Sufficient Conditions for Topology Preserving Additions and General Operators
Péter Kardos, Kálmán Palágyi · 2013
Topology preservation is a crucial issue of digital topology. Various applications of binary image processing rest on topology preserving operators. Earlier studies in this topic mainly concerned with reductions (i.e., operators th at only delete some object points from binary images), as they form the basis for thinning algorithms. However, additions (i.e., operators that never change object points) als o play important role for the purpose of generating discrete Voronoi diagrams or skeletons by influence zones (SKIZ). Furthermore, the use of general operators that may both add and delete some points to and from objects in pictures are suitable for contour smoothing. Therefore, in this paper we present some new sufficient conditions for topology preserving reductions, additions, and general operators. Two additions for 2D and 3D contour smoothing are also reported.