A TV Flow Based Local Scale Measure for Texture Discrimination

  • Thomas Brox
  • Joachim Weickert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3022)


We introduce a technique for measuring local scale, based on a special property of the so-called total variational (TV) flow. For TV flow, pixels change their value with a speed that is inversely proportional to the size of the region they belong to. Exploiting this property directly leads to a region based measure for scale that is well-suited for texture discrimination. Together with the image intensity and texture features computed from the second moment matrix, which measures the orientation of a texture, a sparse feature space of dimension 5 is obtained that covers the most important descriptors of a texture: magnitude, orientation, and scale. A demonstration of the performance of these features is given in the scope of texture segmentation.


Texture Feature Scale Measure Feature Channel Texture Segmentation Moment Matrix 
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.


  1. 1.
    Andreu, F., Ballester, C., Caselles, V., Mazón, J.M.: Minimizing total variation flow. Differential and Integral Equations 14(3), 321–360 (2001)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Bigün, J., Granlund, G.H., Wiklund, J.: Multidimensional orientation estimation with applications to texture analysis and optical flow. IEEE Transactions on Pattern Analysis and Machine Intelligence 13(8), 775–790 (1991)CrossRefGoogle Scholar
  3. 3.
    Brodatz, P.: Textures: a Photographic Album for Artists and Designers. Dover, New York (1966)Google Scholar
  4. 4.
    Brox, T., Welk, M., Steidl, G., Weickert, J.: Equivalence results for TV diffusion and TV regularisation. In: Griffin, L.D., Lillholm, M. (eds.) Scale-Space 2003. LNCS, vol. 2695, pp. 86–100. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Elder, J.H., Zucker, S.W.: Local scale control for edge detection and blur estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence 20(7), 699–716 (1998)CrossRefGoogle Scholar
  6. 6.
    Förstner, W., Gülch, E.: A fast operator for detection and precise location of distinct points, corners and centres of circular features. In: Proc. ISPRS Intercommission Conference on Fast Processing of Photogrammetric Data, Interlaken, Switzerland, June 1987, pp. 281–305 (1987)Google Scholar
  7. 7.
    Gabor, D.: Theory of communication. Journal IEEE 93, 429–459 (1946)Google Scholar
  8. 8.
    Galun, M., Sharon, E., Basri, R., Brandt, A.: Texture segmentation by multiscale aggregation of filter responses and shape elements. In: Proc. IEEE International Conference on Computer Vision, Nice, France (October 2003) (to appear)Google Scholar
  9. 9.
    Gómez, G., Marroquín, J.L., Sucar, L.E.: Probabilistic estimation of local scale. In: Proc. International Conference on Pattern Recognition, Barcelona, Spain, September 2000, vol. 3, pp. 798–801 (2000)Google Scholar
  10. 10.
    Jeong, H., Kim, I.: Adaptive determination of filter scales for edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 14(5), 579–585 (1992)CrossRefGoogle Scholar
  11. 11.
    Lindeberg, T.: Scale-Space Theory in Computer Vision. Kluwer, Boston (1994)Google Scholar
  12. 12.
    Lindeberg, T.: Principles for automatic scale selection. In: Jähne, B., Haußecker, H., Geißler, P. (eds.) Handbook on Computer Vision and Applications, vol. 2, pp. 239–274. Academic Press, Boston (1999)Google Scholar
  13. 13.
    Marcelja, S.: Mathematical description of the response of simple cortical cells. Journal of Optical Society of America 70, 1297–1300 (1980)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Olshausen, B.A., Field, D.J.: Sparse coding with an over-complete basis set: A strategy employed by V1? Vision Research 37, 3311–3325 (1997)CrossRefGoogle Scholar
  15. 15.
    Rao, R., Schunck, B.G.: Computing oriented texture fields. CVGIP: Graphical Models and Image Processing 53, 157–185 (1991)CrossRefGoogle Scholar
  16. 16.
    Reed, T.R., du Buf, J.M.H.: A review of recent texture segmentation and feature extraction techniques. Computer Vision, Graphics and Image Processing 57(3), 359–372 (1993)CrossRefGoogle Scholar
  17. 17.
    Rousson, M., Brox, T., Deriche, R.: Active unsupervised texture segmentation on a diffusion based feature space. In: Proc. 2003 IEEE Computer Society Conf. on Computer Vision and Pattern Recognition, Madison, WI, June 2003, vol. 2, pp. 699–704. IEEE Computer Society Press, Los Alamitos (2003)CrossRefGoogle Scholar
  18. 18.
    Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)zbMATHCrossRefGoogle Scholar
  19. 19.
    Sporring, J., Colios, C.I., Trahanias, P.E.: Generalized scale-selection. Technical Report 264, Foundation for Research and Technology - Hellas, Crete, Greece (December 1999)Google Scholar
  20. 20.
    Weickert, J., ter Haar Romeny, B.M., Viergever, M.A.: Efficient and reliable schemes for nonlinear diffusion filtering. IEEE Transactions on Image Processing 7(3), 398–410 (1998)CrossRefGoogle Scholar
  21. 21.
    Zhu, S.-C., Guo, C., Wu, Y., Wang, W.: What are textons? In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2353, pp. 793–807. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Thomas Brox
    • 1
  • Joachim Weickert
    • 1
  1. 1.Mathematical Image Analysis Group, Faculty of Mathematics and Computer ScienceSaarland UniversitySaarbrückenGermany

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