The contour problem for rectilinear polygons
Information Processing Letters
Computational geometry: an introduction
Computational geometry: an introduction
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Continuous skeleton computation by Voronoi diagram
CVGIP: Image Understanding
Convergence and continuity criteria for discrete approximations of the continuous planar skeleton
CVGIP: Image Understanding
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Computing and simplifying 2D and 3D continuous skeletons
Computer Vision and Image Understanding
Computer Vision and Image Understanding
Proceedings of the fifth ACM symposium on Solid modeling and applications
The Medial axis of a union of balls
Computational Geometry: Theory and Applications
Approximate medial axis as a voronoi subcomplex
Proceedings of the seventh ACM symposium on Solid modeling and applications
Pruning Discrete and Semiocontinuous Skeletons
ICIAP '95 Proceedings of the 8th International Conference on Image Analysis and Processing
Orthogonal Polyhedra: Representation and Computation
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Any open bounded subset of Rn has the same homotopy type than its medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
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
Curve-Skeleton Properties, Applications, and Algorithms
IEEE Transactions on Visualization and Computer Graphics
Defining and computing curve-skeletons with medial geodesic function
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Skeleton extraction by mesh contraction
ACM SIGGRAPH 2008 papers
Straight Skeletons of Three-Dimensional Polyhedra
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Medial Representations: Mathematics, Algorithms and Applications
Medial Representations: Mathematics, Algorithms and Applications
Proceedings of the twenty-fifth annual symposium on Computational geometry
Distance functions and skeletal representations of rigid and non-rigid planar shapes
Computer-Aided Design
Medial Axis Approximation with Bounded Error
ISVD '09 Proceedings of the 2009 Sixth International Symposium on Voronoi Diagrams
Discrete scale axis representations for 3D geometry
ACM SIGGRAPH 2010 papers
Fast parallel surface and solid voxelization on GPUs
ACM SIGGRAPH Asia 2010 papers
Hinged dissection of polypolyhedra
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Exact medial axis computation for triangulated solids with respect to piecewise linear metrics
Proceedings of the 7th international conference on Curves and Surfaces
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Orthogonal shapes are polygons or polyhedra enclosed by axis-aligned edges or faces, respectively. In this paper we present two skeletal representations of orthogonal shapes: the cube skeleton and a family of skeletal representations provided by the scale cube skeleton. Both skeletal representations rely on the L"~ metric. We show that the cube skeleton is homotopically equivalent to its original shape, reduces its dimension, and it is composed of line segments or planar polygons with restricted orientation. We also present an algorithm to compute the scale cube skeleton of orthogonal polygons and compare the presented skeletons with other skeletal representations.