COMPUTATIONAL SYMMETRY VIA PROTOTYPE DISTANCES FOR SYMMETRY GROUPS CLASSIFICATION

M. Agustí-Melchor, Ángel Rodas-Jordá, J. M. Valiente-González

Abstract

Symmetry is an abstract concept that is easily noticed by humans and as a result designers make new creations based on its use, e.g. textile and tiles. Images of these designs belong to a more general group called wallpaper images, and these images exhibit a repetitive pattern on a 2D space. In this paper, we present a novel computational framework for the automatic classification into symmetry groups of images with repetitive patterns. The existing methods in the literature, based on rules and trees, have several drawbacks because of the use of thresholds and heuristics. Also, there is no way to give some measurement of the classification goodness-of-fit. As a consequence, these methods have shown low classification values when images exhibit imperfections due to the manufacturing process or hand made process. To deal with these problems, we propose a classification method that can obtain an automatic parameter estimation for symmetry analysis. Using this approach, the image classification is redefined as distance computation to the binary prototypes of a set of defined classes. Our experimental results improve the state of the art in symmetry group classification methods.

References

  1. Agustí, M., Valiente, J. M., and Rodas, A. (2008). Lattice extraction based on symmetry analysis. In Procs. of 3rd. Int. Conf. on Computer Vision Applications (VISAPP'08), volume 1, pages 396-402.
  2. Edwards, S. (2009). Tiling plane & fancy. www2.spsu.edu/math/tile/index.htm.
  3. Grunbaüm, B. and Shepard, G. (1987). Tilings And Patterns. W.H. Freeman and Company, New York.
  4. Horne, C. (2000). Geometric Symmetry in Patterns and Tilings. Woodhead Publishing, Abington Hall (England).
  5. Joyce, D. (2007). Wallpaper groups (plane symmetry groups). http://www.clarku.edu/ djoyce/.
  6. Liu, Y. and Collins, R. (2000). A computational model for repeated pattern perception using frieze and wallpaper groups. Technical Report CMU-RI-TR-00-08, Robotics Institute, CMU.
  7. Liu, Y., Collins, R., and Tsin, Y. (2004). A computational model for periodic pattern perception based on frieze and wallpaper groups. Trans. on PAMI, 26(3).
  8. Liu, Y., Hel-Or, H., Kaplan, C. S., and Gool, L. V. (2010). Computational symmetry in computer vision and computer graphics. In Foundations and Trends in Computer Graphics and Vision, volume 5, pages 1- 195.
  9. Reddy, S. and Liu, Y. (2005). On improving the performance of the wallpaper symmetry group classification. Technical Report CMU-RI-TR-05-49, Robotics Institute, Carnegie Mellon University.
  10. Savard, J. G. Basic tilings: The 17 wallpaper groups. http://www.quadibloc.com/math/tilint.htm.
  11. Schattschneider, D. (1978). The plane symmetry groups: Their recognition and notation. The American Mathematical Monthly, 85:439-450.
  12. Wang, J., Neskovic, P., and Cooper, L. N. (2007). Improving nearest neighbor rule with a simple adaptive distance measure. Pattern Recognition Letters, 28(2):207-213.
Download


Paper Citation


in Harvard Style

Agustí-Melchor M., Rodas-Jordá Á. and M. Valiente-González J. (2011). COMPUTATIONAL SYMMETRY VIA PROTOTYPE DISTANCES FOR SYMMETRY GROUPS CLASSIFICATION . In Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2011) ISBN 978-989-8425-47-8, pages 85-93. DOI: 10.5220/0003375300850093


in Bibtex Style

@conference{visapp11,
author={M. Agustí-Melchor and Ángel Rodas-Jordá and J. M. Valiente-González},
title={COMPUTATIONAL SYMMETRY VIA PROTOTYPE DISTANCES FOR SYMMETRY GROUPS CLASSIFICATION},
booktitle={Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2011)},
year={2011},
pages={85-93},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003375300850093},
isbn={978-989-8425-47-8},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2011)
TI - COMPUTATIONAL SYMMETRY VIA PROTOTYPE DISTANCES FOR SYMMETRY GROUPS CLASSIFICATION
SN - 978-989-8425-47-8
AU - Agustí-Melchor M.
AU - Rodas-Jordá Á.
AU - M. Valiente-González J.
PY - 2011
SP - 85
EP - 93
DO - 10.5220/0003375300850093