Thinning Methodologies-A Comprehensive Survey
IEEE Transactions on Pattern Analysis and Machine Intelligence
Skeletonization via distance maps and level sets
Computer Vision and Image Understanding
Computing the medial surface of a solid from a domain Delaunay triangulation
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
Geometric shock-capturing eno schemes for subpixel interpolation, computation and curve evolution
Graphical Models and Image Processing
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
Proceedings of the sixth ACM symposium on Solid modeling and applications
Computing Voronoi skeletons of a 3-D polyhedron by space subdivision
Computational Geometry: Theory and Applications
Approximate medial axis as a voronoi subcomplex
Proceedings of the seventh ACM symposium on Solid modeling and applications
International Journal of Computer Vision
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids
IEEE Transactions on Visualization and Computer Graphics
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
Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Characterization and Recognition of 3D Organ Shape in Medical Image Analysis Using Skeletonization
MMBIA '96 Proceedings of the 1996 Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA '96)
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)
Stability and Finiteness Properties of Medial Axis and Skeleton
Journal of Dynamical and Control Systems
Shape Simplification Based on the Medial Axis Transform
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
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
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Computing a family of skeletons of volumetric models for shape description
Computer-Aided Design
Proceedings of the twenty-fifth annual symposium on Computational geometry
Proceedings of the twenty-fifth annual symposium on Computational geometry
User-assisted simplification method for triangle meshes preserving boundaries
Computer-Aided Design
Discrete scale axis representations for 3D geometry
ACM SIGGRAPH 2010 papers
Sampled medial loci for 3D shape representation
Computer Vision and Image Understanding
Computing medial axes of generic 3D regions bounded by B-spline surfaces
Computer-Aided Design
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
Polygonization of volumetric skeletons with junctions
Computer-Aided Design
Skeletal representations of orthogonal shapes
Graphical Models
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We present a novel algorithm to compute a simplified medial axis of a polyhedron. Our simplification algorithm tends to remove unstable features of Blum's medial axis. Moreover, our algorithm preserves the topological structure of the original medial axis and ensures that the simplified medial axis has the same homotopy type as Blum's medial axis. We use the separation angle formed by connecting a point on the medial axis to closest points on the boundary as a measure of the stability of the medial axis at the point. The medial axis is decomposed into its parts that are the sheets, seams and junctions. We present a stability measure of each part of the medial axis based on separation angles and examine the relation between the stability measures of adjacent parts. Our simplification algorithm uses iterative pruning of the parts based on efficient local tests. We have applied the algorithm to compute a simplified medial axis of complex models with tens of thousands of triangles and complex topologies.