Approximating the Medial Axis from the Voronoi Diagram with a Convergence Guarantee

Authors:
Tamal K. Dey;Wulue Zhao
Affiliations:
-;-
Venue:
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Year:
2002

Citing 9
Cited 5

Continuous skeleton computation by Voronoi diagram

CVGIP: Image Understanding
Computing and simplifying 2D and 3D continuous skeletons

Computer Vision and Image Understanding
Accurate computation of the medial axis of a polyhedron

Proceedings of the fifth ACM symposium on Solid modeling and applications
Approximate medial axis as a voronoi subcomplex

Proceedings of the seventh ACM symposium on Solid modeling and applications
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids

IEEE Transactions on Visualization and Computer Graphics
Shape Description By Medial Surface Construction

IEEE Transactions on Visualization and Computer Graphics
The power crust, unions of balls, and the medial axis transform

Computational Geometry: Theory and Applications
Natural neighbor coordinates of points on a surface

Computational Geometry: Theory and Applications
Delaunay conforming iso-surface, skeleton extraction and noise removal

Computational Geometry: Theory and Applications

Approximate medial axis as a voronoi subcomplex

Proceedings of the seventh ACM symposium on Solid modeling and applications
Any open bounded subset of Rn has the same homotopy type than its medial axis

SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Efficient computation of a simplified medial axis

SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Pose-Oblivious Shape Signature

IEEE Transactions on Visualization and Computer Graphics
MOS surfaces: medial surface transforms with rational domain boundaries

Proceedings of the 12th IMA international conference on Mathematics of surfaces XII

Quantified Score

Hi-index	0.00

Visualization

Abstract

We show that the medial axis of a surface S 驴 R3 can be approximated as a subcomplex of the Voronoi diagram of a point sample of S. The subcomplex converges to the true medial axis as the sampling density approaches infinity. Moreover, the subcomplex can be computed in a scale and density independent manner. Experimental results as detailed in a companion paper corroborate our theoretical claims.