Abstract
The symmetry computation has recently been recognized as a topic of interest in many different fields of computer vision and image analysis, which still remains as an open problem. In this work we propose an unified method to compute image symmetries based on finding the minimum-variance partitions of the image that best describe its repetitive nature. We then use a statistical measurement of these partitions as symmetry score. The principal idea is that the same measurement can be used to score symmetries (rotation, reflection, and glide reflection). Finally, a feature vector composed from these symmetry values is used to classify the whole image according to a symmetry group. An increase in the success rate, compared to other reference methods, indicates the improved discriminative capabilities of the proposed symmetry features. Our experimental results improve the state of the art in wallpaper classification methods.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Agustí, M., Rodas, Á., Valiente, J.M.: Computational Symmetry via prototype distances for symmetry groups classification. In: Conf. on Computer Vision Th. and Applications, pp. 85–93 (2011)
Edwards, S.: Tiling Plane & Fancy (2009), http://www2.spsu.edu/math/tile/index.htm
Horne, C.: Geometric Symmetry in Patterns and Tilings. Woodhead Publishing, Abington Hall, England (2000)
Joyce, D.E.: Wallpaper Groups Plane Symmetry Groups, http://www.clarku.edu/~djoyce/ (last visited January 2011)
Liu, Y., Collins, R.T., Tsin, Y.: A computational model for periodic pattern perception based on frieze and wallpaper groups. IEEE Trans. on PAMI 26(3), 354–371 (2004)
Liu, Y., Hel-Or, H., Kaplan, C.S., Van Gool, L.: Computational Symmetry in Computer Vision and Graphics. Foundations and Trends in Computer Graphics and Vision 5(1-2), 1–195 (2010)
Savard, J.G.: Basic tilings: The 17 wallpaper groups, http://www.quadibloc.com/math/tilint.htm (last visited January 2011)
Wikipedia: Wallpaper group, http://www.wikipedia.org (last visited January 2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Agustí-Melchor, M., Rodas-Jordá, A., Valiente-González, J.M. (2011). Symmetry Computation in Repetitive Images Using Minimum-Variance Partitions. In: Real, P., Diaz-Pernil, D., Molina-Abril, H., Berciano, A., Kropatsch, W. (eds) Computer Analysis of Images and Patterns. CAIP 2011. Lecture Notes in Computer Science, vol 6855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23678-5_23
Download citation
DOI: https://doi.org/10.1007/978-3-642-23678-5_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23677-8
Online ISBN: 978-3-642-23678-5
eBook Packages: Computer ScienceComputer Science (R0)