Voronoi diagrams of polygons: A framework for shape representation

Abstract

This paper describes an efficient shape representation framework for planar shapes using Voronoi skeletons. This paper makes the following significant contributions. First a new algorithm for the construction of the Voronoi diagram of a polygon with holes is described. The main features of this algorithm are its robustness in handling the standard degenerate cases (colinearity of more than two points; co-circularity of more than three points), and its ease of implementation. It also features a robust numerical scheme to compute non-linear parabolic edges that avoids having to solve equations of degree greater than two. The algorithm has been fully implemented and tested on a variety of test inputs.Second, the Voronoi diagram of a polygon is used to derive accurate and robust skeletons for planar shapes. The shape representation scheme using Voronoi skeletons possesses the important properties of connectivity as well as Euclidean metrics. Redundant skeletal edges are deleted in apruning step which guarantees that connectivity of the skeleton will be preserved. The resultant representation is stable with respect to being invariant to perturbations along the boundary of the shape. A number of examples of shapes with and without holes are presented to demonstrate the features of this approach.

Skeleton pruning as trade-off between skeleton simplicity and reconstruction error

“…Skeletonizaton approaches can be broadly classified into four categories: 1) thinning/peeling algorithms [22,23,24,25,26], 2) discrete domain algorithms based on the Voronoi diagram [27,28,29], 3) algorithms based on distance transform [30,31,32,33,34], and 4) algorithms based on mathematical morphology [35,36,37,38].…”

Development of Micro Fiber Edge Detection System Based on Grey System Theory

“…The point selection scheme of the grey prediction model is improved to make the detection of the strong edge having more abundant information and according to the strong edge can also accurately identify fiber edge position, but strong edge exist certain fracture phenomenon which cannot satisfy the requirement of complete fiber edge [8]. To extract complete fiber edge information and overcome the incomplete edge of the edge extraction based on the grey prediction model, the Niblack algorithm is used to extract the weak edge of the fiber.…”

A multi-relational approach to spatial classification

“…When working with maps and spatial information, Voronoi diagrams, named after their creator Georgy Feodosevich Voronoy, are prevalent as they naturally represent relationships between entities [8,47,65]. Voronoi diagrams have been used in the domain of computational geometry [47] as well as data mining.…”