Skip to main content
Log in

The Promise and Perils of Near-Regular Texture

  • Published:
International Journal of Computer Vision Aims and scope Submit manuscript

Abstract

Motivated by the low structural fidelity for near-regular textures in current texture synthesis algorithms, we propose and implement an alternative texture synthesis method for near-regular texture. We view such textures as statistical departures from regular patterns and argue that a thorough understanding of their structures in terms of their translation symmetries can enhance existing methods of texture synthesis. We demonstrate the perils of texture synthesis for near-regular texture and the promise of faithfully preserving the regularity as well as the randomness in a near-regular texture sample.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ashikhmin, M. 2001. Synthesizing natural textures. In ACM Symposium on Interactive 3D Graphics, pp. 217–226.

  • Bieberbach, L. 1910. Uber die Bewegungsgruppen der n- dimensional en Euklidischen Riume mit einem endlichen Fundamental bereich. Gottinger Nachrichten, pp. 75–84.

  • Chambers, D.A. (ed.). 1995. DNA: The Double Helix: Perspective and Prospective at Forty Years. New York Academy of Sciences: New York.

    Google Scholar 

  • Chetverikov, D. 2000. Pattern regularity as a visual key. Image and Vision Computing, 18:975–986.

    Article  Google Scholar 

  • Chetverikov, D. 2002. Fundamental structural properties of textures. <nt>PhD thesis, MTA SZTAKI, Budapest.</nt>

  • Conners, R.W. and Harlow, C.A. 1980. Toward a structural textural analyzer based on statistical methods. CGIP, 12(3):224–256.

    Google Scholar 

  • Coxeter, H.S.M. 1980. Introduction to Geometry, 2nd edn. Wiley, New York.

    Google Scholar 

  • Coxeter, H.S.M. and Moser, W.O.J. 1980. Generators and Relations for Discrete Groups, 4th edn. Springer-Verlag: New York.

    Google Scholar 

  • Cross, G.R. and Jain, A.K. 1983. Markov random field texture models. IEEE Trans. PAMI, 5:25–39.

    Google Scholar 

  • De Bonet, J.S. 1997. Multiresolution sampling procedure for anal-ysis and synthesis of texture image. In SIGGRAPH Proceedings, pp. 361–368.

  • Efros, A.A. and Freeman, W.T. 2001. Image quilting for texture synthesis and transfer. In SIGGRAPH, pp. 35–42.

  • Efros, A.A. and Leung, T.K. 1999. Texture synthesis by non-parametric sampling. In International Conference on Computer Vision.

  • Enrich, R. and Foith, J.P. 1978. A view of texture topology and texture description. Computer Graphics Image Processing, 8:174–202.

    Google Scholar 

  • Fedorov, E.S. 1885. The elements of the study of figures. [Russian] (2) 21. In Zapiski Imperatorskogo S. Peterburgskogo Mineralogichesgo Obshchestva [Proc. S. Peterb. Mineral. Soc.], pp. 1–289.

  • Feynman, R.P. 1998. Six Not-so-Easy-Pieses: Einstein’s Rela-tivity, Symmetry, and Space-Time. Perseus Press: Cambridge, MA.

    Google Scholar 

  • Grinbaum, B. and Shephard, G.C. 1987. Tilings and Patterns, W.H. Freeman and Company: New York.

    Google Scholar 

  • Hargittai, I. and Hargittai, M. 2000.In</del>Our Own Image: Personal Symmetry in Discovery. Kluwer Academic Publishers.

  • Henry, N.F.M. and Lonsdale, K. (eds.). 1969. International Tables for Xray Crystallography, Vol. 1, Symmetry Groups. The Kynoch Press: England, The International Union of Crystallography.

    Google Scholar 

  • Hertzmann, A., Jacobs, C.E., Oliver, N., Curless, B., and Salesin, D. H. 2001. Image analogies. In SIGGRAPH.

  • Hsu, T.I. and Wilson, R. 1998. A two-component model of texture for analysis and synthesis. IEEE Trans. on Image Processing, 7(10):1466–1476.

    Article  Google Scholar 

  • Kaplan, C.S. and Salesin, D.H. 2000. Escherization. In the 27th In-ternational Conference on Computer Graphics and Interactive Techniques.

