Triangulating topological spaces
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Topology representing networks
Neural Networks
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
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
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
Journal of the ACM (JACM)
Smooth-surface reconstruction in near-linear time
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Complexity of the delaunay triangulation of points on surfaces the smooth case
Proceedings of the nineteenth annual symposium on Computational geometry
Shape dimension and intrinsic metric from samples of manifolds with high co-dimension
Proceedings of the nineteenth annual symposium on Computational geometry
Nonlinear manifold learning for visual speech recognition
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Provable dimension detection using principal component analysis
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Topology guaranteeing manifold reconstruction using distance function to noisy data
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
Manifold reconstruction in arbitrary dimensions using witness complexes
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Reconstruction using witness complexes
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Sampling and Reconstruction of Surfaces and Higher Dimensional Manifolds
Journal of Mathematical Imaging and Vision
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
On the Locality of Extracting a 2-Manifold in
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Dimension detection via slivers
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Cut locus and topology from surface point data
Proceedings of the twenty-fifth annual symposium on Computational geometry
Isotopic reconstruction of surfaces with boundaries
SGP '09 Proceedings of the Symposium on Geometry Processing
Geometric sampling of manifolds for image representation and processing
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
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)
Non-manifold surface reconstruction from high-dimensional point cloud data
Computational Geometry: Theory and Applications
Boundary of a non-uniform point cloud for reconstruction: extended abstract
Proceedings of the twenty-seventh annual symposium on Computational geometry
A Topological View of Unsupervised Learning from Noisy Data
SIAM Journal on Computing
3D shape from unorganized 3d point clouds
ISVC'05 Proceedings of the First international conference on Advances in Visual Computing
A fast and simple surface reconstruction algorithm
Proceedings of the twenty-eighth annual symposium on Computational geometry
Stability of Delaunay-type structures for manifolds: [extended abstract]
Proceedings of the twenty-eighth annual symposium on Computational geometry
The Journal of Machine Learning Research
Graph induced complex on point data
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We present an algorithm to "reconstruct" a smooth k-dimensional manifold M embedded in an Euclidean space Rd from a "sufficiently dense" point sample from the manifold. The algorithm outputs a simplicial manifold that is homeomorphic and geometrically close to M. The running time is O(n log n) where n is the number of points in the sample (the multiplicative constant depends exponentially on the dimension though).