Differential and Topological Properties of Medial Axis Transforms

verfasst von: Evan C. Sherbrooke, Nicholas M. Patrikalakis, Franz Erich Wolter
Abstract: The medial axis transform is a representation of an object which has been shown to be useful in design, interrogation, animation, finite element mesh generation, performance analysis, manufacturing simulation, path planning, and tolerance specification. In this paper, the theory of the medial axis transform for 3-D objects is developed. For objects with piecewise C² boundaries, relationships between the curvature of the boundary and the position of the medial axis are developed. For n-dimensional submanifolds of ℛⁿ with boundaries which are piecewise C² and completely G¹, a deformation retract is set up between each object and its medial axis, which demonstrates that if the object is path connected, then so is its medial axis. Finally, it is proven that path connected polyhedral solids without cavities have path connected medial axes.
Externe Organisation(en): New Technologies, Inc
Massachusetts Institute of Technology (MIT)
Typ: Artikel
Journal: Graphical Models and Image Processing
Band: 58
Seiten: 574-592
Anzahl der Seiten: 19
ISSN: 1077-3169
Publikationsdatum: 11.1996
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Modellierung und Simulation, Maschinelles Sehen und Mustererkennung, Geometrie und Topologie, Computergrafik und computergestütztes Design
Elektronische Version(en): https://doi.org/10.1006/gmip.1996.0047 (Zugang: Geschlossen)

BibTeX

@article{b6ec98e22175432383cf674ed910a721,
title = "Differential and Topological Properties of Medial Axis Transforms",
abstract = "The medial axis transform is a representation of an object which has been shown to be useful in design, interrogation, animation, finite element mesh generation, performance analysis, manufacturing simulation, path planning, and tolerance specification. In this paper, the theory of the medial axis transform for 3-D objects is developed. For objects with piecewise C2 boundaries, relationships between the curvature of the boundary and the position of the medial axis are developed. For n-dimensional submanifolds of ℛn with boundaries which are piecewise C2 and completely G1, a deformation retract is set up between each object and its medial axis, which demonstrates that if the object is path connected, then so is its medial axis. Finally, it is proven that path connected polyhedral solids without cavities have path connected medial axes.",
author = "Sherbrooke, {Evan C.} and Patrikalakis, {Nicholas M.} and Wolter, {Franz Erich}",
year = "1996",
month = nov,
doi = "10.1006/gmip.1996.0047",
language = "English",
volume = "58",
pages = "574--592",
journal = "Graphical Models and Image Processing",
issn = "1077-3169",
publisher = "Academic Press Inc.",
number = "6",
}