  • Leyton, M. 1992. Symmetry, Causality, Mind. The MIT Press: Cambridge, MA.

    Google Scholar 

  • Liang, L., Liu, C., Xu, Y.Q., Guo, B., and Shum, H.Y. 2001. Real-time texture synthesis by patch-based sampling. ACM Transactions on Graphics (TOG), 20(3):127–150.

    Article  Google Scholar 

  • Liu, Y. 2001. Computational symmetry. In Symmetry 2000, I. Hargittai and T.C. Laurent (Eds.). vol. 80 chapter 21, Wenner-Gren International Series, Portland, London, pp. 231–245. ISBN I 85578 149 2.

    Google Scholar 

  • Liu, Y. and Collins, R.T. 2000. A computational model for repeated pattern perception using frieze and wallpaper groups. In Computer Vision and Pattern Recognition Conference (CVPR’00), IEEE Computer Society Press: Hilton Head, SC, pp. 537–544. (http://www.ri.cmu.edu/pubs/pub_3302.html).

    Google Scholar 

  • Liu, Y. and Collins, R.T. 2001. Skewed symmetry groups. In Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’01), IEEE Computer Society Press: Kauai, HI, pp. 872, 879. (http://www.ri.cmu.edu/ pubs/pub_3815.html).

    Google Scholar 

  • Liu, Y., Collins, R.T., and Tsin, Y. 2003. A computational model for periodic pattern perception based on frieze and wallpaper groups. IEEE Transaction on Pattern Analysis and Machine Intelligence (to appear).

  • Lu, S.Y. and Fu, K.S. 1978. A syntactic approach to texture analysis. Computer Graphics Image Processing, 7:303–330.

    Google Scholar 

  • Miller, W. Jr. 1972. Symmetry Groups and Their Applications. Academic Press: New York.

    Google Scholar 

  • Rao, A.R. and Lohse, G.L. 1993. Identifying high level features of texture perception. CVGIP: Image Processing, 55:218–233.

    Article  Google Scholar 

  • Schattschneider, D. 1978. The plane symmetry groups: Their recog-nition and notation. American Mathematical Monthly, 85:439–450.

    Google Scholar 

  • Senechal, M. 1995. Quasicrystals and Geometry. Cambridge University Press.

  • Tsin, Y., Liu, Y., and Ramesh, V. 2001. Texture replacement in real images. In Proceedings of IEEE Computer So-ciety Conference on Computer Vision and Pattern Recog-nition (CVPR’01), (http://www-2.cs.cmu.edu/ ytsin/research/ texturereplacement/index.html), Kauai, IEEE Computer Society Press.

    Google Scholar 

  • Washburn, D.K. and Crowe, D.W. 1991. Symmetries of Culture: Theory and Practice of Plane Pattern Analysis. University of Washington Press.

  • Wei, L.Y. and Levoy, M. 2000. Fast texture synthesis using tree-structured vector quantization. In SIGGRAPH, pp. 479–488.

  • Xu, Y.Q., Zhu, S.C., Guo, B.N., and Shum, H.Y. 2001. Asymptotically admissible texture synthesis. In International Workshop on Statistical and Computational Theories of Vision.

  • Zee, A. 1999. Fearful Symmetry. Princeton University Press.

  • Zhu, S.C., Guo, C.E., Wu, Y.N., and Wang, Y.Z. 2002. What are textons. In Proceeding of European Conference on Computer Vision, Copenhagen, Denmark.

    Google Scholar 

  • Zhu, S.C., Liu, X., and Wu, Y. 2000. Exploring texture ensembles by efficitn markov chain monte carlo. IEEE Transaction on PAMI, 22(6).

  • Zhu, S.C., Wu, Y., and Mumford, D.B. 1997. Minimax entropy principle and its application to texture modeling. Neural Computation, 9:1627–1660.

    Google Scholar 

  • Zucker, S.W. 1976. Toward amodel of texture. CGIP, 5(2):190–202.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, Y., Tsin, Y. & Lin, WC. The Promise and Perils of Near-Regular Texture. Int J Comput Vision 62, 145–159 (2005). https://doi.org/10.1023/B:VISI.0000046593.03875.01

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:VISI.0000046593.03875.01

Keywords

Navigation