EDGE-PRESERVING SMOOTHING OF NATURAL IMAGES BASED ON GEODESIC TIME FUNCTIONS

Jacopo Grazzini, Pierre Soille

Abstract

In this paper, we address the problem of edge-preserving smoothing of natural images. We introduce a novel adaptive approach derived from mathematical morphology as a preprocessing stage in feature extraction and/or image segmentation. Like other filtering methods, it assumes that the local neighbourhood of a pixel contains the essential information required for the estimation of local image properties. It performs a weighted averaging by combining both spatial and tonal information in a single similarity measure based on the local calculation of geodesic time functions from the estimated pixel. By designing relevant geodesic masks, it can deal with specific situation and type of images. We describe in the following two possible strategies and we show their capabilities at smoothing heterogeneous areas while preserving relevant structures in natural - greyscale or multispectral - images displaying different features.

References

  1. Arbeláez, P. and Cohen, L. (2003). Path variation and image segmentation. In Proc. of EMMCVPR, volume 2683 of LNCS, pages 246-260. Springer.
  2. Barash, D. (2002). A fundamental relationship between bilateral filtering, adaptive smoothing and the nonlinear diffusion equation. IEEE Trans. Patt. Ana. Mach. Intel., 24(6):844-847.
  3. Borgefors, G. (1986). Distance transformations in digital images. Comp. Vis. Graph. Im. Proc., 34:344-371.
  4. Brownrigg, D. (1984). The weighted median filter. Comm. of ACM, 27(8):807-818.
  5. Cohen, L. and Kimmel, R. (1997). Global minimum for active contour models: a minimal path approach. Int. J. Comp. Vis., 24:57-78.
  6. Comaniciu, D. and Meer, P. (2002). Mean shift: a robust approach toward feature space analysis. IEEE Trans. Patt. Ana. Mach. Intel., 24(5):603-619.
  7. Di Zenzo, S. (1986). A note on the gradient of a multiimage. Comp. Vis. Graph. Im. Proc., 33:116-125.
  8. Gomez, G. (2000). Local smoothness in terms of variance. In Proc. of BMVC, volume 2, pages 815-824.
  9. Grazzini, J., Turiel, A., Yahia, H., and Herlin, I. (2004). Edge-preserving smoothing of high-resolution images with a partial multifractal reconstruction scheme. In Proc. of ISPRS, pages 1125-1129.
  10. Ikonen, L. (2007). Priority pixel queue algorithm for geodesic distance transforms. Im. Vis. Comp., 25:1520-1529.
  11. Ikonen, L. and Toivanen, P. (2007). Distance and nearest neighbor transforms on gray-level surfaces. Patt. Recogn. Lett., 28:604-612.
  12. Jähne, B. (1997). Digital Image Processing: Concepts, Algorithms and Scientific Applications. Springer-Verlag. 4thedition.
  13. Lantuéjoul, C. and Maisonneuve, F. (1984). Geodesic methods in image analysis. Patt. Recogn., 17:177-187.
  14. Levi, G. and Montanari, U. (1970). A grey-weighted skeleton. Inform. Cont., 17:62-91.
  15. Mrázek, P., J. Weickert, J., and Bruhn, A. (2006). On robust estimation and smoothing with spatial and tonal kernels. In Klette, R., Kozera, R., Noakes, L., and Weickert, J., editors, Geometric Properties from Incomplete Data, pages 335-352. Springer.
  16. Narendra, P. (1981). A separable median filter for image noise smoothing. IEEE Trans. Patt. Ana. Mach. Intel., 3(1):20-29.
  17. Nitzberg, M. and Shiota, T. (1992). Nonlinear image filtering with edge and corner enhancement. IEEE Trans. Patt. Ana. Mach. Intel., 14(8):826-833.
  18. Perona, P. and Malik, J. (1990). Scale space and edge detection using anisotropic diffusion. IEEE Trans. Patt. Ana. Mach. Intel., 12:629-639.
  19. Saint-Marc, P. Chen, J. and Medioni, G. (1991). Adaptive smoothing: A general tool for early vision. IEEE Trans. Patt. Ana. Mach. Intel., 13:514-529.
  20. Sapiro, G. and Ringach, D. (1996). Anisotropic diffusion of multivalued images with applications to color filtering. IEEE Trans. Im. Proc., 5(11):15-82.
  21. Scheunders, P. and Sijbers, J. (2001). Multiscale anisotropic filtering of color images. In Proc. of IEEE ICIP, volume 3, pages 170-173.
  22. Soille, P. (1994a). Generalized geodesic distances applied to interpolation and shape description. In Serra, J. and Soille, P., editors, Mathematical Morphology and its Applications to Image Processing, pages 193-200. Kluwer Academic Publishers.
  23. Soille, P. (1994b). Generalized geodesy via geodesic time. Patt. Recogn. Lett., 15(12):1235-1240.
  24. Soille, P. (2004). Morphological Image Analysis: Principles and Applications. Springer-Verlag.
  25. Soille, P. and Grazzini, J. (2007). Extraction of river networks from satellite images by combining mathematical morphology and hydrology. In Proc. of CAIP, volume 4673 of LNCS, pages 636-644. Springer-Verlag.
  26. Sumengen, B., Bertelli, L., and Manjunath, B. (2006). Fast and adaptive pairwise similarities for graph cuts-based image segmentation. In Proc. of IEEE POCV.
  27. Takeda, H., Farsiu, S., and Milanfar, P. (2007). Kernel regression for image processing and reconstruction. IEEE Trans. Im. Proc., 16(2):349-366.
  28. Tomasi, C. and Manduchi, R. (1998). Bilateral filtering for gray and color images. In Proc. of ICCV, pages 839- 846.
  29. van den Boomgaard, R. and van de Weijer, J. (2002). On the equivalence of local-mode finding, robust estimation and mean-shift analysis as used in early vision tasks. In Proc. of ICPR, volume 3, pages 927-930.
  30. van den Boomgaard, R. and van de Weijer, J. (2003). Linear and robust estimation of local image structure. In Proc. of Scale-Space, volume 2695 of LNCS, pages 237-254. Springer.
  31. Verwer, B., Verbeek, P., and Dekker, S. (1989). An efficient uniform cost algorithm applied to distance transforms. IEEE Trans. Patt. Ana. Mach. Intel., 11(4):425-429.
  32. Winkler, G., Aurich, V., Hahn, K., and Martin, A. (1999). Noise reduction in images: some recent edgepreserving methods. Patt. Recogn. Im. Ana., 9(4):749- 766.
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Paper Citation


in Harvard Style

Grazzini J. and Soille P. (2008). EDGE-PRESERVING SMOOTHING OF NATURAL IMAGES BASED ON GEODESIC TIME FUNCTIONS . In Proceedings of the Third International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2008) ISBN 978-989-8111-21-0, pages 20-27. DOI: 10.5220/0001087400200027


in Bibtex Style

@conference{visapp08,
author={Jacopo Grazzini and Pierre Soille},
title={EDGE-PRESERVING SMOOTHING OF NATURAL IMAGES BASED ON GEODESIC TIME FUNCTIONS},
booktitle={Proceedings of the Third International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2008)},
year={2008},
pages={20-27},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001087400200027},
isbn={978-989-8111-21-0},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Third International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2008)
TI - EDGE-PRESERVING SMOOTHING OF NATURAL IMAGES BASED ON GEODESIC TIME FUNCTIONS
SN - 978-989-8111-21-0
AU - Grazzini J.
AU - Soille P.
PY - 2008
SP - 20
EP - 27
DO - 10.5220/0001087400200027