Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
The union of balls and its dual shape
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Approximating polyhedra with spheres for time-critical collision detection
ACM Transactions on Graphics (TOG)
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Computing and simplifying 2D and 3D continuous skeletons
Computer Vision and Image Understanding
Design and analysis of planar shape deformation
Proceedings of the fourteenth annual symposium on Computational geometry
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
r-regular shape reconstruction from unorganized points
Computational Geometry: Theory and Applications - special issue on applied computational geometry
Accurate computation of the medial axis of a polyhedron
Proceedings of the fifth ACM symposium on Solid modeling and applications
Crust and anti-crust: a one-step boundary and skeleton extraction algorithm
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Curve reconstruction, the traveling salesman problem and Menger's theorem on length
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A simple provable algorithm for curve reconstruction
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Approximating curves via alpha shapes
CVGIP: Graphical Models and Image Processing
A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
TSP-based curve reconstruction in polynomial time
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Curve reconstruction: connecting dots with good reason
Computational Geometry: Theory and Applications
Geometric structures for three-dimensional shape representation
ACM Transactions on Graphics (TOG)
Shape Description By Medial Surface Construction
IEEE Transactions on Visualization and Computer Graphics
The Ball-Pivoting Algorithm for Surface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
Proceedings of the sixth ACM symposium on Solid modeling and applications
Nice point sets can have nasty Delaunay triangulations
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Dense point sets have sparse Delaunay triangulations: or "…but not too nasty"
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Smooth-surface reconstruction in near-linear time
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Undersampling and oversampling in sample based shape modeling
Proceedings of the conference on Visualization '01
Reliable Path for Virtual Endoscopy: Ensuring Complete Examination of Human Organs
IEEE Transactions on Visualization and Computer Graphics
Optimal Net Surface Problems with Applications
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Approximating the Medial Axis from the Voronoi Diagram with a Convergence Guarantee
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Shape dimension and intrinsic metric from samples of manifolds with high co-dimension
Proceedings of the nineteenth annual symposium on Computational geometry
Approximation by skin surfaces
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Ambient isotopic approximations for surface reconstruction and interval solids
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Approximate medial axis for CAD models
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
A geometric convection approach of 3-D reconstruction
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Approximating and intersecting surfaces from points
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Computational topology: ambient isotopic approximation of 2-manifolds
Theoretical Computer Science - Topology in computer science
A Formal Classification of 3D Medial Axis Points and Their Local Geometry
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spectral watertight surface reconstruction
ACM SIGGRAPH 2003 Sketches & Applications
Provable surface reconstruction from noisy samples
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Rough Interface Reconstruction Using the Level Set Method
VIS '04 Proceedings of the conference on Visualization '04
Provable dimension detection using principal component analysis
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Delaunay triangulations approximate anchor hulls
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
MAP: medial axis based geometric routing in sensor networks
Proceedings of the 11th annual international conference on Mobile computing and networking
Shape Simplification Based on the Medial Axis Transform
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Graphical Models
Simultaneous shape decomposition and skeletonization
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Building triangulations using ε-nets
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Medial axis approximation and unstable flow complex
Proceedings of the twenty-second annual symposium on Computational geometry
Skeleton based solid representation with topology preservation
Graphical Models - Special issue on SPM 05
Provable surface reconstruction from noisy samples
Computational Geometry: Theory and Applications
Accurate and Scalable Surface Representation and Reconstruction from Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
An effective condition for sampling surfaces with guarantees
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
Computational topology for isotopic surface reconstruction
Theoretical Computer Science - Spatial representation: Discrete vs. continous computational models
Medial axis approximation from inner Voronoi balls: a demo of the Mesecina tool
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Pose-Oblivious Shape Signature
IEEE Transactions on Visualization and Computer Graphics
Curve-Skeleton Properties, Applications, and Algorithms
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Direct visibility of point sets
ACM SIGGRAPH 2007 papers
Atomic volumes for mesh completion
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
An adaptive MLS surface for reconstruction with guarantees
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Surface reconstruction from noisy point clouds
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Poisson surface reconstruction
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Defining and computing curve-skeletons with medial geodesic function
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Overfitting control for surface reconstruction
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Geometric and topological guarantees for the WRAP reconstruction algorithm
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Map: medial axis based geometric routing in sensor networks
Wireless Networks
Efficient Surface Reconstruction using Generalized Coulomb Potentials
