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Combinatorial Properties of 2D Discrete Rigid Transformations under Pixel-Invariance Constraints

  • Phuc Ngo
  • Yukiko Kenmochi
  • Nicolas Passat
  • Hugues Talbot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7655)

Abstract

Rigid transformations are useful in a wide range of digital image processing applications. In this context, they are generally considered as continuous processes, followed by discretization of the results. In recent works, rigid transformations on ℤ2 have been formulated as a fully discrete process. Following this paradigm, we investigate – from a combinatorial point of view – the effects of pixel-invariance constraints on such transformations. In particular we describe the impact of these constraints on both the combinatorial structure of the transformation space and the algorithm leading to its generation.

Keywords

Combinatorial structure Discrete rigid transformation Pixel– invariance constraints 

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References

  1. 1.
    Amintoosi, M., Fathy, M., Mozayani, N.: A fast image registration approach based on SIFT key-points applied to super-resolution. Imaging Science Journal (2011)Google Scholar
  2. 2.
    Amir, A., Kapah, O., Tsur, D.: Faster two-dimensional pattern matching with rotations. Theoretical Computer Science 368(3), 196–204 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Hundt, C., Liśkiewicz, M.: Combinatorial Bounds and Algorithmic Aspects of Image Matching under Projective Transformations. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 395–406. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Hundt, C., Liśkiewicz, M., Ragnar, N.: A combinatorial geometrical approach to two-dimensional robust pattern matching with scaling and rotation. Theoretical Computer Science 410(51), 5317–5333 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Ngo, P., Kenmochi, Y., Passat, N., Talbot, H.: Combinatorial structure of rigid transformations in 2D digital images. Technical Report, HAL 00643734 (2012)Google Scholar
  6. 6.
    Sharir, M.: Recent Developments in the Theory of Arrangements of Surfaces. In: Pandu Rangan, C., Raman, V., Sarukkai, S. (eds.) FST TCS 1999. LNCS, vol. 1738, pp. 1–21. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  7. 7.
    Thibault, Y.: Rotations in 2D and 3D discrete spaces. PhD thesis, University Paris-Est (2010)Google Scholar
  8. 8.
    Yilmaz, A., Javed, O., Shah, M.: Object tracking: A survey. ACM Computing Surveys 38(4), 1–45 (2006)CrossRefGoogle Scholar
  9. 9.
    Zitová, B., Flusser, J.: Image registration methods: A survey. Image and Vision Computing 21(11), 977–1000 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Phuc Ngo
    • 1
  • Yukiko Kenmochi
    • 1
  • Nicolas Passat
    • 2
    • 3
  • Hugues Talbot
    • 1
  1. 1.LIGM, UPEMLV-ESIEE-CNRSUniversité Paris-EstFrance
  2. 2.LSIIT, UMR 7005 CNRSUniversité de StrasbourgFrance
  3. 3.CReSTICUniversité de ReimsFrance

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