Geometric Structure and Randomness in Texture Analysis and Synthesis

  • Georgy Gimel’farb
  • Linjiang Yu
  • Dongxiao Zhou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2616)


Gibbs random field models describe image textures in terms of geometric structure and energy of pixel interactions. The interaction means statistical interdependence of signals, the structure is given by characteristic pixel neighbourhoods, and the energy depends on signal co- occurrences over the neighbourhoods. In translation invariant textures all the neighbourhoods have the same relative geometry. The interaction structure of such a texture is reflected in a model-based interaction map (MBIM) giving spatial distribution of the interaction energies over a large neighbourhood. We show that due to scale / orientation robustness, the MBIM allows to partition a given training sample into tiles acting as structural elements, or texels. Large-size textured images can be synthesised by replicating the training texels.


Training Sample Texture Analysis Geometric Structure Pixel Neighbourhood Texture Synthesis 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Barndorff-Nielsen, O.: Information and Exponential Families in Statistical Theory. John Wiley & Sons: Chichester (1978).zbMATHGoogle Scholar
  2. [2]
    Brodatz, P.: Textures: A Photographic Album for Artists and Designers. Dover Publications: New York (1966).Google Scholar
  3. [3]
    Campbell, L. L.: Equivalence of Gauss’s principle and minimum discrimination information estimation of probabilities. Annals of Mathematical Statistics 41:3 (1970) 1011–1015.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    De Bonet, J. S.: Multiresolution sampling procedure for analysis and synthesis of texture images. In: Proc. ACM Conf. Computer Graphics SIGGRAPH’97 (1997) 361–368.Google Scholar
  5. [5]
    Efros, A. A., Leung, T. K.: Texture synthesis by non-parametric sampling. In: Proc. IEEE Int. Conf. Computer Vision ICCV’99, Greece, Corfu, Sept. 1999, vol.2 (1999) 1033–1038.Google Scholar
  6. [6]
    Efros, A. A., Freeman, W. T.: Image quilting for texture synthesis and transfer. In: Proc. ACM SIGGRAPH’01, Los Angeles, Calif., August 2001, pp.341–346.Google Scholar
  7. [7]
    Gimel’farb, G. L.: Image Textures and Gibbs Random Fields. Kluwer Academic: Dordrecht (1999).Google Scholar
  8. [8]
    Gimel’farb, G.: Characteristic interaction structures in Gibbs texture modeling. In: Blanc-Talon, J., Popescu, D. C. (Eds.): Imaging and Vision Systems: Theory, Assessment and Applications. Nova Science: Huntington, N.Y. (2001) 71–90.Google Scholar
  9. [9]
    Gimel’farb, G.: Estimation of texels for regular mosaics using model-based interaction maps. In: Proc. Joint IAPR Int. Workshops SSPR 2002 and SPR 2002, Windsor, Ontario, Canada, August 2002 (Lecture Notes in Computer Science 2396), Springer: Berlin (2002) 177–185.Google Scholar
  10. [10]
    Haralick, R. M., Shapiro, L. G.: Computer and Robot Vision, vol.2. Addison-Wesley: Reading (1993).Google Scholar
  11. [11]
    Heeger, D., Bergen, J.: Pyramid-based texture analysis/synthesis. In: Computer Graphics 29 (Proc. ACM SIGGRAPH’95 Conf., Los Angeles, CA.) (1995) 229–238.Google Scholar
  12. [12]
    Julesz, B.: Textons, the elements of texture perception, and their interactions. Nature, no. 290 (1981) 91–97.Google Scholar
  13. [13]
    Kullback, S.: Information Theory and Statistics. John Wiley & Sons: New York (1959).zbMATHGoogle Scholar
  14. [14]
    Liang, L., Liu, C., Xu, Y., Guo, B., Shum, H. Y.: Real-Time Texture Synthesis by Patch-Based Sampling. MSR-TR-2001-40. Microsoft Research (2001).Google Scholar
  15. [15]
    Picard, R., Graszyk, S., Mann, S., e.a.: VisTex Database. MITMedia Lab.: Cambridge, Mass. (1995).Google Scholar
  16. [16]
    Paget, R., Longsta., I. D.: Texture synthesis via a noncausal nonparametric multiscale Markov random field. IEEE Trans. on Image Processing 7 (1998) 925–931.CrossRefGoogle Scholar
  17. [17]
    Portilla, J., Simoncelli, E. P.: A parametric texture model based on joint statistics of complex wavelet coefficients. Int. Journal on Computer Vision 40 (2000) 49–71. 120, 121zbMATHCrossRefGoogle Scholar
  18. [18]
    Zalesny, A., Van Gool, L.: A compact model for viewpoint dependent texture synthesis. In: Pollefeys, M., Van Gool, L., Zisserman, A., Fitzgibbon, A. (Eds.): 3D Structure from Images (Lecture Notes in Computer Science 2018). Springer: Berlin (2001) 124–143.CrossRefGoogle Scholar
  19. [19]
    Zhu, S. C., Wu, Y., Mumford, D.: Minimax entropy principle and its application to texture modeling. Neural Computation 9 (1997) 1627–1660.CrossRefGoogle Scholar
  20. [20]
    Zhu, S. C., Wu, Y., Mumford, D.: Filters, random fields and maximum entropy (FRAME): towards a unified theory for texture modeling. Int. Journal of Computer Vision 27 (1998) 107–126.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Georgy Gimel’farb
    • 1
  • Linjiang Yu
    • 1
  • Dongxiao Zhou
    • 1
  1. 1.Centre for Image Technology and Robotics Department of Computer Science, Tamaki CampusUniversity of AucklandAucklandNew Zealand

Personalised recommendations