Semi-continuity of skeletons in 2-manifold and discrete Voronoi approximation

Yong-Jin Liu Tsinghua University

Computational Geometry Geometric Analysis and Geometric Topology Geometric Modeling and Processing mathscidoc:1608.09003

IEEE Transactions on Pattern Analysis and Machine Intelligence, 37, (9), 1938-1944, 2015.9
The skeleton of a 2D shape is an important geometric structure in pattern analysis and computer vision. In this paper we study the skeleton of a 2D shape in a two-manifold M, based on a geodesic metric. We present a formal definition of the skeleton S(\Omega) for a shape V in M and show several properties that make S(\Omega) distinct from its Euclidean counterpart in R^2. We further prove that for a shape sequence {\Omega_i} that converge to a shape V in M, the mapping \Omega\rightarrow S(\Omega_i) is lower semi-continuous. A direct application of this result is that we can use a set P of sample points to approximate the boundary of a 2D shape V in M, and the Voronoi diagram of P inside \Omega\subset M gives a good approximation to the skeleton S(\Omega). Examples of skeleton computation in topography and brain morphometry are illustrated.
2D shape sequence, Voronoi skeleton, two-manifold, geodesic
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@inproceedings{yong-jin2015semi-continuity,
  title={Semi-continuity of skeletons in 2-manifold and discrete Voronoi approximation},
  author={Yong-Jin Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160819120002380497258},
  booktitle={IEEE Transactions on Pattern Analysis and Machine Intelligence},
  volume={37},
  number={9},
  pages={1938-1944},
  year={2015},
}
Yong-Jin Liu. Semi-continuity of skeletons in 2-manifold and discrete Voronoi approximation. 2015. Vol. 37. In IEEE Transactions on Pattern Analysis and Machine Intelligence. pp.1938-1944. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160819120002380497258.
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