Abstract

One of the authors has proposed a study of homotopy and simplicity in partially ordered sets 1,2 (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 ff-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 ff-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 ff-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 ff-simple points, consisting in the repetition of two subiterations.

Citations