This paper is composed of two parts. In the first one, we present an analysis of existing discrete surface segmentation algorithms. We show that two classes of algorithms can actually be defined according to discrete surface and plane definitions. In the second part, we prove the link between the two classes presented. To do so, we propose a new labelling of the surface elements which leads to a segmentation algorithm of the first class that can be easily transformed into a segmentation algorithm of the second class.