Defining and Computing Curve-skeletons with Medial Geodesic Function

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The Eurographics Association
Many applications in geometric modeling, computer graphics, visualization and computer vision benefit from a reduced representation called curve-skeletons of a shape. These are curves possibly with branches which compactly represent the shape geometry and topology. The lack of a proper mathematical definition has been a bottleneck in developing and applying the the curve-skeletons. A set of desirable properties of these skeletons has been identified and the existing algorithms try to satisfy these properties mainly through a procedural definition. We define a function called medial geodesic on the medial axis which leads to a methematical definition and an approximation algorithm for curve-skeletons. Empirical study shows that the algorithm is robust against noise, operates well with a single user parameter, and produces curve-skeletons with the desirable properties. Moreover, the curveskeletons can be associated with additional attributes that follow naturally from the definition. These attributes capture shape eccentricity, a local measure of how far a shape is away from a tubular one.

, booktitle = {
Symposium on Geometry Processing
}, editor = {
Alla Sheffer and Konrad Polthier
}, title = {{
Defining and Computing Curve-skeletons with Medial Geodesic Function
}}, author = {
Dey, Tamal K.
Sun, Jian
}, year = {
}, publisher = {
The Eurographics Association
}, ISSN = {
}, ISBN = {
}, DOI = {
} }