Voronoi Diagram: The Generator Recognition Problem

Abstract

For the analysis of systems consisting of small, regular objects, the methods of mathematical morphology applied to images of these systems are well-suited. One of these methods is the use of Voronoi polygons. It was found that the Voronoi tessellation method represents a powerful tool for the analysis of thin film morphology and provides nanostructural information to many multi-particle assemblies. In these notes, several morphological algorithms are analyzed and we study how to join all of them to design a graphical user interface (GUI) that provides as input for the system the "AFM image" and interprets the output of the system in terms of errors and generators coordinates.