Advertisement

Nonlinear Optimization for Polygonalization

  • Truong Kieu Linh
  • Atsushi Imiya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)

Abstract

In this paper, we first derive a set of inequalities for the parameters of a Euclidean line from sample pixels, and an optimization criterion with respect to this set of constraints for the recognition of the Euclidean line. Second, using this optimization problem, we prove uniqueness and ambiguity theorems for the reconstruction of a Euclidean line. Finally, we develop a polygonalization algorithm for the boundary of a discrete shape.

Keywords

Nonlinear Optimization Linear Manifold Boundary Pixel Sample Pixel Digital Line 
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.

References

  1. 1.
    Andres, E., Nehlig, P., Francon, J.: Supercover of straight lines, planes, and triangles. In: Ahronovitz, E. (ed.) DGCI 1997. LNCS, vol. 1347, pp. 243–254. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  2. 2.
    Francon, J., Schramm, J.M., Tajine, M.: Recognizing arithmetic straight lines and planes. In: Miguet, S., Ubéda, S., Montanvert, A. (eds.) DGCI 1996. LNCS, vol. 1176, pp. 141–150. Springer, Heidelberg (1996)Google Scholar
  3. 3.
    Buzer, L.: An incremental linear time algorithm for digital line and plane recognition using a linear incrimental feasibility problem. In: Braquelaire, A., Lachaud, J.-O., Vialard, A. (eds.) DGCI 2002. LNCS, vol. 2301, pp. 372–381. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Barneva, R.P., Brimkov, V.E., Nehlig, P.: Thin discrete triangular meshes. Theoretical Computer Science 246, 73–105 (2000D)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Schramm, J.M.: Coplanar tricubes. In: Ahronovitz, E. (ed.) DGCI 1997. LNCS, vol. 1347, pp. 87–98. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  6. 6.
    Vittone, J., Chassery, J.M.: Digital naive planes understanding. In: Proceedings of SPIE, vol. 3811, pp. 22–32 (1999)Google Scholar
  7. 7.
    Reveilles, J.-P.: Combinatorial pieces in digital lines and planes. In: Proceedings of SPIE, vol. 2573, pp. 23–34 (1995)Google Scholar
  8. 8.
    SS253TL2 in Graphic Ornaments, Agile Rabbit Edition. The Pepin Press, Amsterdam (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Truong Kieu Linh
    • 1
  • Atsushi Imiya
    • 2
    • 3
  1. 1.School of Science and TechnologyChiba UniversityJapan
  2. 2.National Institute of InformaticsJapan
  3. 3.Insutitute of Media and Information TechnologyChiba UniversityJapan

Personalised recommendations