Approximate medial axis as a Voronoi subcomplex

Medial axis as a compact representation of shapes has evolved as an essential geometric structure in a number of applications involving 3D geometric shapes. Since exact computation of the medial axis is difficult in general, efforts continue to approximate them. One line of research considers the po...

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Vydáno v:Computer aided design Ročník 36; číslo 2; s. 195 - 202
Hlavní autoři: Dey, Tamal K., Zhao, Wulue
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.02.2004
Témata:
Algorithms
Design
Experimentation
I.3.5 [ Computer Graphics]: Computational Geometry and Object Modeling
I.4 [ Image Processing and Computer Vision]: Reconstruction, Image Representation
Medial axis
Point cloud
Theory
Voronoi diagram
Design
Voronoi diagram
I.4 [ Image Processing and Computer Vision]: Reconstruction, Image Representation
Algorithms
Point cloud
Theory
Experimentation
Medial axis
I.3.5 [ Computer Graphics]: Computational Geometry and Object Modeling
ISSN:0010-4485, 1879-2685
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Popis
Shrnutí:Medial axis as a compact representation of shapes has evolved as an essential geometric structure in a number of applications involving 3D geometric shapes. Since exact computation of the medial axis is difficult in general, efforts continue to approximate them. One line of research considers the point cloud representation of the boundary surface of a solid and then attempts to compute an approximate medial axis from this point sample. It is known that the Voronoi vertices converge to the medial axis for a curve in 2D as the sample density approaches infinity. Unfortunately, the same is not true in 3D. Recently, it is discovered that a subset of Voronoi vertices called poles converge to the medial axis in 3D. However, in practice, a continuous approximation as opposed to a discrete one is sought. Recently few algorithms have been proposed which use the Voronoi diagram and its derivatives to compute this continuous approximation. These algorithms are scale or density dependent. Most of them do not have convergence guarantees, and one of them computes it indirectly from the power diagram of the poles. Recently, we proposed a new algorithm that approximates the medial axis straight from the Voronoi diagram in a scale and density independent manner with convergence guarantees. In this paper, we present several experimental results with this algorithm that support our theoretical claims and also show its effectiveness on practical data sets.
Bibliografie:ObjectType-Article-2
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ISSN:0010-4485
1879-2685
DOI:10.1016/S0010-4485(03)00061-7