# 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

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#### 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