Axial representations of shape
Computer Vision, Graphics, and Image Processing
Voronoi diagram for multiply-connected polygonal domains 1: algorithm
IBM Journal of Research and Development
Using a mixed wave/diffusion process to elicit the symmetry set
Image and Vision Computing - 4th Alvey Vision Meeting
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On the computational geometry of pocket machining
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Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Continuous skeleton computation by Voronoi diagram
CVGIP: Image Understanding
Continuous skeletons of discrete objects
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
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Boundary surface recovery from skeleton curves and surfaces
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Computation of the Medial Axis Transform of 3-D polyhedra
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3-D shape interrogation by medial axis transform
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The bisector surface of rational space curves
ACM Transactions on Graphics (TOG)
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Skeletonization of Three-Dimensional Object Using Generalized Potential Field
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the sixth ACM symposium on Solid modeling and applications
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Linear onesided stability of MAT for weakly injective 3D domain
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Approximate medial axis as a voronoi subcomplex
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International Journal of Computer Vision
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Approximating the Medial Axis from the Voronoi Diagram with a Convergence Guarantee
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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Exact computation of the medial axis of a polyhedron
Computer Aided Geometric Design
Homotopy-preserving medial axis simplification
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IEEE Transactions on Pattern Analysis and Machine Intelligence
Medial axis extraction and shape manipulation of solid objects using parabolic PDEs
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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ESA '08 Proceedings of the 16th annual European symposium on Algorithms
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Computers and Graphics
Transformation of a thin-walled solid model into a surface model via solid deflation
Computer-Aided Design
Algebraic reduction of beams for CAD-integrated analysis
Computer-Aided Design
Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces
Computer-Aided Design
3D block-based medial axis transform and chessboard distance transform based on dominance
Image and Vision Computing
Computing medial axes of generic 3D regions bounded by B-spline surfaces
Computer-Aided Design
Efficient retrieval of 3d models based on integer medial axis skeleton
ICAT'06 Proceedings of the 16th international conference on Advances in Artificial Reality and Tele-Existence
Exact medial axis computation for triangulated solids with respect to piecewise linear metrics
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Computer-Aided Design
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The medial axis transform (MAT) 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, an algorithm for determining the MAT is developed for general 3D polyhedral solids of arbitrary genus without cavities, with nonconvex vertices and edges. The algorithm is based on a classification scheme which relates different pieces of the medial axis (MA) to one another even in the presence of degenerate MA points. Vertices of the MA are connected to one another by tracing along adjacent edges, and finally the faces of the axis are found by traversing closed loops of vertices and edges. Representation of the MA and associated radius function is addressed, and pseudocode for the algorithm is given along with recommended optimizations. A connectivity theorem is proven to show the completeness of the algorithm. Complexity estimates and stability analysis for the algorithms are presented. Finally, examples illustrate the computational properties of the algorithm for convex and nonconvex 3D polyhedral solids with polyhedral holes.