NDLI: The scale axis transform

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The scale axis transform

Content Provider	ACM Digital Library
Author	Giesen, Joachim Miklos, Balint Pauly, Mark Wormser, Camille
Abstract	We introduce the scale axis transform, a new skeletal shape representation for bounded open sets O ⊂ $R^{d}.$ The scale axis transform induces a family of skeletons that captures the important features of a shape in a scale-adaptive way and yields a hierarchy of successively simplified skeletons. Its definition is based on the medial axis transform and the simplification of the shape under multiplicative scaling: the s-scaled shape $O_{s}$ is the union of the medial balls of O with radii scaled by a factor of s. The s-scale axis transform of O is the medial axis transform of $O_{s},$ with radii scaled back by a factor of 1/s. We prove topological properties of the scale axis transform and we describe the evolution s → $O_{s}$ by defining the multiplicative distance function to the shape and studying properties of the corresponding steepest ascent flow. All our theoretical results hold for any dimension. In addition, using a discrete approximation, we present several examples of two-dimensional scale axis transforms that illustrate the practical relevance of our new framework.
Starting Page	106
Ending Page	115
Page Count	10
File Format	PDF
ISBN	9781605585017
DOI	10.1145/1542362.1542388
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2009-06-08
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Skeleton Medial axis Topology
Content Type	Text
Resource Type	Article

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