Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barndorff-Nielsen, O.: Information and Exponential Families in Statistical Theory. John Wiley & Sons: Chichester (1978).
Brodatz, P.: Textures: A Photographic Album for Artists and Designers. Dover Publications: New York (1966).
Campbell, L. L.: Equivalence of Gauss’s principle and minimum discrimination information estimation of probabilities. Annals of Mathematical Statistics 41:3 (1970) 1011–1015.
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.
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.
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.
Gimel’farb, G. L.: Image Textures and Gibbs Random Fields. Kluwer Academic: Dordrecht (1999).
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.
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.
Haralick, R. M., Shapiro, L. G.: Computer and Robot Vision, vol.2. Addison-Wesley: Reading (1993).
Heeger, D., Bergen, J.: Pyramid-based texture analysis/synthesis. In: Computer Graphics 29 (Proc. ACM SIGGRAPH’95 Conf., Los Angeles, CA.) (1995) 229–238.
Julesz, B.: Textons, the elements of texture perception, and their interactions. Nature, no. 290 (1981) 91–97.
Kullback, S.: Information Theory and Statistics. John Wiley & Sons: New York (1959).
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).
Picard, R., Graszyk, S., Mann, S., e.a.: VisTex Database. MITMedia Lab.: Cambridge, Mass. (1995).
Paget, R., Longsta., I. D.: Texture synthesis via a noncausal nonparametric multiscale Markov random field. IEEE Trans. on Image Processing 7 (1998) 925–931.
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, 121
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.
Zhu, S. C., Wu, Y., Mumford, D.: Minimax entropy principle and its application to texture modeling. Neural Computation 9 (1997) 1627–1660.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gimel’farb, G., Yu, L., Zhou, D. (2003). Geometric Structure and Randomness in Texture Analysis and Synthesis. In: Asano, T., Klette, R., Ronse, C. (eds) Geometry, Morphology, and Computational Imaging. Lecture Notes in Computer Science, vol 2616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36586-9_8
Download citation
DOI: https://doi.org/10.1007/3-540-36586-9_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00916-0
Online ISBN: 978-3-540-36586-0
eBook Packages: Springer Book Archive