Computational Topology for Point Data: Betti Numbers of α-Shapes

  • Vanessa Robins
Part of the Lecture Notes in Physics book series (LNP, volume 600)


The problem considered belowis that of determining information about the topology of a subset X ⊂ ℝn given only a finite point approximation to X. The basic approach is to compute topological properties — such as the number of components and number of holes — at a sequence of resolutions, and then to extrapolate. Theoretical foundations for taking this limit come from the inverse limit systems of shape theory and Čech homology. Computer implementations involve constructions from discrete geometry such as alpha shapes and the minimal spanning tree.


Simplicial Complex Minimal Span Tree Voronoi Diagram Homology Group Betti Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Vanessa Robins
    • 1
  1. 1.Department of Applied Mathematics, Research School of Physical Sciences and EngineeringAustralian National UniversityCanberra

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