The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
Journal of the ACM (JACM)
The Nonlinear Statistics of High-Contrast Patches in Natural Images
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
Non-linear dimensionality reduction techniques for classification and visualization
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
Semi-Supervised Learning on Riemannian Manifolds
Machine Learning
Shape Dimension and Intrinsic Metric from Samples of Manifolds
Discrete & Computational Geometry
Discrete & Computational Geometry
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Stability of persistence diagrams
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Manifold reconstruction from point samples
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A New Nonlinear Dimensionality Reduction Technique for Pose and Lighting Invariant Face Recognition
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Workshops - Volume 03
Topology guaranteeing manifold reconstruction using distance function to noisy data
Proceedings of the twenty-second annual symposium on Computational geometry
A sampling theory for compact sets in Euclidean space
Proceedings of the twenty-second annual symposium on Computational geometry
Provably good sampling and meshing of Lipschitz surfaces
Proceedings of the twenty-second annual symposium on Computational geometry
Weak witnesses for Delaunay triangulations of submanifolds
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Reconstruction using witness complexes
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Finding the Homology of Submanifolds with High Confidence from Random Samples
Discrete & Computational Geometry
Topological estimation using witness complexes
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Weak witnesses for Delaunay triangulations of submanifolds
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Geodesic Delaunay triangulation and witness complex in the plane
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Towards persistence-based reconstruction in euclidean spaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Dimension detection via slivers
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Constructing Laplace operator from point clouds in Rd
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Integral estimation from point cloud in d-dimensional space: a geometric view
Proceedings of the twenty-fifth annual symposium on Computational geometry
Cut locus and topology from surface point data
Proceedings of the twenty-fifth annual symposium on Computational geometry
A growing self-organizing network for reconstructing curves and surfaces
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Approximating loops in a shortest homology basis from point data
Proceedings of the twenty-sixth annual symposium on Computational geometry
Manifold reconstruction using tangential Delaunay complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Geodesic delaunay triangulations in bounded planar domains
ACM Transactions on Algorithms (TALG)
Algorithms and theory of computation handbook
A fast and simple surface reconstruction algorithm
Proceedings of the twenty-eighth annual symposium on Computational geometry
Linear-size approximations to the vietoris-rips filtration
Proceedings of the twenty-eighth annual symposium on Computational geometry
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
| Hi-index | 0.00 |
It is a well-established fact that the witness complex is closelyrelated to the restricted Delaunay triangulation in lowdimensions. Specifically, it has been proved that the witness complexcoincides with the restricted Delaunay triangulation on curves, and isstill a subset of it on surfaces, under mild samplingassumptions. Unfortunately, these results do not extend tohigher-dimensional manifolds, even under stronger samplingconditions. In this paper, we show how the sets of witnesses andlandmarks can be enriched, so that the nice relations that existbetween both complexes still hold on higher-dimensional manifolds. Wealso use our structural results to devise an algorithm thatreconstructs manifolds of any arbitrary dimension or co-dimension atdifferent scales. The algorithm combines a farthest-point refinementscheme with a vertex pumping strategy. It is very simple conceptually,and it does not require the input point sample W to be sparse. Itstime complexity is bounded by c(d) |W|2, where c(d) is a constantdepending solely on the dimension d of the ambient space.