On Shape Orientation When the Standard Method Does Not Work

  • Joviša Žunić
  • Lazar Kopanja
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3773)


In this paper we consider some questions related to the orientation of shapes when the standard method does not work. A typical situation is when a shapes under consideration has more than two axes of symmetry or if the shape is n-fold rotationally symmetric, when n > 2. Those situations are well studied in literature. Here, we give a very simple proof of the main result from [11] and slightly adapt their definition of principal axes for rotationally symmetric shapes. We show some desirable properties that hold if the orientation of such shapes is computed in such a modified way.


Shape orientation image processing early vision 


  1. 1.
    Horn, B.K.P.: Robot Vision. MIT Press, Cambridge (1986)Google Scholar
  2. 2.
    Jain, R., Kasturi, R., Schunck, B.G.: Machine Vision. McGraw-Hill, New York (1995)Google Scholar
  3. 3.
    Klette, R., Žunić, J.: Digital approximation of moments of convex regions. Graphical Models and Image Processing 61, 274–298 (1999)CrossRefGoogle Scholar
  4. 4.
    Lin, J.-C., Tsai, W.-H., Chen, J.-A.: Detecting Number of Folds by a Simple Mathematical Property. Patt. Rec. Letters 15, 1081–1088 (1994)CrossRefGoogle Scholar
  5. 5.
    Lin, J.-C.: The Family of Universal Axes. Patt. Rec. 29, 477–485 (1996)CrossRefGoogle Scholar
  6. 6.
    Mach, E.: The analysis of sensations (Beiträge zur Analyse der Empfindungen), Routledge, London (1996)Google Scholar
  7. 7.
    Marola, G.: On the Detection of Axes of Symmetry of Symmetric and Almost Symmetric Planar Images. IEEE Trans. PAMI 11(6), 104–108 (1989)zbMATHGoogle Scholar
  8. 8.
    Palmer, S.E.: Vision Science: Photons to Phenomenology. MIT Press, Cambridge (1999)Google Scholar
  9. 9.
    Shen, D., Ip, H.H.S.: Optimal Axes for Defining the Orientations of Shapes. Electronic Letters 32(20), 1873–1874 (1996)CrossRefGoogle Scholar
  10. 10.
    Shen, D., Ip, H.H.S., Cheung, K.K.T., Teoh, E.K.: Symmetry Detection by Generalized Complex (GC) Moments: A Close-Form Solution. IEEE Trans. PAMI 21(5), 466–476 (1999)Google Scholar
  11. 11.
    Tsai, W.H., Chou, S.L.: Detection of Generalized Principal Axes in Rotationally Symmetric Shapes. Patt. Rec. 24, 95–104 (1991)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Joviša Žunić
    • 1
  • Lazar Kopanja
    • 2
  1. 1.Computer ScienceExeter UniversityExeterU.K.
  2. 2.Department of Mathematics and InformaticsNovi Sad UniversityNovi SadSerbia and Montenegro

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