Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
The union of balls and its dual shape
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
A survey of methods for recovering quadrics in triangle meshes
ACM Computing Surveys (CSUR)
Computing Voronoi skeletons of a 3-D polyhedron by space subdivision
Computational Geometry: Theory and Applications
International Journal of Computer Vision
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Estimating the tensor of curvature of a surface from a polyhedral approximation
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Estimating differential quantities using polynomial fitting of osculating jets
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
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)
A Formal Classification of 3D Medial Axis Points and Their Local Geometry
IEEE Transactions on Pattern Analysis and Machine Intelligence
Exact computation of the medial axis of a polyhedron
Computer Aided Geometric Design
Estimating Curvatures and Their Derivatives on Triangle Meshes
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Determining the Geometry of Boundaries of Objects from Medial Data
International Journal of Computer Vision
Homotopy-preserving medial axis simplification
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Shape Simplification Based on the Medial Axis Transform
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Graphical Models
The Medial Scaffold of 3D Unorganized Point Clouds
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient and robust computation of an approximated medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Revealing Significant Medial Structure in Polyhedral Meshes
3DPVT '06 Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06)
Tree Structure for Contractible Regions in R3
International Journal of Computer Vision
Retrieving articulated 3-D models using medial surfaces
Machine Vision and Applications
Medial Representations: Mathematics, Algorithms and Applications
Medial Representations: Mathematics, Algorithms and Applications
Medial Axis Approximation with Bounded Error
ISVD '09 Proceedings of the 2009 Sixth International Symposium on Voronoi Diagrams
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Three-Dimensional Shape Description Using the Symmetric Axis Transform I: Theory
IEEE Transactions on Pattern Analysis and Machine Intelligence
Normal and feature approximations from noisy point clouds
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
| Hi-index | 0.00 |
The medial axis transform is valuable for shape representation as it is complete and captures part structure. However, its exact computation for arbitrary 3D models is not feasible. We introduce a novel algorithm to approximate the medial axis of a polyhedron with a dense set of medial points, with a guarantee that each medial point is within a specified tolerance from the medial axis. Given this discrete approximation to the medial axis, we use Damon's work on radial geometry (Damon, 2005 [1]) to design a numerical method that recovers surface curvature of the object boundary from the medial axis transform alone. We also show that the number of medial sheets comprising this representation may be significantly reduced without substantially compromising the quality of the reconstruction, to create a more useful part-based representation.