The geometry of fractal sets
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)
Topology representing networks
Neural Networks
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Visualization of scalar topology for structural enhancement
Proceedings of the conference on Visualization '98
Tracking scalar features in unstructured datasets
Proceedings of the conference on Visualization '98
Extremal feature extraction from 3-D vector and noisy scalar fields
Proceedings of the conference on Visualization '98
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
On the definition and the construction of pockets in macromolecules
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
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
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
Nice point sets can have nasty Delaunay triangulations
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Detecting undersampling in surface reconstruction
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Nonlinear manifold learning for visual speech recognition
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Property testing of data dimensionality
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Estimating surface normals in noisy point cloud data
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
An incremental algorithm for reconstruction of surfaces of arbitrary codimension
Computational Geometry: Theory and Applications
Curvature-aware adaptive re-sampling for point-sampled geometry
Computer-Aided Design
Integral estimation from point cloud in d-dimensional space: a geometric view
Proceedings of the twenty-fifth annual symposium on Computational geometry
Bounds on the k-neighborhood for locally uniformly sampled surfaces
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
SMI 2013: Voronoi-based feature curves extraction for sampled singular surfaces
Computers and Graphics
Distance preserving embeddings for general n-dimensional manifolds
The Journal of Machine Learning Research
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There are many scientific and engineering applications where an automatic detection of shape dimension from sample data is necessary. Topological dimensions of shapes constitute an important global feature of them. We present a Voronoi based dimension detection algorithm that assigns a dimension to a sample point which is the topological dimension of the manifold it belongs to. Based on this dimension detection, we also present an algorithm to approximate shapes of arbitrary dimension from their samples. Our empirical results with data sets in three dimensions support our theory.