Efficient Neighbourhood Computing for Discrete Rigid Transformation Graph Search

  • Yukiko Kenmochi
  • Phuc Ngo
  • Hugues Talbot
  • Nicolas Passat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8668)

Abstract

Rigid transformations are involved in a wide variety of image processing applications, including image registration. In this context, we recently proposed to deal with the associated optimization problem from a purely discrete point of view, using the notion of discrete rigid transformation (DRT) graph. In particular, a local search scheme within the DRT graph to compute a locally optimal solution without any numerical approximation was formerly proposed. In this article, we extend this study, with the purpose to reduce the algorithmic complexity of the proposed optimization scheme. To this end, we propose a novel algorithmic framework for just-in-time computation of sub-graphs of interest within the DRT graph. Experimental results illustrate the potential usefulness of our approach for image registration.

Keywords

image registration discrete rigid transformation discrete optimization DRT graph 

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References

  1. 1.
    Nouvel, B., Rémila, É.: Characterization of bijective discretized rotations. In: Klette, R., Žunić, J. (eds.) IWCIA 2004. LNCS, vol. 3322, pp. 248–259. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Nouvel, B., Rémila, E.: Configurations induced by discrete rotations: Periodicity and quasi-periodicity properties. Discrete Appl. Math. 147, 325–343 (2005)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Berthé, V., Nouvel, B.: Discrete rotations and symbolic dynamics. Theor. Comput. Sci. 380, 276–285 (2007)CrossRefMATHGoogle Scholar
  4. 4.
    Nouvel, B.: Self-similar discrete rotation configurations and interlaced Sturmian words. In: Coeurjolly, D., Sivignon, I., Tougne, L., Dupont, F. (eds.) DGCI 2008. LNCS, vol. 4992, pp. 250–261. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Jacob, M.A., Andres, E.: On discrete rotations. In: Proc. DGCI, pp. 161–174 (1995)Google Scholar
  6. 6.
    Amir, A., Kapah, O., Tsur, D.: Faster two-dimensional pattern matching with rotations. Theor. Comput. Sci. 368, 196–204 (2006)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Reveillès, J.P.: Géométrie discrète, calcul en nombres entiers et algorithmique. Thèse d’État, Université Strasbourg 1 (1991)Google Scholar
  8. 8.
    Andres, E.: The quasi-shear rotation. In: Miguet, S., Ubéda, S., Montanvert, A. (eds.) DGCI 1996. LNCS, vol. 1176, pp. 307–314. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  9. 9.
    Richman, M.S.: Understanding discrete rotations. In: Proc. ICASSP, vol. 3, pp. 2057–2060. IEEE (1997)Google Scholar
  10. 10.
    Andres, E., Fernandez-Maloigne, C.: Discrete rotation for directional orthogonal wavelet packets. In: Proc. ICIP, vol. 2, pp. 257–260. IEEE (2001)Google Scholar
  11. 11.
    Ngo, P., Passat, N., Kenmochi, Y., Talbot, H.: Topology-preserving rigid transformation of 2D digital images. IEEE T. Image Process. 23, 885–897 (2014)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Ngo, P., Kenmochi, Y., Passat, N., Talbot, H.: Combinatorial structure of rigid transformations in 2D digital images. Comput. Vis. Image Und. 117, 393–408 (2013)CrossRefGoogle Scholar
  13. 13.
    Nouvel, B.: Rotations discrètes et automates cellulaires. PhD thesis, École Normale Supérieure de Lyon (2006)Google Scholar
  14. 14.
    Nouvel, B., Rémila, É.: Incremental and transitive discrete rotations. In: Reulke, R., Eckardt, U., Flach, B., Knauer, U., Polthier, K. (eds.) IWCIA 2006. LNCS, vol. 4040, pp. 199–213. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Thibault, Y., Kenmochi, Y., Sugimoto, A.: Computing upper and lower bounds of rotation angles from digital images. Pattern Recogn. 42, 1708–1717 (2009)CrossRefMATHGoogle Scholar
  16. 16.
    Ngo, P., Kenmochi, Y., Passat, N., Talbot, H.: On 2D constrained discrete rigid transformations. Ann. Math. Artif. Intell. (in press), doi:10.1007/s10472-014-9406-xGoogle Scholar
  17. 17.
    Ngo, P., Kenmochi, Y., Passat, N., Talbot, H.: Topology-preserving conditions for 2D digital images under rigid transformations. J. Math. Imaging Vis. 49, 418–433 (2014)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Ngo, P., Sugimoto, A., Kenmochi, Y., Passat, N., Talbot, H.: Discrete rigid transformation graph search for 2D image registration. In: Huang, F., Sugimoto, A. (eds.) PSIVT 2013. LNCS, vol. 8334, pp. 228–239. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  19. 19.
    Zitová, B., Flusser, J.: Image registration methods: A survey. Image Vision Comput. 21, 977–1000 (2003)CrossRefGoogle Scholar
  20. 20.
    Schowengerdt, R.A.: Remote Sensing: Models and Methods for Image Processing, 3rd edn. Elsevier Academic Press (2007)Google Scholar
  21. 21.
    Noblet, V., Heinrich, C., Heitz, F., Armspach, J.P.: Recalage d’images médicales. Tech Ing (MED910) (2014)Google Scholar
  22. 22.
    Edelsbrunner, H., Guibas, L.J.: Topologically sweeping an arrangement. Journal Comput. Syst. Sci. 38, 165–194 (1989); Corrig. 42, 249–251 (1991)Google Scholar
  23. 23.
    Hoare, C.A.R.: Algorithm 65: find. Commun. ACM 4, 321–322 (1961)CrossRefGoogle Scholar
  24. 24.
    Boykov, Y., Kolmogorov, V., Cremers, D., Delong, A.: An integral solution to surface evolution PDEs via geo-cuts. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3953, pp. 409–422. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  25. 25.
    Flusser, J., Zitová, B., Suk, T.: Moments and Moment Invariants in Pattern Recognition. Wiley (2009)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Yukiko Kenmochi
    • 1
  • Phuc Ngo
    • 2
  • Hugues Talbot
    • 1
  • Nicolas Passat
    • 3
  1. 1.Université Paris-Est, LIGM, CNRSFrance
  2. 2.CEA LIST – DIGITEO LabsFrance
  3. 3.Université de Reims Champagne-Ardenne, CReSTICFrance

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