Visual Form pp 303-312 | Cite as

Determining the Symmetry of Polyhedra

  • X. Y. Jiang
  • H. Bunke


In this paper we present an algorithm for determining the rotational symmetries of polyhedral objects in O(m(n + m + h)) time and O(n + m + h) space where n, m and h represent the number of vertices, edges and faces of the object, respectively. In the case of objects consisting of c disjoint components the time complexity increases to O(m(cn + m + h)). The symmetry information detected by our algorithm can be utilized for various purposes in artificial intelligence, such as robotics, assembly planning and machine vision.


Rotational Symmetry Bijective Mapping Initial Vertex Neighboring Vertex Neighbor List 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H. Alt et al., Congruence, similarity and symmetries of geometric objects, Discrete & Computational Geometry 3, 1988, 237–256.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    M. J. Atallah, On symmetry detection, IEEE Trans, on Computers 34, 1985, 663–666.MathSciNetCrossRefGoogle Scholar
  3. [3]
    B. Bhanu and C. C. Chen, CAD-based 3D Object Representation for Robot Vision, IEEE Computer 20, No. 8, 1987, 19–35.CrossRefGoogle Scholar
  4. [4]
    R. C. Bolles and R. A. Cain, Recognising and locating partially visible objects, Int. Journal of Robotics Research 1, No. 3, 1982, 57–82.CrossRefGoogle Scholar
  5. [5]
    H. Chiyokura, Solid modelling with Designbase: theory and implementation, Addison-Wesley Publishing Company, 1988.Google Scholar
  6. [6]
    L. De Floriani and E. Bruzzone, Decomposing a solid object into elementary features, in Recent issues in pattern analysis and recognition (V. Cantoni et al., Eds.), pp. 226-237, Springer-Verlag, 1989.Google Scholar
  7. [7]
    P. J. Flynn and A. K. Jain, CAD-based computer vision: From CAD models to relational models, IEEE Trans. on Pattern Analysis and Machine Intelligence 13, No. 2, 1991, 114–132.CrossRefGoogle Scholar
  8. [8]
    T. Glauser, E. Gmür, X. Y. Jiang and H. Bunke, Deductive generation of vision representations from CAD-models, in Proc. of 6th Scand. Conf. on Image Analysis, Oulu, Finland, 1989, pp. 645-651.Google Scholar
  9. [9]
    X. Y. Jiang and H. Bunke, Recognition of overlapping convex objects using interpretation tree search and EGI matching, in Proc. of SPIE Conf. on Applications of Digital Image Processing XII, Vol. 1153, San Diego, 1989, pp. 611–620.CrossRefGoogle Scholar
  10. [10]
    X. Y. Jiang and H. Bunke, Recognizing 3-D objects in needle maps, in Proc. of 10th Int. Conf on Pattern Recognition, Atlantic City, New Jersey, 1990, pp. 237-239.Google Scholar
  11. [11]
    X. Y. Jiang and H. Bunke, Optimal Vertex Ordering of a Graph and its Application to Symmetry Detection, in Proc. of 17th Int. Workshop on Graph-Theoretic Concepts in Computer Science, Richterheim Fischbachau, Germany, 1991.Google Scholar
  12. [12]
    R. J. Popplestone, Y. Liu and R. Weiss, A group theoretic approach to assembly planning, AI magazine, 11, No. 1, 1990, 82–97.Google Scholar
  13. [13]
    B. Radig and C. Schlieder, RS-automorphisms and symmetrical objects, in Proc. of 7th Int. Conf. on Pattern Recognition, Montreal, Canada, 1984, pp. 1138-1140.Google Scholar
  14. [14]
    M. Shneier, A compact relational structure representation, in Proc. of 6th IJCAI, Tokyo, Japan, 1979, pp. 818-826.Google Scholar
  15. [15]
    J. D. Wolter, R. A. Volz and T. C. Woo, Automatic generation of gripping positions, University of Michigan, Ann Arbor, February, 1984.Google Scholar
  16. [16]
    J. D. Wolter, T. C. Woo and R. A. Volz, Optimal algorithms for symmetry detection in two and three dimensions, The Visual Computer, 1, 1985, 37–48.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • X. Y. Jiang
    • 1
  • H. Bunke
    • 1
  1. 1.Institute of Informatics and Applied MathematicsUniversity of BernBernSwitzerland

Personalised recommendations