Delaunay triangulation and Voronoi diagram in image processing

1. What is the relationship among distance map Voronoi diagram and Delaunay triangulation?
2. Why do we use Delaunay triangulation?
3. What is the use of Voronoi diagram?
4. What is Delaunay triangulation simple?

What is the relationship among distance map Voronoi diagram and Delaunay triangulation?

There is a one-to-one relation between the Voronoi cells and the cells of the Delaunay triangulation. A vertex of the Voronoi diagram is a point where at least three sites (points of P) are equally distant. They are centrepoints for circumcenters in the Delaunay triangulation.

Why do we use Delaunay triangulation?

Delaunay triangulations are often used to generate meshes for space-discretised solvers such as the finite element method and the finite volume method of physics simulation, because of the angle guarantee and because fast triangulation algorithms have been developed.

What is the use of Voronoi diagram?

In hydrology, Voronoi diagrams are used to calculate the rainfall of an area, based on a series of point measurements. In this usage, they are generally referred to as Thiessen polygons.

What is Delaunay triangulation simple?

The Delaunay triangulation is a triangulation which is equivalent to the nerve of the cells in a Voronoi diagram, i.e., that triangulation of the convex hull of the points in the diagram in which every circumcircle of a triangle is an empty circle (Okabe et al. 1992, p. 94).