A Voronoi based Labeling Approach to Curve Reconstruction and Medial Axis Approximation

Peethambaran, Jiju; Parakkat, Amal Dev; Muthuganapathy, Ramanathan

A Voronoi based Labeling Approach to Curve Reconstruction and Medial Axis Approximation

Files

077-082.pdf (498.45 KB)

Date

2015

Authors

Peethambaran, Jiju
Parakkat, Amal Dev
Muthuganapathy, Ramanathan

Publisher

The Eurographics Association

Abstract

In this paper, we present a Voronoi based algorithm for closed curve reconstruction and medial axis approximation from planar points. In principle, the algorithm estimates one of the poles (farthest Voronoi vertices of a Voronoi cell) and hence the normals at each sample point by drawing an analogy between a residential water distribution system and Voronoi diagram of input samples. The algorithm then labels Voronoi vertices as either inner or outer with respect to the original curve and subsequently construct a piece-wise linear approximation to the boundary and the interior medial axis of the original curve for a class of curves having bi-tangent neighborhood convergence (BNC). The proposed algorithm has been evaluated for its usefulness using various test data. Results indicate that, even sparsely and non-uniformly sampled curves with sharp corners, outliers or collection of curves are faithfully reconstructed by the proposed algorithm.

        @inproceedings{10.2312:pg.20151285
,
booktitle = {Pacific Graphics Short Papers
},
editor = {Stam, Jos and Mitra, Niloy J. and Xu, Kun
},
title = {{A Voronoi based Labeling Approach to Curve Reconstruction and Medial Axis Approximation
}},
author = {Peethambaran, Jiju and 
Parakkat, Amal Dev and 
Muthuganapathy, Ramanathan
},
year = {2015
},
publisher = {The Eurographics Association
},
ISBN = {978-3-905674-96-5
},
DOI = {10.2312/pg.20151285
}
}