The Scale Axis Transform

被引：72

作者：

Giesen, Joachim

Miklos, Balint ^{[1
]}

Pauly, Mark ^{[1
]}

Wormser, Camille ^{[1
]}

机构：

[1] Swiss Fed Inst Technol, Appl Geometry Grp, Zurich, Switzerland

来源：

PROCEEDINGS OF THE TWENTY-FIFTH ANNUAL SYMPOSIUM ON COMPUTATIONAL GEOMETRY (SCG'09) | 2009年

关键词：

medial axis; skeleton; topology; MEDIAL AXIS;

D O I：

10.1145/1542362.1542388

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the scale axis transform, a new skeletal shape representation for bounded open sets O subset of 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.

引用

页码：106 / 115

页数：10

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