Detecting Symmetry and Symmetric Constellations of Features

  • Gareth Loy
  • Jan-Olof Eklundh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3952)


A novel and efficient method is presented for grouping feature points on the basis of their underlying symmetry and characterising the symmetries present in an image. We show how symmetric pairs of features can be efficiently detected, how the symmetry bonding each pair is extracted and evaluated, and how these can be grouped into symmetric constellations that specify the dominant symmetries present in the image. Symmetries over all orientations and radii are considered simultaneously, and the method is able to detect local or global symmetries, locate symmetric figures in complex backgrounds, detect bilateral or rotational symmetry, and detect multiple incidences of symmetry.


Feature Point Rotational Symmetry Bilateral Symmetry Symmetric Pair Sift Descriptor 
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.


  1. 1.
    Carlsson, S.: Symmetry in perspective. In: Burkhardt, H.-J., Neumann, B. (eds.) ECCV 1998. LNCS, vol. 1406, pp. 249–263. Springer, Heidelberg (1998)Google Scholar
  2. 2.
    Dakin, S.C., Herbert, A.M.: The spatial region of integration for visual symmetry detection. Proc. of the Royal Society London B. Bio. Sci. 265, 659–664 (1998)CrossRefGoogle Scholar
  3. 3.
    Davis, L.S.: Understanding shape, ii: Symmetry. SMC 7, 204–212 (1977)Google Scholar
  4. 4.
    Ferrari, V., Tuytelaars, T., Van Gool, L.: Simultaneous object recognition and segmentation from single or multiple model views. Int. J. of Comp. Vis. (2005)Google Scholar
  5. 5.
    Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004); ISBN: 0521540518Google Scholar
  6. 6.
    Hong, W., Yang, A.Y., Huang, K., Ma, Y.: On symmetry and multiple-view geometry: Structure, pose, and calibration from a single image. Int. J. of Comp. Vis. (2004)Google Scholar
  7. 7.
    Jurie, F., Schmid, C.: Scale-invariant shape features for recognition of object categories. In: CVPR (2004)Google Scholar
  8. 8.
    Kaufman, L., Richards, W.: Spontaneous fixation tendencies of visual forms. Perception and Psychophysics 5(2), 85–88 (1969)CrossRefGoogle Scholar
  9. 9.
    Ke, Y., Sukthankar, R.: Pca-sift: A more distinctive representation for local image descriptors. In: CVPR, vol. (2), pp. 506–513 (2004)Google Scholar
  10. 10.
    Keller, Y., Shkolnisky, Y.: An algebraic approach to symmetry detection. In: ICPR, vol. (3), pp. 186–189 (2004)Google Scholar
  11. 11.
    Kiryati, N., Gofman, Y.: Detecting symmetry in grey level images: The global optimization approach. Int. J. of Comp. Vis. 29(1), 29–45 (1998)CrossRefGoogle Scholar
  12. 12.
    Kuehnle, A.: Symmetry-based recognition of vehicle rears. Pattern Recognition Letters 12(4), 249–258 (1991)CrossRefGoogle Scholar
  13. 13.
    Lazebnik, S., Schmid, C., Ponce, J.: Semi-local affine parts for object recognition. In: BMVC (2004)Google Scholar
  14. 14.
    Liu, J., Mundy, J., Zisserman, A.: Grouping and structure recovery for images of objects with finite rotational symmetry. In: ACCV, vol. I, pp. 379–382 (1995)Google Scholar
  15. 15.
    Locher, P., Nodine, C.: Symmetry catches the eye. In: O’Regan, J., Lévy-Schoen, A. (eds.) Eye Movements: from physiology to cognition, Elsevier, Amsterdam (1987)Google Scholar
  16. 16.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. of Comp. Vis. 60(2), 91–110 (2004)CrossRefGoogle Scholar
  17. 17.
    Loy, G., Zelinsky, A.: Fast radial symmetry for detecting points of interest. IEEE Trans Pat. Rec. & Mach. Int. 25(8), 959–973 (2003)CrossRefzbMATHGoogle Scholar
  18. 18.
    Mancas, M., Gosselin, B., Macq, B.: Fast and automatic tumoral area localisation using symmetry. In: Proc. of the IEEE ICASSP Conference (2005)Google Scholar
