Computing and simplifying 2D and 3D continuous skeletons
Computer Vision and Image Understanding
A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
Linear onesided stability of MAT for weakly injective 3D domain
Proceedings of the seventh ACM symposium on Solid modeling and applications
Approximate medial axis as a voronoi subcomplex
Proceedings of the seventh ACM symposium on Solid modeling and applications
Approximating the Medial Axis from the Voronoi Diagram with a Convergence Guarantee
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Delaunay conforming iso-surface, skeleton extraction and noise removal
Computational Geometry: Theory and Applications
Homotopy-preserving medial axis simplification
Proceedings of the 2005 ACM symposium on Solid and physical modeling
MAP: medial axis based geometric routing in sensor networks
Proceedings of the 11th annual international conference on Mobile computing and networking
A condition for isotopic approximation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Stability and homotopy of a subset of the medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Medial axis approximation from inner Voronoi balls: a demo of the Mesecina tool
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Curve-Skeleton Properties, Applications, and Algorithms
IEEE Transactions on Visualization and Computer Graphics
Map: medial axis based geometric routing in sensor networks
Wireless Networks
Robust construction of the three-dimensional flow complex
Proceedings of the twenty-fourth annual symposium on Computational geometry
Approximating the pathway axis and the persistence diagram of a collection of balls in 3-space
Proceedings of the twenty-fourth annual symposium on Computational geometry
Segmenting a sensor field: Algorithms and applications in network design
ACM Transactions on Sensor Networks (TOSN)
Distance functions and skeletal representations of rigid and non-rigid planar shapes
Computer-Aided Design
Segmenting simplified surface skeletons
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
A family of skeletons for motion planning and geometric reasoning applications
Artificial Intelligence for Engineering Design, Analysis and Manufacturing - Representing and Reasoning About Three-Dimensional Space
Medial zones: Formulation and applications
Computer-Aided Design
The medial axis of the union of inner Voronoi balls in the plane
Computational Geometry: Theory and Applications
Robust classification and analysis of anatomical surfaces using 3D skeletons
EG VCBM'08 Proceedings of the First Eurographics conference on Visual Computing for Biomedicine
Topological maps and robust hierarchical Euclidean skeletons in cubical complexes
Computer Vision and Image Understanding
Skeletal representations of orthogonal shapes
Graphical Models
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Medial Axis Transform is sometimes used as an intermediate representation in algorithms for meshing or recognition of shapes from digitized data. This raises the question whether the Medial Axis captures fundamental topological invariants of the object. The (positive) answer has been known already in the case of smooth objects. The main result presented here is the homotopy equivalence of any bounded open subset of Rn with its Medial Axis.