Proceedings of the sixth ACM symposium on Solid modeling and applications
Feature-Preserving Medial Axis Noise Removal
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Multiscale Medial Loci and Their Properties
International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
Homotopy-preserving medial axis simplification
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Graphical Models
Recursive geometry of the flow complex and topology of the flow complex filtration
Computational Geometry: Theory and Applications
Proceedings of the twenty-fifth annual symposium on Computational geometry
Discrete scale axis representations for 3D geometry
ACM SIGGRAPH 2010 papers
Analysis, reconstruction and manipulation using arterial snakes
ACM SIGGRAPH Asia 2010 papers
Polygonization of volumetric skeletons with junctions
Computer-Aided Design
Scale filtered euclidean medial axis
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Skeletal representations of orthogonal shapes
Graphical Models
Watershed delineation from the medial axis of river networks
Computers & Geosciences
Progressive medial axis filtration
SIGGRAPH Asia 2013 Technical Briefs
Robust diameter-based thickness estimation of 3D objects
Graphical Models
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We introduce the scale axis transform, a new skeletal shape representation for bounded open sets O ⊂ Rd. 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 Os 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 Os, 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 → Os 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.