Skip to main content

Scale Selection for Compact Scale-Space Representation of Vector-Valued Images

  • Conference paper
Scale Space and Variational Methods in Computer Vision (SSVM 2007)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4485))

  • 2811 Accesses

Abstract

This paper investigates the scale selection problem for vector-valued nonlinear diffusion scale-spaces. We present a new approach for the localization scale selection, which aims at maximizing the image content’s presence by finding the scale having a maximum correlation with the noise-free image. For scale-space discretization, we propose to address an adaptation of the optimal diffusion stopping time criterion introduced by Mrázek and Navara [1], in such a way that it identifies multiple scales of importance.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Mrázek, P., Navara, M.: Selection of optimal stopping time for nonlinear diffusion filtering. Int. J. of Comp. Vis. 52(2-3), 189–203 (2003)

    Article  Google Scholar 

  2. Lindeberg, T.: Feature detection with automatic scale selection. Int. J. of Comp. Vis. 30(2), 77–116 (1998)

    Google Scholar 

  3. Pratikakis, I., Sahli, H., Cornelis, J.: Low level image partitioning guided by the gradient watershed hierarchy. Signal Processing 75(2), 173–195 (1998)

    Article  Google Scholar 

  4. Vanhamel, I., Pratikakis, I., Sahli, H.: Multi-scale gradient watersheds of color images. IEEE Trans. on IP 12(6), 617–626 (2003)

    Google Scholar 

  5. Petrovic, A., Divorra Escoda, O., Vandergheynst, P.: Multiresolution segmentation of natural images: From linear to non-linear scale-space representations. IEEE Trans. on IP 13(8), 1104–1114 (2004)

    Google Scholar 

  6. Katartzis, A., Vanhamel, I., Sahli, H.: A hierarchical markovian model for multiscale region-based classification of vector-valued images. IEEE Trans. on Geoscience and Remote Sensing 43(3), 548–558 (2005)

    Article  Google Scholar 

  7. Catté, F., et al.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. on Numerical Analysis 29(1), 182–193 (1992)

    Article  MATH  Google Scholar 

  8. Whitaker, R.T., Gerig, G.: Vector-valued diffusion. In: Geometry-Driven Diffusion in Computer Vision. Computational Imaging and Vision, vol. 1, pp. 93–134. Kluwer Academic Publishers, Dordrecht (1994)

    Google Scholar 

  9. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. on PAMI 12(7), 629–639 (1990)

    Google Scholar 

  10. Black, M., et al.: Robust anisotropic diffusion. IEEE Trans. on IP 7(3), 421–432 (1998)

    Google Scholar 

  11. You, Y.-L., et al.: Behavioral analysis of anisotropic diffusion in image processing. IEEE Trans. on IP 5(11), 1539–1553 (1996)

    Google Scholar 

  12. Geman, D., Reynolds, G.: Constrained restoration and the recovery of discontinuities. IEEE Trans. on PAMI 14( 3), 367–383 (1992)

    Google Scholar 

  13. Koenderink, J.J.: The structure of images. Biological Cybernetics 50, 363–370 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  14. Weickert, J.: Coherence-enhancing diffusion of colour images. Image and Vision Computing 17(3-4), 201–212 (1999)

    Article  Google Scholar 

  15. Mrázek, P.: Selection of optimal stopping time for nonlinear diffusion filtering. In: Kerckhove, M. (ed.) Scale-Space 2001. LNCS, vol. 2106, pp. 290–298. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  16. Lin, Z., Shi, Q.: An anisotropic diffusion PDE for noise reduction and thin edge preservation. In: Int. Conf. on Image Analysis and Processing, pp. 102–107 (1999)

    Google Scholar 

  17. Gilboa, G., Sochen, N., Zeevi, Y.: Estimation of optimal pde-based denoising in the snr sense. CCIT report 499, Technion-Israel (2004)

    Google Scholar 

  18. Hampel, F.R.: The influence curve and its role in robust estimation. J. Amer. Statist. Assoc. 69, 383–393 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  19. Sporring, J., Colios, C.J., Trahanias, P.E.: Generalized scale-selection. In: IEEE Int. Conf. on Image Processing, vol. 1, pp. 920–923. IEEE Computer Society Press, Los Alamitos (2000)

    Google Scholar 

  20. Sporring, J., Weickert, J.: Information measures in scale-spaces. IEEE Transactions on Information Theory 45, 1051–1058 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  21. Hadjidemetriou, E., Grossberg, M.D., Nayar, S.K.: Resolution Selection Using Generalized Entropies of Multiresolution Histograms. In: Heyden, A., et al. (eds.) ECCV 2002. LNCS, vol. 2350, pp. 220–235. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  22. Vanhamel, I.: Vector valued nonlinear diffusion and its application to image segmentation. PhD thesis, ETRO/IRIS: Vrije Universiteit Brussel, Brussels, Belgium (2006)

    Google Scholar 

  23. Wang, Z., et al.: Image quality assessment: From error visibility to structural similarity. IEEE Trans. on Image Processing 13(4), 600–612 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Fiorella Sgallari Almerico Murli Nikos Paragios

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this paper

Cite this paper

Mihai, C., Vanhamel, I., Sahli, H., Katartzis, A., Pratikakis, I. (2007). Scale Selection for Compact Scale-Space Representation of Vector-Valued Images. In: Sgallari, F., Murli, A., Paragios, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2007. Lecture Notes in Computer Science, vol 4485. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72823-8_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72823-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72822-1

  • Online ISBN: 978-3-540-72823-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics