Thinning Methodologies-A Comprehensive Survey
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Euclidean distance transform
The Euclidean distance transform
The Euclidean distance transform in arbitrary dimensions
Pattern Recognition Letters
Computation of the Medial Axis Transform of 3-D polyhedra
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Computing and simplifying 2D and 3D continuous skeletons
Computer Vision and Image Understanding
Skeleton-based modeling operations on solids
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Proceedings of the fifth ACM symposium on Solid modeling and applications
Accurate computation of the medial axis of a polyhedron
Proceedings of the fifth ACM symposium on Solid modeling and applications
Motion planning for a rigid body using random networks on the medial axis of the free space
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
Geometric structures for three-dimensional shape representation
ACM Transactions on Graphics (TOG)
Proceedings of the sixth ACM symposium on Solid modeling and applications
A linear bound on the complexity of the delaunay triangulation of points on polyhedral surfaces
Proceedings of the seventh ACM symposium on Solid modeling and applications
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
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Automatic and Robust Computation of 3D Medial Models Incorporating Object Variability
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
IEEE Computer Graphics and Applications
Shape Simplification Based on the Medial Axis Transform
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Graphical Models
Interactive 3D distance field computation using linear factorization
I3D '06 Proceedings of the 2006 symposium on Interactive 3D graphics and games
A sampling theory for compact sets in Euclidean space
Proceedings of the twenty-second annual symposium on Computational geometry
Skeleton based solid representation with topology preservation
Graphical Models - Special issue on SPM 05
Tracking shape change using a 3D skeleton hierarchy
ACM SIGGRAPH 2006 Research posters
Efficient and robust computation of an approximated medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
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
Stability and homotopy of a subset of the medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Computing a family of skeletons of volumetric models for shape description
Computer-Aided Design
Liquid simulation on lattice-based tetrahedral meshes
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
Adaptively sampled particle fluids
ACM SIGGRAPH 2007 papers
Computing the Voronoi cells of planes, spheres and cylinders in R3
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Computer-Aided Design
Computing the Voronoi cells of planes, spheres and cylinders in R3
Computer Aided Geometric Design
b-morphs between b-compatible curves in the plane
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Discrete scale axis representations for 3D geometry
ACM SIGGRAPH 2010 papers
Sampled medial loci for 3D shape representation
Computer Vision and Image Understanding
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Extended grassfire transform on medial axes of 2D shapes
Computer-Aided Design
Skeletonization and distance transforms of 3D volumes using graphics hardware
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Computing a family of skeletons of volumetric models for shape description
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Non-manifold medial surface reconstruction from volumetric data
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Generalized Swept Mid-structure for Polygonal Models
Computer Graphics Forum
Generalized distance transforms and skeletons in graphics hardware
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
Polygonization of volumetric skeletons with junctions
Computer-Aided Design
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Applications of of the medial axis have been limited because of its instability and algebraic complexity. In this paper, we use a simplification of the medial axis, the θ-SMA, that is parameterized by a separation angle (θ) formed by the vectors connecting a point on the medial axis to the closest points on the boundary. We present a formal characterization of the degree of simplification of the θ-SMA as a function of θ, and we quantify the degree to which the simplified medial axis retains the features of the original polyhedron.We present a fast algorithm to compute an approximation of the θ-SMA. It is based on a spatial subdivision scheme, and uses fast computation of a distance field and its gradient using graphics hardware. The complexity of the algorithm varies based on the error threshold that is used, and is a linear function of the input size. We have applied this algorithm to approximate the SMA of models with tens or hundreds of thousands of triangles. Its running time varies from a few seconds, for a model consisting of hundreds of triangles, to minutes for highly complex models.