Angular bisector network, a simplified generalized Voronoi diagram: application to processing complex intersections in biomedical images

2000 ◽  
Vol 22 (1) ◽  
pp. 120-128 ◽  
Author(s):  
F. Cloppet ◽  
J.-M. Oliva ◽  
G. Stamon
Keyword(s):  
Voronoi Diagram ◽  
Biomedical Images ◽  
Angular Bisector ◽  
Generalized Voronoi Diagram

Visual Servoing on the Generalized Voronoi Diagram Using an Omnidirectional Camera

2018 ◽  
Vol 94 (3-4) ◽  
pp. 793-804 ◽  
Author(s):  
Romain Marie ◽  
Hela Ben Said ◽  
Joanny Stéphant ◽  
Ouiddad Labbani-Igbida
Keyword(s):  
Voronoi Diagram ◽  
Visual Servoing ◽  
Omnidirectional Camera ◽  
Generalized Voronoi Diagram

BOAT-SAIL VORONOI DIAGRAM AND ITS APPLICATION

2009 ◽  
Vol 19 (05) ◽  
pp. 425-440 ◽  
Author(s):  
TETSUSHI NISHIDA ◽  
KOKICHI SUGIHARA
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Voronoi Diagram ◽  
Water Surface ◽  
Eikonal Equation ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Marching Method ◽  
Generalized Voronoi Diagram

A new generalized Voronoi diagram, called a boat-sail Voronoi diagram, is defined on the basis of the time necessary for a boat to reach on water surface with flow. A new concept called a boat-sail distance is introduced on the surface of water with flow, and it is used to define a generalized Voronoi diagram, in such a way that the water surface is partitioned into regions belonging to the nearest harbors with respect to this distance. The problem of computing this Voronoi diagram is reduced to a boundary value problem of a partial differential equation, and a numerical method for solving this problem is constructed. The method is a modification of a so-called fast marching method originally proposed for the eikonal equation. Computational experiments show the efficiency and the stableness of the proposal method. We also apply our equation to the shortest path problem and the simulation of the forest fire.

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