  19. 19.
    Marola, G.: On the detection of the axes of symmetry of symmetric and almost symmetric planar images. IEEE Trans Pat. Rec. & Mach. Int. 11(1), 104–108 (1989)CrossRefzbMATHGoogle Scholar
  20. 20.
    Masuda, T., Yamamoto, K., Yamada, H.: Detection of partial symmetry using correlation with rotated-reflected images. Pattern Recognition 26(8), 1245–1253 (1993)CrossRefGoogle Scholar
  21. 21.
    Mikolajczyk, K., Schmid, C.: A performance evaluation of local descriptors. IEEE Trans. Pat. Rec. & Mach. Int., 1615–1630 (October 2005)Google Scholar
  22. 22.
    Mikolajczyk, K., Tuytelaars, T., Schmid, C., Zisserman, A., Matas, J., Schaffalitzky, F., Kadir, T., Van Gool, L.: A comparison of affine region detectors. Int. J. of Comp. Vis (2006)Google Scholar
  23. 23.
    Mitra, S., Liu, Y.: Local facial asymmetry for expression classification. In: CVPR (2004)Google Scholar
  24. 24.
    Reisfeld, D., Wolfson, H., Yeshurun, Y.: Context free attentional operators: the generalized symmetry transform. Int. J. of Comp. Vis. 14(2), 119–130 (1995)CrossRefGoogle Scholar
  25. 25.
    Scognamillo, R., Rhodes, G., Morrone, C., Burr, D.: A feature-based model of symmetry detection. Proc. R Soc. Lond. B Biol. Sci. 270, 1727–1733 (2003)CrossRefGoogle Scholar
  26. 26.
    Scott, G., Longuet-Higgins, H.C.: Feature grouping by “relocalisation” of eigenvectors of the proximity matrix. In: BMVC, pp. 103–108 (1990)Google Scholar
  27. 27.
    Sela, G., Levine, M.D.: Real-time attention for robotic vision. Real-Time Imaging 3, 173–194 (1997)CrossRefGoogle Scholar
  28. 28.
    Sharvit, D., Chan, J., Tek, H., Kimia, B.B.: Symmetry-based indexing of image databases. In: Proc. IEEE Workshop on Content-Based Access of Image and Video Libraries (1998)Google Scholar
  29. 29.
    Shen, D., Ip, H.H.S., Teoh, E.K.: Robust detection of skewed symmetries. In: ICPR, vol. 3, pp. 1010–1013 (2000)Google Scholar
  30. 30.
    Shen, D.G., Ip, H.H.S., Teoh, E.K.: Affine invariant detection of perceptually parallel 3d planar curves. Pattern Recognition 33(11), 1909–1918 (2000)CrossRefGoogle Scholar
  31. 31.
    Sun, C., Si, D.: Fast reflectional symmetry detection using orientation histograms. Journal of Real Time Imaging 5(1), 63–74 (1999)CrossRefGoogle Scholar
  32. 32.
    Tuytelaars, T., Turina, A., Van Gool, L.J.: Noncombinatorial detection of regular repetitions under perspective skew. IEEE Trans Pat. Rec. & Mach. Int. 25(4), 418–432 (2003)CrossRefGoogle Scholar
  33. 33.
    Tyler, C.W., Hardage, L., Miller, R.T.: Multiple mechanisms for the detection of mirror symmetry. Spatial Vision 9(1), 79–100 (1995)CrossRefGoogle Scholar
  34. 34.
    Yang, A.Y., Rao, S., Huang, K., Hong, W., Ma, Y.: Geometric segmentation of perspective images based on symmetry groups. In: ICCV, pp. 1251–1258 (2003)Google Scholar
  35. 35.
    Yip, R.K.K.: A hough transform technique for the detection of reflectional symmetry and skew-symmetry. Pattern Recognition Letters 21(2), 117–130 (2000)CrossRefGoogle Scholar
  36. 36.
    Zabrodsky, H., Peleg, S., Avnir, D.: Completion of occluded shapes using symmetry. In: CVPR, pp. 678–679 (1993)Google Scholar
  37. 37.
    Zabrodsky, H., Peleg, S., Avnir, D.: Symmetry as a continuous feature. IEEE Trans Pat. Rec. & Mach. Int. 17(12), 1154–1166 (1995)CrossRefGoogle Scholar
  38. 38.
    Zielke, T., Brauckmann, M., von Seelen, W.: Intensity and edge-based symmetry detection with an application to car-following. CVGIP: Image Underst 58(2), 177–190 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gareth Loy
    • 1
  • Jan-Olof Eklundh
    • 1
  1. 1.Computational Vision & Active Perception LaboratoryRoyal Institute of Technology (KTH)Sweden

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