Topological dimensions of shapes constitute an important feature of sample data. 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, the shapes of arbitrary dimension can be reconstructed from their samples.
< Output of the algorithm >
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Curves |
Foot |
Engine |
Ball |
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* Points classified one dimensional by the algorithm are colored red * Points classified two-dimensional are colored green * Points classified three-dimensional are colored blue |
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Dimension detection |
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Shape reconstruction |
T. K. Dey, J. Giesen, S. Goswami and W. Zhao. Shape dimension and approximation from samples. Proc. 13th ACM-SIAM Sympos. Discrete Algorithms,772-780, 2002.