One of the authors has proposed a study of homotopy and simplicity in partially ordered sets (or posets). The notion of unipolar point was introduced: a unipolar point can be seen as an 'inessential' element for the topology. Thus, the iterative deletion of unipolar points constitutes a first thinning algorithm. We show in this paper, that such an algorithm does not 'thin enough' certain images. This is the reason why we use the notion of (alpha) -simple point, introduced in the framework of posets, in Ref. 1. The definition of such a point is recursive. As we can locally decide whether a point is (alpha) -simple, we can use classical techniques (such as a binary decision diagram) to characterize them more quickly. Furthermore, it is possible to remove in parallel (alpha) -simple points in a poset, while preserving the topology of the image. Then, we discuss the characterization of end points in order to produce various skeletons. Particularly, we propose a new approach to characterize surface end points. This approach permits us to keep certain junctions of surfaces. Then, we propose very simple parallel algorithms based on the deletion of (alpha) - simple points, consisting in the repetition of two subiterations.