Abstract
Symmetry is an important feature in vision. Several detectors or transforms have been proposed. In this paper we concentrate on a measure of symmetry. Given a transform S, the kernel SK of a pattern is defined as the maximal included symmetric sub-set of this pattern. The maximum being taken over all directions, the problem arises to know which center to use. Then the optimal direction triggers the shift problem too. We prove that, in any direction, the optimal axis corresponds to the maximal correlation of a pattern with its flipped version. That leads to an efficient algorithm. As for the measure we compute a modified difference between respective surfaces of a pattern and its kernel. A series of experiments supports actual algorithm validation.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Khöler, W., Wallach, H.: Figural after-effects: an investigation of visual processes. Proc. Amer. phil. Soc. 88, 269–357 (1944)
O’Mara, D.: Automated facial metrology, ch. 4, Symmetry detection and measurement. PhD thesis (February 2002)
Blum, H., Nagel, R.N.: Shape description using weighted symmetric axis features. Pattern recognition 10, 167–180 (1978)
Brady, M., Asada, H.: Smoothed Local Symmetries and their implementation. The International Journal of Robotics Research 3(3), 36–61 (1984)
Sewisy, A., Lebert, F.: Detection of ellipses by finding lines of symmetry inthe images via an Hough transform applied to staright lines. Image and Vision Computing 19 - 12, 857–866 (2001)
Marola, G.: On the detection of the axes of symmetry of symmetric and almost symmetric planar images. IEEE Trans.of PAMI 11, 104–108 (1989)
Manmatha, R., Sawhney, H.: Finding symmetry in Intensity Images, Technical Report (1997)
Kiryati, N., Gofman, Y.: Detecting symmetry in grey level images (the global optimization approach) (1997) (preprint)
Di Gesù, V., Valenti, C.: Symmetry operators in computer vision. Vistas in Astronomy, Pergamon 40(4), 461–468 (1996)
Di Gesù, V., Valenti, C.: Detection of regions of interest via the Pyramid Discrete Symmetry Transform. In: Solina, K., Klette, B. (eds.) Advances in Computer Vision. Springer, Heidelberg (1997)
Cross, A.D.J., Hancock, E.R.: Scale space vector fields for symmetry detection. Image and Vision Computing 17, 5-6, 337–345 (1999)
Shen, D., Ip, H., Teoh, E.K.: An energy of assymmetry for accurate detection of global reflexion axes. Image Vision and Computing 19, 283–297 (2001)
Zabrodsky, H.: Symmetry - A review., Technical Report 90-16, CS Dep. The Hebrew University of Jerusalem
DiGesu, V., Zavidovique, B.: A note on the Iterative Object Symmetry Transform. Pattern Recognition Letters 25, 1533–1545 (2004)
Boyton, R.M., Elworth, C.L., Onley, J., Klingberg, C.L.: Form discrimination as predicted by overlap and area. RADC-TR-60-158 (1960)
Fukushima, S.: Division-based analysis of symmetry and its applications. IEEE PAMI 19-2 (1997)
Shen, D., Ip, H., Cheung, K.T., Teoh, E.K.: Symmetry detection by Generalized complex moments: a close-form solution. IEEE PAMI 21-5 (1999)
Bigun, J., DuBuf, J.M.H.: N-folded symmetries by complex moments in Gabor space and their application to unsupervized texture segmentation. IEEE PAMI 16-1 (1994)
Masuda, T., Yamamoto, K., Yamada, H.: Detection of partial symmetyr using correlation with rotated-reflected images. Pattern Recognition 26-8 (1993)
O’Maraa, D., Owens, R.: Measuring bilateral symmetry in digital images. IEEE TENCON, Digital signal processing aplications (1996)
Kazhdan, M., Chazelle, B., Dobkin, D., Finkelstein, A., Funkhouser, T.: A reflective symmetry descriptor. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2351, pp. 642–656. Springer, Heidelberg (2002)
Reisfeld, D., Wolfson, H., Yeshurun, Y.: Detection of interest points using symmetry. In: 3rd IEEE ICCV, Osaka, (December 1990)
Bonneh, Y., Reisfeld, D., Yeshurun, Y.: Texture discrimination by local generalized symmetry. In: 4th IEEE ICCV, Berlin (May 1993)
Merigot, A., Zavidovique, B.: Image analysis on massively parallel computers: An architectural point of view. J. of pattern recognition and artificial intelligence 6(2-3), 387–393 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zavidovique, B., Di Gesù, V. (2005). The S-Kernel and a Symmetry Measure Based on Correlation. In: Kalviainen, H., Parkkinen, J., Kaarna, A. (eds) Image Analysis. SCIA 2005. Lecture Notes in Computer Science, vol 3540. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499145_21
Download citation
DOI: https://doi.org/10.1007/11499145_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26320-3
Online ISBN: 978-3-540-31566-7
eBook Packages: Computer ScienceComputer Science (R0)