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)
Automatic reconstruction of surfaces and scalar fields from 3D scans
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
r-regular shape reconstruction from unorganized points
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
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
Voronoi-based interpolation with higher continuity
Proceedings of the sixteenth annual symposium on Computational geometry
Curve reconstruction: connecting dots with good reason
Computational Geometry: Theory and Applications
Geometric structures for three-dimensional shape representation
ACM Transactions on Graphics (TOG)
New techniques for topologically correct surface reconstruction
Proceedings of the conference on Visualization '00
Shape Reconstruction with Delaunay Complex
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Delaunay based shape reconstruction from large data
PVG '01 Proceedings of the IEEE 2001 symposium on parallel and large-data visualization and graphics
Shape dimension and approximation from samples
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate medial axis as a voronoi subcomplex
Proceedings of the seventh ACM symposium on Solid modeling and applications
Undersampling and oversampling in sample based shape modeling
Proceedings of the conference on Visualization '01
PMR: point to mesh rendering, a feature-based approach
Proceedings of the conference on Visualization '02
Efficient Simplicial Reconstructions of Manifolds from Their Samples
IEEE Transactions on Pattern Analysis and Machine Intelligence
The flow complex: a data structure for geometric modeling
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Perturbations and vertex removal in a 3D delaunay triangulation
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Robustness Issues in Surface Reconstruction
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Optimal Net Surface Problems with Applications
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Shape dimension and intrinsic metric from samples of manifolds with high co-dimension
Proceedings of the nineteenth annual symposium on Computational geometry
Alpha-shapes and flow shapes are homotopy equivalent
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Tight cocone: a water-tight surface reconstructor
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
Reconstruction of surfaces of revolution with partial sampling
Journal of Computational and Applied Mathematics - Special issue on proceedings of the international symposium on computational mathematics and applications
Improvements to surface reconstruction by the CRUST algorithm
SCCG '03 Proceedings of the 19th spring conference on Computer graphics
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
Shape Simplification Based on the Medial Axis Transform
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Provable surface reconstruction from noisy samples
Computational Geometry: Theory and Applications
An incremental algorithm for reconstruction of surfaces of arbitrary codimension
Computational Geometry: Theory and Applications
Topology, Accuracy, and Quality of Isosurface Meshes Using Dynamic Particles
IEEE Transactions on Visualization and Computer Graphics
Boundary filtering approach in surface reconstruction
International Journal of Computational Science and Engineering
Automatic 3D skull reconstruction using invariant features
CSTST '08 Proceedings of the 5th international conference on Soft computing as transdisciplinary science and technology
Consolidation of unorganized point clouds for surface reconstruction
ACM SIGGRAPH Asia 2009 papers
Provable surface reconstruction from noisy samples
Computational Geometry: Theory and Applications
Isotopic reconstruction of surfaces with boundaries
SGP '09 Proceedings of the Symposium on Geometry Processing
Technical Section: Visibility of noisy point cloud data
Computers and Graphics
Perturbations for Delaunay and weighted Delaunay 3D triangulations
Computational Geometry: Theory and Applications
Non-manifold surface reconstruction from high-dimensional point cloud data
Computational Geometry: Theory and Applications
SMI 2011: Full Paper: Localized Cocone surface reconstruction
Computers and Graphics
Plausible 3d colour surface completion using non-parametric techniques
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Edge-aware point set resampling
ACM Transactions on Graphics (TOG)
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Current surface reconstruction algorithms perform satisfactorily on we ll-sampled, smooth surfaces without boundaries. However, these algorithms face difficulty with undersampling. Cases of undersampling are prevalent in real data since often they sample a part of the boundary of an object, or are derived from a surface with high curvature or nonsmoothness. In this paper we present an algorithm to detect the boundaries where dense sampling stops and undersampling begins. This information can be used to reconstruct surfaces with boundaries, and also to localize small and sharp features where usually undersampling happens. We report the effectiveness of the algorithm with a number of experimental results. Theoretically, we justify the algorithm with some mild assumptions that are valid for most practical data.