IEEE Transactions on Visualization and Computer Graphics
Visibility-based feature extraction from discrete models
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Approximating the pathway axis and the persistence diagram of a collection of balls in 3-space
Proceedings of the twenty-fourth annual symposium on Computational geometry
Retrieving articulated 3-D models using medial surfaces
Machine Vision and Applications
Pareto-Optimality of Cognitively Preferred Polygonal Hulls for Dot Patterns
Proceedings of the international conference on Spatial Cognition VI: Learning, Reasoning, and Talking about Space
Proceedings of the twenty-fifth annual symposium on Computational geometry
Hierarchical Discrete Medial Axis for Sphere-Tree Construction
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Parallel Poisson Surface Reconstruction
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Reconstructing Polygons from Scanner Data
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Surface Reconstruction of Engine Intake Ports with Mixed Constraints
ICIRA '09 Proceedings of the 2nd International Conference on Intelligent Robotics and Applications
Recovering structure from r-sampled objects
SGP '09 Proceedings of the Symposium on Geometry Processing
Manifold homotopy via the flow complex
SGP '09 Proceedings of the Symposium on Geometry Processing
A robust approach for 3D cars reconstruction
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
MOS surfaces: medial surface transforms with rational domain boundaries
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Discrete scale axis representations for 3D geometry
ACM SIGGRAPH 2010 papers
Optimal reconstruction might be hard
Proceedings of the twenty-sixth annual symposium on Computational geometry
Reconstructing shapes with guarantees by unions of convex sets
Proceedings of the twenty-sixth annual symposium on Computational geometry
Photo-consistent surface reconstruction from noisy point clouds
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Adaptive surface reconstruction based on implicit PHT-splines
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Cone carving for surface reconstruction
ACM SIGGRAPH Asia 2010 papers
Computing the volume of a union of balls: A certified algorithm
ACM Transactions on Mathematical Software (TOMS)
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
A surface reconstruction algorithm using weighted alpha shapes
FSKD'05 Proceedings of the Second international conference on Fuzzy Systems and Knowledge Discovery - Volume Part I
A family of skeletons for motion planning and geometric reasoning applications
Artificial Intelligence for Engineering Design, Analysis and Manufacturing - Representing and Reasoning About Three-Dimensional Space
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
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
What is the region occupied by a set of points?
GIScience'06 Proceedings of the 4th international conference on Geographic Information Science
Ensembles for normal and surface reconstructions
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Shape reconstruction from unorganized set of points
ICIAR'10 Proceedings of the 7th international conference on Image Analysis and Recognition - Volume Part I
Medial axis transform of a planar domain with infinite curvature boundary points
Computer Aided Geometric Design
Computation and evaluation of medial surfaces for shape representation of abdominal organs
MICCAI'11 Proceedings of the Third international conference on Abdominal Imaging: computational and Clinical Applications
The medial axis of the union of inner Voronoi balls in the plane
Computational Geometry: Theory and Applications
A fast and simple surface reconstruction algorithm
Proceedings of the twenty-eighth annual symposium on Computational geometry
Computer Graphics Forum
A fast algorithm for approximate surface reconstruction from sampled points
Advances in Engineering Software
SkelTre - fast skeletonisation for imperfect point cloud data of botanic trees
EG 3DOR'09 Proceedings of the 2nd Eurographics conference on 3D Object Retrieval
On normals and projection operators for surfaces defined by point sets
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Shape segmentation and matching from noisy point clouds
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Surface reconstruction from noisy point clouds using coulomb potentials
VG'07 Proceedings of the Sixth Eurographics / Ieee VGTC conference on Volume Graphics
Automatic feature modeling techniques for volume segmentation applications
VG'07 Proceedings of the Sixth Eurographics / Ieee VGTC conference on Volume Graphics
3D reconstruction of cultural heritages: Challenges and advances on precise mesh integration
Computer Vision and Image Understanding
3D object reconstruction using convex hull improved by a peeling process
IWAAL'12 Proceedings of the 4th international conference on Ambient Assisted Living and Home Care
Advances in Engineering Software
SMI 2013: Minimizing edge length to connect sparsely sampled unstructured point sets
Computers and Graphics
Vision-based virtual force guidance for tele-robotic system
Computers and Electrical Engineering
SIGGRAPH Asia 2013 Technical Briefs
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The medial axis transform (or MAT) is a representation of an object as an infinite union of balls. We consider approximating the MAT of a three-dimensional object, and its complement, with a finite union of balls. Using this approximate MAT we define a new piecewise-linear approximation to the object surface, which we call the power crust. We assume that we are given as input a sufficiently dense sample of points from the object surface. We select a subset of the Voronoi balls of the sample, the polar balls, as the union of balls representation. We bound the geometric error of the union, and of the corresponding power crust, and show that both representations are topologically correct as well. Thus, our results provide a new algorithm for surface reconstruction from sample points. By construction, the power crust is always the boundary of a polyhedral solid, so we avoid the polygonization, hole-filling or manifold extraction steps used in previous algorithms. The union of balls representation and the power crust have corresponding piecewise-linear dual representations, which in some sense approximate the medial axis. We show a geometric relationship between these duals and the medial axis by proving that, as the sampling density goes to infinity, the set of poles, the centers of the polar balls, converges to the medial axis.