The Visual Computer

, Volume 11, Issue 2, pp 105–112 | Cite as

Computational morphology of curves

  • Luiz Henrique de Figueiredo
  • Jonas de Miranda Gomes
Article

Abstract

We prove that euclidean minimal spanning trees correctly reconstruct differentiable arcs from sufficiently dense samples. The proof is based on a combinatorial characterization of minimal spanning paths and on a description of the local geometry of ares inside tubular neighborhoods. We also present simple heuristics for reconstruting more general curves.

Key words

Computational morphology Curve reconstruction Minimal spanning trees 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arnon DS (1983) Topologically reliable display of algebraic curves. Comput Graph 17:219–227Google Scholar
  2. 2.
    Boissonnat J-D (1984) Geometric structures for three-dimensional shape representation. ACM Trans Graph 3:266–286Google Scholar
  3. 3.
    Duda RO, Hart PE (1973) Pattern Classification and Scene Analysis. WileyGoogle Scholar
  4. 4.
    Figueiredo LH (1992) Computational Morphology of Implicit Curves. Doctoral thesis, IMPA, Rio de JaneiroGoogle Scholar
  5. 5.
    Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W (1992) Surface reconstruction from unorganized points. Comput Graph 26:71–78Google Scholar
  6. 6.
    Hirsh MW (1976) Differential Topology, Graduate Texts in Mathematics 33, Springer, Berlin, Heidelberg, New YorkGoogle Scholar
  7. 7.
    Kirkpatrick DG, Radke JD (1985) A framework for computational morphology. In: Toussaint G (ed) Computational Geometry. North-Holland, pp 217–248Google Scholar
  8. 8.
    Prim RC (1957) Shortest connection matrix network and some generalizations. Bell Syst Tech J 36:1389–1401Google Scholar
  9. 9.
    Toussaint G (1980) Pattern recognition and computational complexity. Proceedings of the Fifth International Conference on Pattern Recognition, pp 1324–1347Google Scholar
  10. 10.
    Veltkamp RC (1992) The ψ-neighborhood graph. Comput Geom Theory Appl 1:227–246Google Scholar
  11. 11.
    Zahn CT (1971) Graph-theoretical methods for detecting and describing gestalt clusters. IEEE Trans Comput C 20:68–86Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Luiz Henrique de Figueiredo
    • 1
  • Jonas de Miranda Gomes
    • 1
  1. 1.IMPA-Instituto de Matemática Pura e AplicadaRio de JaneiroBrazil

Personalised recommendations