Dynamic 3D Models with Local and Global Deformations: Deformable Superquadrics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Geometric concepts for geometric design
Geometric concepts for geometric design
International Journal of Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Differential and topological properties of medial axis transforms
Graphical Models and Image Processing
Two- and three-dimensional patterns of the face
Two- and three-dimensional patterns of the face
The 3L Algorithm for Fitting Implicit Polynomial Curves and Surfaces to Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
The digital Michelangelo project: 3D scanning of large statues
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Lecture Notes on Bucket Algorithms
Lecture Notes on Bucket Algorithms
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
Boundary Smoothing via Symmetry Transforms
Journal of Mathematical Imaging and Vision
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
International Journal of Computer Vision
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids
IEEE Transactions on Visualization and Computer Graphics
RSVP: A Geometric Toolkit for Controlled Repair of Solid Models
IEEE Transactions on Visualization and Computer Graphics
IEEE Computer Graphics and Applications
Transitions of the 3D Medial Axis under a One-Parameter Family of Deformations
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Symmetry Maps of Free-Form Curve Segments via Wave Propagation
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
On the Local Form and Transitions of Symmetry Sets, Medial Axes, and Shocks
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
CGI '00 Proceedings of the International Conference on Computer Graphics
A shock grammar for recognition
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Skeleton Based Shape Matching and Retrieval
SMI '03 Proceedings of the Shape Modeling International 2003
On the Intrinsic Reconstruction of Shape from Its Symmetries
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Recognition of Shapes by Editing Their Shock Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
3D Shape Registration using Regularized Medial Scaffolds
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Towards Surface Regularization via Medial Axis Transitions
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
A sampling theory for compact sets in Euclidean space
Proceedings of the twenty-second annual symposium on Computational geometry
A generative theory of shape
Computation of the shock scaffold for unorganized point clouds in 3D
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
Surface reconstruction from point clouds by transforming the medial scaffold
Computer Vision and Image Understanding
Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces
Computer-Aided Design
3D block-based medial axis transform and chessboard distance transform based on dominance
Image and Vision Computing
Sampled medial loci for 3D shape representation
Computer Vision and Image Understanding
Measuring 3D shape similarity by graph-based matching of the medial scaffolds
Computer Vision and Image Understanding
Computing medial axes of generic 3D regions bounded by B-spline surfaces
Computer-Aided Design
Research on 3D medial axis transform via the saddle point programming method
Computer-Aided Design
A general approach to model biomedical data from 3D unorganised point clouds with medial scaffolds
EG VCBM'10 Proceedings of the 2nd Eurographics conference on Visual Computing for Biology and Medicine
Efficient computation of clipped Voronoi diagram for mesh generation
Computer-Aided Design
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We introduce the notion of the medial scaffold, a hierarchical organization of the medial axis of a 3D shape in the form of a graph constructed from special medial curves connecting special medial points. A key advantage of the scaffold is that it captures the qualitative aspects of shape in a hierarchical and tightly condensed representation. We propose an efficient and exact method for computing the medial scaffold based on a notion of propagation along the scaffold itself, starting from initial sources of the flow and constructing the scaffold during the propagation. We examine this method specifically in the context of an unorganized cloud of points in 3D, e.g., as obtained from laser range finders, which typically involve hundreds of thousands of points, but the ideas are generalizable to data arising from geometrically described surface patches. The computational bottleneck in the propagation-based scheme is in finding the initial sources of the flow. We thus present several ideas to avoid the unnecessary consideration of pairs of points which cannot possibly form a medial point source, such as the "visibility” of a point from another given a third point and the interaction of clusters of points. An application of using the medial scaffold for the representation of point samplings of real-life objects is also illustrated.