Adaptive Morphological Filtering Using Similarities Based on Geodesic Time

  • Jacopo Grazzini
  • Pierre Soille
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4992)

Abstract

In this paper, we introduce a novel image-dependent filtering approach derived from concepts known in mathematical morphology. Like other adaptive methods, it assumes that the local neighbourhood of a pixel contains the essential process required for the estimation of local properties. Indeed, it performs a local weighted averaging by combining both spatial and tonal information in a single similarity measure based on the local calculation of discrete geodesic time functions. Therefore, the proposed approach does not require the definition of any initial spatial window but determines adaptively, directly from the input data, the neighbouring sample points and the associated weights. The resulting adaptive filters are consistent with the content of the image and, therefore, they are particularly designed for the purpose of denoising and smoothing of digital images.

Keywords

Priority Queue Central Pixel Multispectral Image Mathematical Morphology Geodesic Path 
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.
    Fisher, R., Dawson-Howe, K., Fitzgibbon, A., Robertson, C., Trucco, E.: Dictionary of Computer Vision and Image Processing. Wiley, Chichester (2005)Google Scholar
  2. 2.
    Jähne, B.: Digital Image Processing: Concepts, Algorithms and Scientific Applications, 4th edn. Springer, Heidelberg (1997)MATHGoogle Scholar
  3. 3.
    Saint-Marc, P., Chen, J., Medioni, G.: Adaptive smoothing: A general tool for early vision. IEEE Trans. Patt. Ana. Mach. Intel. 13, 514–529 (1991)CrossRefGoogle Scholar
  4. 4.
    Paranjape, R., Rangayyan, R., Morrow, W.: Adaptive neighborhood mean and median image filtering. J. Elec. Im. 3, 360–367 (1994)CrossRefGoogle Scholar
  5. 5.
    Pitas, I., Venetsanopoulos, A.: Nonlinear Digital Filters: Principles and Applications. Kluwer Academic Publishers, Norwell, USA (1990)MATHGoogle Scholar
  6. 6.
    Nitzberg, M., Shiota, T.: Nonlinear image filtering with edge and corner enhancement. IEEE Trans. Patt. Ana. Mac. Intel. 14(8), 826–833 (1992)CrossRefGoogle Scholar
  7. 7.
    Cheng, F., Venetsanopoulos, A.: Adaptive morphological operators, fast algorithms and their applications. Patt. Recog. 33, 917–933 (2000)CrossRefGoogle Scholar
  8. 8.
    Debayle, J., Gavet, Y., Pinoli, J.C.: General adaptive neighborhood image restoration, enhancement and segmentation. In: Campilho, A., Kamel, M. (eds.) ICIAR 2006. LNCS, vol. 4141, pp. 29–40. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Mrázek, P., Weickert, J.J., Bruhn, A.: On robust estimation and smoothing with spatial and tonal kernels. In: Geometric Properties for Incomplete Data, pp. 335–352. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Debayle, J., Pinoli, J.C.: General adaptive neighborhood image processing. J. Math. Im. Vis. 25(2), 245–284 (2006)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Buades, A., Coll, B., Morel, J.M.: Neighborhood filters and PDE’s. Num. Math. 105(1), 1–34 (2006)CrossRefMathSciNetMATHGoogle Scholar
  12. 12.
    Soille, P.: Morphological Image Analysis: Principles and Applications, 2nd edn. Springer, Heidelberg (2004)Google Scholar
  13. 13.
    Braga-Neto, U.: Alternating sequential filters by adaptive-neighborhood structuring functions. In: Mathematical Morphology and its Applications to Image and Signal Processing, pp. 139–146. Kluwer Academic Publishers, Dordrecht (1996)Google Scholar
  14. 14.
    Lerallut, R., Decencière, E., Meyer, F.: Image filtering using morphological amoebas. In: Proc. of ISMM. CIV, pp. 13–22. Springer, Heidelberg (2005)Google Scholar
  15. 15.
    Meyer, F., Maragos, P.: Nonlinear scale-space representation with morphological levelings. J. Vis. Comm. Im. Repres. 11(3), 245–265 (2000)CrossRefGoogle Scholar
  16. 16.
    Soille, P.: Constrained connectivity for hierarchical image decomposition and partitioning. IEEE Trans. Patt. Ana. Mac. Intel (2008) (available online since October 2007)Google Scholar
  17. 17.
    Soille, P., Grazzini, J.: Advances in constrained connectivity. In: Proc. of DGCI. LNCS, vol. 4992, pp. 423–433. Springer, Heidelberg (2008)Google Scholar
  18. 18.
    Lavialle, O., Delord, D., Baylou, P.: Adaptive morphology applied to grey level object transformation. In: Proc. of ESPC, pp. 231–234 (2000)Google Scholar
  19. 19.
    Soille, P.: Generalized geodesy via geodesic time. Patt. Recog. Lett. 15(12), 1235–1240 (1994)CrossRefGoogle Scholar
  20. 20.
    Lantuéjoul, C., Maisonneuve, F.: Geodesic methods in image analysis. Patt. Recog. 17, 177–187 (1984)CrossRefMATHGoogle Scholar
  21. 21.
    Verwer, B., Verbeek, P., Dekker, S.: An efficient uniform cost algorithm applied to distance transforms. IEEE Trans. Patt. Ana. Mach. Intel. 11(4), 425–429 (1989)CrossRefGoogle Scholar
  22. 22.
    Coeurjolly, D., Miguet, D., Tougne, L.: 2D and 3D visibility in discrete geometry: an application to discrete geodesic paths. Patt. Recog. Lett. 25(5), 561–570 (2004)CrossRefGoogle Scholar
  23. 23.
    Ikonen, L., Toivanen, P.: Distance and nearest neighbor transforms on gray-level surfaces. Patt. Recog. Lett. 28, 604–612 (2007)CrossRefGoogle Scholar
  24. 24.
    Borgefors, G.: Distance transformations in digital images. Comp. Vis. Graph. Im. Proc. 34, 344–371 (1986)CrossRefGoogle Scholar
  25. 25.
    Levi, G., Montanari, U.: A grey-weighted skeleton. Inform. Cont. 17, 62–91 (1970)CrossRefMATHGoogle Scholar
  26. 26.
    Cohen, L., Kimmel, R.: Global minimum for active contour models: a minimal path approach. Int. J. Comp. Vis. 24, 57–78 (1997)CrossRefGoogle Scholar
  27. 27.
    Ikonen, L.: Pixel queue algorithm for geodesic distance transforms. In: Andrès, É., Damiand, G., Lienhardt, P. (eds.) DGCI 2005. LNCS, vol. 3429, pp. 228–239. Springer, Heidelberg (2005)Google Scholar
  28. 28.
    Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: Proc. of ICCV, pp. 839–846 (1998)Google Scholar
  29. 29.
    Di Zenzo, S.: A note on the gradient of a multi-image. Comp. Vis. Graph Im. Proc. 33, 116–125 (1986)CrossRefGoogle Scholar
  30. 30.
    Grazzini, J., Soille, P.: Edge-preserving smoothing of natural images based on geodesic time functions. In: Proc. of VISAPP, pp. 20–27 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jacopo Grazzini
    • 1
  • Pierre Soille
    • 1
  1. 1.Spatial Data Infrastructures Unit Institute for Environment and SustainabilityJoint Research Centre - European CommissionIspra (VA)Italy

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