Construction and optimization of CSG representations
Computer-Aided Design - Beyond solid modelling
Continuous skeleton computation by Voronoi diagram
CVGIP: Image Understanding
Separation for boundary to CSG conversion
ACM Transactions on Graphics (TOG)
Skeletonization via distance maps and level sets
Computer Vision and Image Understanding
Computation of the Medial Axis Transform of 3-D polyhedra
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
The bisector surface of rational space curves
ACM Transactions on Graphics (TOG)
Proceedings of the fourteenth annual symposium on Computational geometry
Evaluation of Methods for Ridge and Valley Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Computational and Applied Mathematics
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Shock Graphs and Shape Matching
International Journal of Computer Vision
Skeleton-based three-dimensional geometric morphing
Computational Geometry: Theory and Applications - special issue on virtual reality
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Convex Decomposition of Simple Polygons
ACM Transactions on Graphics (TOG)
An efficient algorithm for finding the CSG representation of a simple polygon
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
International Journal of Computer Vision
Voronoi Diagrams for Planar Shapes
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
Straight-skeleton based contour interpolation
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Finding the Medial Axis of a Simple Polygon in Linear Time
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
Computing Point/Curve and Curve/Curve Bisectors
Proceedings of the 5th IMA Conference on the Mathematics of Surfaces
The Role of Propagation and Medial Geometry in Human Vision
BMCV '02 Proceedings of the Second International Workshop on Biologically Motivated Computer Vision
Polygon decomposition based on the straight line skeleton
Proceedings of the nineteenth annual symposium on Computational geometry
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
Automating the CAD/CAE dimensional reduction process
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Approximate medial axis for CAD models
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Representation and Self-Similarity of Shapes
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
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)
Exact computation of the medial axis of a polyhedron
Computer Aided Geometric Design
Recognition of Shapes by Editing Their Shock Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stability and Finiteness Properties of Medial Axis and Skeleton
Journal of Dynamical and Control Systems
Determining the Geometry of Boundaries of Objects from Medial Data
International Journal of Computer Vision
Canonical Skeletons for Shape Matching
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 02
Handbook of Image and Video Processing (Communications, Networking and Multimedia)
Handbook of Image and Video Processing (Communications, Networking and Multimedia)
Medial axis extraction and shape manipulation of solid objects using parabolic PDEs
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Medial axis based solid representation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Shape sensitivity of constructive representations
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Shape and topology optimization of compliant mechanisms using a parameterization level set method
Journal of Computational Physics
Computation of medial axis and offset curves of curved boundaries in planar domain
Computer-Aided Design
Strategies for shape matching using skeletons
Computer Vision and Image Understanding
An application of singularity theory to robust geometric calculation of interactions among dynamically deforming geometric objects
Gray skeletons and segmentation of shapes
Computer Vision and Image Understanding
Tracking point-curve critical distances
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Model based foot shape classification using 2D foot outlines
Computer-Aided Design
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
Skeletal representations of orthogonal shapes
Graphical Models
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Shape skeletons are fundamental concepts for describing the shape of geometric objects, and have found a variety of applications in a number of areas where geometry plays an important role. Two types of skeletons commonly used in geometric computations are the straight skeleton of a (linear) polygon, and the medial axis of a bounded set of points in the k-dimensional Euclidean space. However, exact computation of these skeletons of even fairly simple planar shapes remains an open problem. In this paper we propose a novel approach to construct exact or approximate (continuous) distance functions and the associated skeletal representations (a skeleton and the corresponding radius function) for solid 2D semi-analytic sets that can be either rigid or undergoing topological deformations. Our approach relies on computing constructive representations of shapes with R-functions that operate on real-valued halfspaces as logic operations. We use our approximate distance functions to define a new type of skeleton, i.e, the C-skeleton, which is piecewise linear for polygonal domains, generalizes naturally to planar and spatial domains with curved boundaries, and has attractive properties. We also show that the exact distance functions allow us to compute the medial axis of any closed, bounded and regular planar domain. Importantly, our approach can generate the medial axis, the straight skeleton, and the C-skeleton of possibly deformable shapes within the same formulation, extends naturally to 3D, and can be used in a variety of applications such as skeleton-based shape editing and adaptive motion planning.