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. It is easily proven that, in any direction, the optimal axis corresponds to the maximal correlation of a pattern with its flipped version. For the measure we compute a modified difference between respective surfaces of a pattern and its kernel. That founds an efficient algorithm to attention focusing on symmetric patterns.
Chapter PDF
Similar content being viewed by others
References
Khöler, W., Wallach, H.: Figural after-effects: an investigation of visual processes. Proc. Amer. phil. Soc. 88, 269–357 (1944)
Zabrodsky, H.: Symmetry - A review, Technical Report 90-16, CS Dep. The Hebrew University of Jerusalem (1990)
Boyton, R.M., Elworth, C.L., Onley, J., Klingberg, C.L.: Form discrimination as predicted by overlap and area, RADC-TR-60-158 (1960)
Zusne, L.: Measures of symmetry. Perception and Psychophysics 9(3B) (1971)
Yodogawa, E.: Symmetropy, an entropy-like measure of visual symmetry. Perception and Psychophysics 32(3) (1983)
O’Mara, D.: Automated facial metrology, chapter 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 in the images via an Hough transform applied to staright lines. Image and Vision Computing 19(12), 857–866 (2001)
Fukushima, S.: Division-based analysis of symmetry and its applications. IEEE PAMI 19(2) (1997)
Mukhergee, D.P., Zisserman, A., Brady, M.: Shape form symmetry: detecting and exploiting symmetry in affine images. Philosofical Transaction of Royal Society of London Academy 351, 77–101 (1995)
Chan, T.J., Cipolla, R.: Symmetry detection through local skewed symmetries. Image and Vision Computing 13(5), 439–455 (1995)
Sato, J., Cipolla, R.: Affine integral invariants for extracting symmetry axes. Image and Vision Computing 15(5), 627–635 (1997)
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)
Gesù, V.D., Valenti, C.: Symmetry operators in computer vision. Vistas in Astronomy, Pergamon 40(4), 461–468 (1996)
Manmatha, R., Sawhney, H.: Finding symmetry in Intensity Images, Technical Report (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)
Kiryati, N., Gofman, Y.: Detecting symmetry in grey level images (the global optimization approach) (1997) (preprint)
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)
Cross, A.D.J., Hancock, E.R.: Scale space vector fields for symmetry detection. Image and Vision Computing, Volume 17(5-6), 337–345 (1999)
Di Gesù, V., Valenti, C.: Detection of regions of interest via the Pyramid Discrete Symmetry Transform. In: Solina, Kropatsch, Klette, Bajcsy (eds.) Advances in Computer Vision, Springer, Heidelberg (1997)
Reisfeld, D., Wolfson, H., Yeshurun, Y.: Detection of interest points using symmetry. In: 3rd IEEE ICCV, Osaka (1990)
Bonneh, Y., Reisfeld, D., Yeshurun, Y.: Texture discrimination by local generalized symmetry. In: 4th IEEE ICCV, Berlin (1993)
Santini, S., Jain, R.: Similarity measures. IEEE PAMI 21(9) (1999)
Heijmans, H.J.A.M., Tuzikof, A.: Similarity and Symmetry measuresfro convex shapes using Minkowski addition. IEEE PAMI 20(9), 980–993 (1998)
Zabrodsky, H., Peleg, S., Avnir, D.: Symmetry as a continuous feature. IEEE PAMI 17(12) (1995)
Kanatani, K.: Comments on Symmetry as a continuous feature. IEEE PAMI 19(3) (1997)
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)
Di Gesu, V., Zavidovique, B.: A note on the Iterative Object Symmetry Transform. Pattern Recognition Letters, Pattern Recognition Letters 25, 1533–1545 (2004)
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
Di Gesù, V., Zavidovique, B. (2005). S_Kernel: A New Symmetry Measure. In: Pal, S.K., Bandyopadhyay, S., Biswas, S. (eds) Pattern Recognition and Machine Intelligence. PReMI 2005. Lecture Notes in Computer Science, vol 3776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11590316_8
Download citation
DOI: https://doi.org/10.1007/11590316_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30506-4
Online ISBN: 978-3-540-32420-1
eBook Packages: Computer ScienceComputer Science (R0)