Advertisement

Optimal Triangle Stripifications as Minimum Energy States in Hopfield Nets

  • Jiří Šíma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3696)

Abstract

The important task of generating the minimum number of sequential triangle strips for a given triangulated surface model is motived by applications in computer graphics. This hard combinatorial optimization problem is reduced to the minimum energy problem in Hopfield nets by a linear-size construction. First practical experiments have confirmed that computing the semi-optimal stripifications by using Hopfield nets is a promising approach. In this work we provide a theoretical justification of this method by proving that the classes of equivalent optimal stripifications are mapped one to one to the minimum energy states.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Barahona, F.: On the computational complexity of Ising spin glass models. Journal of Physics A: Mathematical and General 15(10), 3241–3253 (1982)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Estkowski, R., Mitchell, J.S.B., Xiang, X.: Optimal decomposition of polygonal models into triangle strips. In: Proceedings of the 18th Annual Symposium on Computational Geometry, pp. 254–263. ACM Press, New York (2002)Google Scholar
  3. 3.
    Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences USA 79(8), 2554–2558 (1982)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Hopfield, J.J., Tank, D.W.: “Neural” computation of decision in optimization problems. Biological Cybernetics 52(3), 141–152 (1985)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Pospíšil, D.: Generating triangle strips by Hopfield network. In: Pospíšil, D. (ed.) Student’s project (in Czech), Faculty of Informatics, Masaryk University, Czech Republic (2002) Google Scholar
  6. 6.
    Šíma, J.: Tristrips on Hopfield networks. Technical report V-908, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague (2004)Google Scholar
  7. 7.
    Šíma, J.: Generating sequential triangle strips by using Hopfield nets. In: Proceedings of the ICANNGA 2005 7th International Conference on Adaptive and Natural Computing Algorithms, pp. 25–28. Springer, Vienna (2005)Google Scholar
  8. 8.
    Šíma, J., Orponen, P.: General-purpose computation with neural networks: A survey of complexity theoretic results. Neural Computation 15(12), 2727–2778 (2003)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jiří Šíma
    • 1
  1. 1.Institute of Computer ScienceAcademy of Sciences of the Czech RepublicPrague 8Czech Republic

Personalised recommendations