On Voronoi diagrams and medial axes

Medial axes and Voronoi diagrams stand among the most influencing ideas in computer vision and image analysis. Relationships between them, with respect to polygons, had been noted decades ago, and recently this was extended for a broader class of shapes. More specifically, Voronoi diagrams have been considered as a means through which optimal computational geometry algorithms can be applied for performing symmetry axis calculation. This paper is aimed at establishing a closer theoretical relation between Voronoi diagrams and medial axes. Extensions of the definitions of these concepts are proposed, and the advantages of these definitions with respect to some specific but relevant cases are highlighted. In addition, medial axes are characterized as a particular case of Voronoi diagrams, and the implications of this fact are discussed.