A Rotation-Invariant Approach to 2D Shape Representation Using the Hilbert Curve

  • Jeffrey Armstrong
  • Maher Ahmed
  • Siu-Cheung Chau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5627)


A novel approach to 2D shape representation which is invariant to the rotation is introduced. The proposed system determines how any given shape should be rotated depending on the principal axis of the image. After rotation, a space-filling curve is applied to obtain a 1D vector representation of the image. This vector is later compressed in order to obtain a very small 1D vector that adequately represents an image – this is called the Shape Feature Vector (SFV). The system can import these SFVs into a database and perform retrieval queries for the best possible match to a query image. The SFV of a query image is obtained and the euclidean distance measure is used to determine a best match. Three different space-filling curves, Hilbert, Moore, and Z-order, are compared through the recognition rate results. Results from testing have shown significant improvement over previous shape representation methods using the Hilbert curve in the case of similar shapes with different initial orientations while not sacrificing precision in cases where the orientation is similar. Additionally, it was found that all three space-filling curves performed similarly.


Shape Representation Shape Recognition Hilbert curve Shape Feature Vector Image Recognition Space-filling curves 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. IEEE Transactions on Pattern Analysis and Machine Intelligence, 509–522 (2002)Google Scholar
  2. 2.
    Berretti, S., Del Bimbo, A., Pala, P.: Retrieval by Shape Similarity with Perceptual Distance and Effective Indexing. IEEE Transactions on Multimedia, 225–239 (2000)Google Scholar
  3. 3.
    Bartolini, I., Ciaccia, P., Patella, M.: WARP – Accurate retrieval of shapes using phase of Fourier descriptors and time warping distance. IEEE Transactions on Pattern Analysis and Machine Intelligence, 142–147 (2005)Google Scholar
  4. 4.
    Lu, G.J., Sajjanhar, A.: Region-based shape representation and similarity measure suitable for content-based image retrieval. Multimedia Syst. 7(2), 165–174 (1999)CrossRefGoogle Scholar
  5. 5.
    Kim, W.-Y., Kim, Y.-S.: A region-based shape descriptor using Zernike moments. Signal Processing: Image Communication 16(1-2), 95–102 (2000)Google Scholar
  6. 6.
    Gorelick, L., Galun, M., Sharon, E., Basri, R., Brandt, A.: Shape Representation and Classification using the Poisson Equation. In: 2004 IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 61–67. IEEE Press, New York (2004)Google Scholar
  7. 7.
    Ebrahim, Y., Ahmed, M., Chau, S.C., Abdelsalem, W.: Shape Representation and Description Using the Hilbert Curve. Pattern Recognition Letters 30(4), 348–358 (2008)CrossRefGoogle Scholar
  8. 8.
    Ebrahim, Y., Ahmed, M., Chau, S.-C., Abdelsalam, W.: A View-Based 3D Object Shape Representation Technique. In: Kamel, M.S., Campilho, A. (eds.) ICIAR 2007. LNCS, vol. 4633, pp. 411–422. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jeffrey Armstrong
    • 1
  • Maher Ahmed
    • 2
  • Siu-Cheung Chau
    • 2
  1. 1.Department of Computing and Information ScienceUniversity of GuelphGuelphCanada
  2. 2.Department of Physics and Computer ScienceWilfrid Laurier UniversityWaterlooCanada

Personalised recommendations