Local Scale Measure for Remote Sensing Images

  • Bin Luo
  • Jean-François Aujol
  • Yann Gousseau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5567)


This paper addresses the problem of defining a scale measure for digital images, that is, the problem of assigning a meaningful scale information to each pixel. We propose a method relying on the set of level lines of an image, the so-called topographic map. We make use of the hierarchical structure of level lines to associate a level line to each pixel, enabling the computation of local scales. This computation is made under the assumption that blur is constant over the image, and therefore adapted to the case of satellite images. We then investigate the link between the proposed definition of local scale and recent methods relying on total variation diffusion. Eventually, we perform various experiments illustrating the spatial accuracy of the proposed approach.


Satellite Image Local Scale Level Line Remote Sensing Image Panchromatic Image 
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.


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  1. 1.
    Alter, F., Caselles, V.: Uniqueness of the cheeger set of a convex body (submitted, 2007) (preprint)Google Scholar
  2. 2.
    Bellettini, G., Caselles, V., Novaga, M.: The total variation flow in R n. Journal of differential equation 184, 475–525 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Bellettini, G., Caselles, V., Novaga, M.: Explicit solutions of the eigenvalue problem \(-div \left(\frac{Du}{|Du|}\right)=u\) in R 2. SIAM Journal on Mathematical Analysis 36, 1095–1129 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Brox, T., Weickert, J.: A TV flow based local scale estimate and its application to texture discrimination. Journal of Visual Communication and Image Representation 17, 1053–1073 (2006)CrossRefGoogle Scholar
  5. 5.
    Caselles, V., Coll, B., Morel, J.-M.: Topographic maps and local contrast changes in natural images. Int. J. Comp. Vision 33, 5–27 (1999)CrossRefGoogle Scholar
  6. 6.
    Caselles, V., Monasse, P.: Geometric Description of Topographic Maps and Applications to Image Processing. Lecture Notes in Mathematics. Springer, Heidelberg (to appear, 2009)zbMATHGoogle Scholar
  7. 7.
    Chanussot, J., Benediktsson, J., Fauvel, M.: Classification of remote sensing images from urban areas using a fuzzy possibilistic model. IEEE Geoscience and Remote Sensing Letters 3, 40–44 (2006)CrossRefGoogle Scholar
  8. 8.
    Desolneux, A., Moisan, L., Morel, J.: Edge detection by helmholtz principle. Int. J. of Computer Vision 14, 271–284 (2001)zbMATHGoogle Scholar
  9. 9.
    Dibos, F., Koepfler, G., Monasse, P.: Total variation minimization for scalar/vector regularization. In: Osher, S., Paragios, N. (eds.) Geometric Level Set Methods in Imaging, Vision, and Graphics, pp. 121–140 (2003)Google Scholar
  10. 10.
    Haas, A., Matheron, G., Serra, J.: Morphologie mathématique et granulométries en place. Annales des mines, 736–753 (1967)Google Scholar
  11. 11.
    Jägerstand, M.: Saliency maps and attention selection in scale and spatial coordinates: An information theoretic approach. In: Proc. 5th Int. Conf. on Computer Vision, Cambridge, MA, USA, pp. 195–202 (1995)Google Scholar
  12. 12.
    Latry, C., Rouge, B.: SPOT5 THR mode. In: Proc. SPIE Earth Observing Systems III, October 1998, vol. 3493, pp. 480–491 (1998)Google Scholar
  13. 13.
    Lindeberg, T.: Feature detection with automatic scale selection. Int. J. of Computer Vision 30, 79–116 (1998)CrossRefGoogle Scholar
  14. 14.
    Luo, B., Aujol, J.-F., Gousseau, Y.: Local scale measure from the topographic map and application to remote sensing images. SIAM Multiscale Modeling and Simulation (to appear)Google Scholar
  15. 15.
    Luo, B., Aujol, J.-F., Gousseau, Y., Ladjal, S., Maître, H.: Resolution independent characteristic scale dedicated to satellite images. IEEE Trans. on Image Processing 16, 2503–2514 (2007)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Maragos, P.: Pattern spectrum and multiscale shape representation. IEEE Trans. Pattern Anal. Mach. Intell. 11, 701–716 (1989)CrossRefzbMATHGoogle Scholar
  17. 17.
    Masnou, S., Morel, J.-M.: Image restoration involving connectedness. In: DIP 1997, pp. 84–95. SPIE (1997)Google Scholar
  18. 18.
    Matas, J., Chum, O., Martin, U., Pajdla, T.: Robust wide baseline stereo from maximally stable extremal regions. In: Proceedings of the British Machine Vision Conference, vol. 1, pp. 384–393 (2002)Google Scholar
  19. 19.
    Monasse, P.: Mophological representation of digital images and application to registration. PhD thesis, University Paris IX (2000)Google Scholar
  20. 20.
    Monasse, P., Guichard, F.: Fast computation of a contrast-invariant image representation. IEEE Trans. on Image Processing 9, 860–872 (2000)CrossRefGoogle Scholar
  21. 21.
    Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Salembier, P., Serra, J.: Flat zones filtering, connected operators, and filters by reconstruction. IEEE Transactions on Image Processing 4, 1153–1160 (1995)CrossRefGoogle Scholar
  23. 23.
    Sporring, J., Weickert, J.: On generalized entropies and scale-space. In: Scale-Space Theories in Computer Vision, pp. 53–64 (1997)Google Scholar
  24. 24.
    Steidl, G., Weickert, J., Brox, T., Mrazek, P., Welk, M.: On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and sides. SIAM Journal on Numerical Analysis 42, 686–713 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    Stoyan, D., Kendall, W.S., Mecke, J.: Stochastic Geometry and its Applications, 2nd edn. Wiley, Chichester (1995)zbMATHGoogle Scholar
  26. 26.
    Strong, D., Aujol, J.-F., Chan, T.: Scale recognition, regularization parameter selection, and Meyer’s G norm in total variation regularization. SIAM Journal on Multiscale Modeling and Simulation 5, 273–303 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  27. 27.
    Strong, D., Chan, T.: Edge-preserving and scale-dependent properties of total variation regularization. Inverse Problems 19, 165–187 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Winter, A., Maître, H., Cambou, N., Legrand, E.: An Original Multi-Sensor Approach to Scale-Based Image Analysis for Aerial and Satellite Images. In: IEEE-ICIP 1997, Santa Barbara, CA, USA, vol. II, pp. 234–237 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Bin Luo
    • 1
  • Jean-François Aujol
    • 2
  • Yann Gousseau
    • 3
  1. 1.CNES/DLR/ENST Competence Center and Telecom ParisTechFrance
  2. 2.CMLA, ENS Cachan, CNRS, UniverSudFrance
  3. 3.Telecom ParisTech, LTCI CNRSFrance

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