Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Dynamic deformation of solid primitives with constraints
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Thinning Methodologies-A Comprehensive Survey
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Computing the differential characteristics of isointensity surface
Computer Vision and Image Understanding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ridges, crests and sub-parabolic lines of evolving surfaces
International Journal of Computer Vision
A fully parallel 3D thinning algorithm and its applications
Computer Vision and Image Understanding
Computing and simplifying 2D and 3D continuous skeletons
Computer Vision and Image Understanding
Two- and three-dimensional patterns of the face
Two- and three-dimensional patterns of the face
Geometric Modeling
Approximate medial axis as a voronoi subcomplex
Proceedings of the seventh ACM symposium on Solid modeling and applications
Boundary Smoothing via Symmetry Transforms
Journal of Mathematical Imaging and Vision
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 Sets and Medial Axes in Two and Three Dimensions
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Fragment Grouping via the Principle of Perceptual Occlusion
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
On the Intrinsic Reconstruction of Shape from Its Symmetries
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-dimensional shape representation via shock flows
Three-dimensional shape representation via shock flows
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
Approximate medial axis for CAD models
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Higher order symmetry for non-linear classification of human walk detection
Pattern Recognition Letters
The Medial Scaffold of 3D Unorganized Point Clouds
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Defining and computing curve-skeletons with medial geodesic function
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Retrieving articulated 3-D models using medial surfaces
Machine Vision and Applications
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Volume decomposition and hierarchical skeletonization
VRCAI '08 Proceedings of The 7th ACM SIGGRAPH International Conference on Virtual-Reality Continuum and Its Applications in Industry
Surface reconstruction from point clouds by transforming the medial scaffold
Computer Vision and Image Understanding
Population-based fitting of medial shape models with correspondence optimization
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Segmenting simplified surface skeletons
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
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
On the computation of the {3, 4, 5} curve skeleton of 3D objects
Pattern Recognition Letters
Curve-skeletons based on the fat graph approximation
ACIVS'11 Proceedings of the 13th international conference on Advanced concepts for intelligent vision systems
Computing medial axes of generic 3D regions bounded by B-spline surfaces
Computer-Aided Design
A classification of centres of maximal balls in Z3
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Computing 3d symmetry sets; a case study
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Retrieving articulated 3-d models using medial surfaces and their graph spectra
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
SMI 2012: Full Medial design of blades for hydroelectric turbines and ship propellers
Computers and Graphics
A fast algorithm for constructing approximate medial axis of polygons, using Steiner points
Advances in Engineering Software
Research on 3D medial axis transform via the saddle point programming method
Computer-Aided Design
Robust classification and analysis of anatomical surfaces using 3D skeletons
EG VCBM'08 Proceedings of the First Eurographics conference on Visual Computing for Biomedicine
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
Guaranteed quality tetrahedral Delaunay meshing for medical images
Computational Geometry: Theory and Applications
Hi-index | 0.14 |
Abstract--This paper proposes a novel hypergraph skeletal representation for 3D shape based on a formal derivation ofthe generic structure of its medial axis. By classifying each skeletal point by its order of contact, we show that, generically, the medial axis consists of five types of points, which are then organized into sheets, curves, and points: 1) sheets (manifolds with boundary) which are the locus of bitangent spheres with regular tangency A_1^2 (A_k^n notation means n distinct k{\hbox{-}}{\rm{fold}} tangencies of the sphere of contact, as explained in the text); two types of curves, 2) the intersection curve of three sheets and the locus of centers of tritangent spheres, A_1^3, and 3) the boundary of sheets, which are the locus of centers of spheres whose radius equals the larger principal curvature, i.e., higher order contact A_3 points; and two types of points, 4) centers of quad-tangent spheres, A_1^4, and 5) centers of spheres with one regular tangency and one higher order tangency, A_1A_3. The geometry of the 3D medial axis thus consists of sheets (A_1^2) bounded by one type of curve (A_3) on their free end, which corresponds to ridges on the surface, and attached to two other sheets at another type of curve (A_1^3), which support a generalized cylinder description. The A_3 curves can only end in A_1A_3 points where they must meet an A_1^3 curve. The A_1^3 curves meet together in fours at an A_1^4 point. This formal result leads to a compact representation for 3D shape, referred to as the medial axis hypergraph representation consisting of nodes (A_1^4 and A_1 A_3 points), links between pairs of nodes (A_1^3 and A_3 curves) and hyperlinks between groups of links (A_1^2 sheets). The description of the local geometry at nodes by itself is sufficient to capture qualitative aspects of shapes, in analogy to 2D. We derive a pointwise reconstruction formula to reconstruct a surface from this medial axis hypergraph together with the radius function. Thus, this information completely characterizes 3D shape and lays the theoretical foundation for its use in recognition, morphing, design, and manipulation of shapes.