In this work we develop two algorithms to compute the skeleton of a binary 2D image. Both algorithms follow a geometric approach and work directly with the boundary of the image which is an orthogonal polygon (OP). One of these algorithms processes the edges of the polygon while the other one uses its vertices. Compared with a thinning method, the presented algorithms show a good performance. This is a work in progress as our final goal is to extend the vertex-based algorithm method to 3D in order to compute the surface skeleton of a binary volume.