGCI'99), Mar 1999, Marne-la-Vallée, France. pp.136-150, ⟨10.1007/3-540-49126-0_11⟩. ⟨hal-01319676⟩