Texture Regimes for Entropy-Based Multiscale Image Analysis

  • Sylvain Boltz
  • Frank Nielsen
  • Stefano Soatto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6313)


We present an approach to multiscale image analysis. It hinges on an operative definition of texture that involves a “small region”, where some (unknown) statistic is aggregated, and a “large region” within which it is stationary. At each point, multiple small and large regions co-exist at multiple scales, as image structures are pooled by the scaling and quantization process to form “textures” and then transitions between textures define again “structures.” We present a technique to learn and agglomerate sparse bases at multiple scales. To do so efficiently, we propose an analysis of cluster statistics after a clustering step is performed, and a new clustering method with linear-time performance. In both cases, we can infer all the “small” and “large” regions at multiple scale in one shot.


Dictionary Learning Texture Segmentation Critical Scale Dictionary Element Nuisance Factor 
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.
    Aharon, M., Elad, M., Bruckstein, A.M.: The k-svd: An algorithm for designing of overcomplete dictionaries for sparse representation. IEEE Transactions On Signal Processing 54(11), 4311–4322 (2006)CrossRefGoogle Scholar
  2. 2.
    Awate, S.P., Tasdizen, T., Whitaker, R.T.: Unsupervised texture segmentation with nonparametric neighborhood statistics. In: European Conference on Computer Vision, Graz, Austria, pp. 494–507 (2006)Google Scholar
  3. 3.
    Boltz, S., Debreuve, E., Barlaud, M.: High-dimensional statistical distance for region-of-interest tracking: Application to combining a soft geometric constraint with radiometry. In: IEEE International Conference on Computer Vision and Pattern Recognition, Minneapolis, USA (2007)Google Scholar
  4. 4.
    Chazal, F., Guibas, L.J., Oudot, S.Y., Skraba, P.: Persistence-based clustering in Riemannian manifolds. Research Report 6968, INRIA (June 2009)Google Scholar
  5. 5.
    Georgescu, B., Shimshoni, I., Meer, P.: Mean shift based clustering in high dimensions: A texture classification example. In: IEEE International Conference on Computer Vision, p. 456 (2003)Google Scholar
  6. 6.
    Hong, B.W., Soatto, S., Ni, K., Chan, T.F.: The scale of a texture and its application to segmentation. In: IEEE International Conference on Computer Vision and Pattern Recognition (2008)Google Scholar
  7. 7.
    Julesz, B.: Textons, the elements of texture perception and their interactions. Nature (1981)Google Scholar
  8. 8.
    Kadir, T., Zisserman, A., Brady, M.: An affine invariant salient region detector. In: European Conference on Computer Vision (2004)Google Scholar
  9. 9.
    Lindeberg, T.: Scale-space theory in computer vision. Kluwer Academic, Dordrecht (1994)Google Scholar
  10. 10.
    Nock, R., Nielsen, F.: Statistical region merging. IEEE Transactions Pattern Analysis Machine Intelligence 26(11), 1452–1458 (2004)CrossRefGoogle Scholar
  11. 11.
    Robert, C.P.: The Bayesian Choice. Springer, New York (2001)zbMATHGoogle Scholar
  12. 12.
    Soatto, S.: Towards a mathematical theory of visual information (2010) (preprint)Google Scholar
  13. 13.
    Sundaramoorthi, G., Petersen, P., Varadarajan, V.S., Soatto, S.: On the set of images modulo viewpoint and contrast changes. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (June 2009)Google Scholar
  14. 14.
    Terrell, G.R., Scott, D.W.: Variable kernel density estimation. The Annals of Statistics 20, 1236–1265 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Varma, M., Zisserman, A.: A statistical approach to material classification using image patch exemplars. In: IEEE Transactions Pattern Analysis Machine Intelligence (to appear)Google Scholar
  16. 16.
    Vedaldi, A., Soatto, S.: Quick shift and kernel methods for mode seeking. In: European Conference on Computer Vision, vol. IV, pp. 705–718 (2008)Google Scholar
  17. 17.
    Wu, Y.N., Guo, C., Zhu, S.C.: Perceptual scaling. Applied Bayesian Modeling and Causal Inference from an Incomplete Data Perspective (2004)Google Scholar
  18. 18.
    Zhu, S.C., Wu, Y.N., Mumford, D.: Minimax entropy principle and its application to texture modeling. Neural Computation 9, 1627–1660 (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Sylvain Boltz
    • 1
    • 2
  • Frank Nielsen
    • 1
  • Stefano Soatto
    • 1
  1. 1.Laboratoire d’InformatiqueÉcole PolytechniquePalaiseau CedexFrance
  2. 2.UCLA Vision LabUniversity of CaliforniaLos Angeles

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