Toward a computational theory of shape: an overview
ECCV 90 Proceedings of the first european conference on Computer vision
Algorithms on Trees and Graphs
Algorithms on Trees and Graphs
International Journal of Computer Vision
Transitions of the 3D Medial Axis under a One-Parameter Family of Deformations
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Symmetry Sets and Medial Axes in Two and Three Dimensions
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Deformable M-Reps for 3D Medical Image Segmentation
International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
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)
Determining the Geometry of Boundaries of Objects from Medial Data
International Journal of Computer Vision
A survey on tree edit distance and related problems
Theoretical Computer Science
Medial Representations: Mathematics, Algorithms and Applications
Medial Representations: Mathematics, Algorithms and Applications
Swept regions and surfaces: Modeling and volumetric properties
Theoretical Computer Science
Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces
Computer-Aided Design
Sampled medial loci for 3D shape representation
Computer Vision and Image Understanding
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For contractible regions 驴in 驴3 with generic smooth boundary, we determine the global structure of the Blum medial axis M. We give an algorithm for decomposing M into "irreducible components" which are attached to each other along "fin curves". The attaching cannot be described by a tree structure as in the 2D case. However, a simplified but topologically equivalent medial structure 驴 M with the same irreducible components can be described by a two level tree structure. The top level describes the simplified form of the attaching, and the second level tree structure for each irreducible component specifies how to construct the component by attaching smooth medial sheets to the network of Y-branch curves. The conditions for these structures are complete in the sense that any region whose Blum medial axis satisfies the conditions is contractible.