Skip to content


  • Research Article
  • Open Access

Recognition of Planar Objects Using Multiresolution Analysis

EURASIP Journal on Advances in Signal Processing20062007:070351

Received: 29 August 2005

Accepted: 16 July 2006

Published: 9 October 2006


By using affine-invariant shape descriptors, it is possible to recognize an unknown planar object from an image taken from an arbitrary view when standard view images of candidate objects exist in a database. In a previous study, an affine-invariant function calculated from the wavelet coefficients of the object boundary has been proposed. In this work, the invariant is constructed from the multiwavelet and (multi)scaling function coefficients of the boundary. Multiwavelets are known to have superior performance compared to scalar wavelets in many areas of signal processing due to their simultaneous orthogonality, symmetry, and short support properties. Going from scalar wavelets to multiwavelets is challenging due to the increased dimensionality of multiwavelets. This increased dimensionality is exploited to construct invariants with better performance when the multiwavelet "detail" coefficients are available. However, with (multi)scaling function coefficients, which are more stable in the presence of noise, scalar wavelets cannot be defeated.


Information TechnologySignal ProcessingQuantum InformationSuperior PerformanceWavelet Coefficient


Authors’ Affiliations

Department of Electrical and Electronics Engineering, Boḡaziçi University, Bebek, Turkey


  1. Weiss I: Geometric invariants and object recognition. International Journal of Computer Vision 1993,10(3):207-231. 10.1007/BF01539536View ArticleGoogle Scholar
  2. Arbter K, Snyder WE, Burkhardt H, Hirzinger G: Application of affine-invariant Fourier descriptors to recognition of 3-D objects. IEEE Transactions on Pattern Analysis and Machine Intelligence 1990,12(7):640-647. 10.1109/34.56206View ArticleGoogle Scholar
  3. Alferez R, Wang Y-F: Geometric and illumination invariants for object recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 1999,21(6):505-536. 10.1109/34.771318View ArticleGoogle Scholar
  4. Khalil MI, Bayoumi MM: A dyadic wavelet affine invariant function for 2D shape recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 2001,23(10):1152-1164. 10.1109/34.954605View ArticleGoogle Scholar
  5. Tieng QM, Boles WW: Wavelet-based affine invariant representation: a tool for recognizing planar objects in 3D space. IEEE Transactions on Pattern Analysis and Machine Intelligence 1997,19(8):846-857. 10.1109/34.608288View ArticleGoogle Scholar
  6. Bala E, Cetin AE: Computationally efficient wavelet affine invariant functions for shape recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 2004,26(8):1095-1099. 10.1109/TPAMI.2004.39View ArticleGoogle Scholar
  7. Mallat S, Zhong S: Characterization of signals from multiscale edges. IEEE Transactions on Pattern Analysis and Machine Intelligence 1992,14(2):710-732.View ArticleGoogle Scholar
  8. Martin MB, Bell AE: New image compression techniques using multiwavelets and multiwavelet packets. IEEE Transactions on Image Processing 2001,10(4):500-510. 10.1109/83.913585View ArticleMATHGoogle Scholar
  9. Bui TD, Chen G: Translation-invariant denoising using multiwavelets. IEEE Transactions on Signal Processing 1998,46(12):3414-3420. 10.1109/78.735315View ArticleGoogle Scholar
  10. Bala E, Ertüzün A: A multivariate thresholding technique for image denoising using multiwavelets. EURASIP Journal on Applied Signal Processing 2005,2005(8):1205-1211. 10.1155/ASP.2005.1205View ArticleMATHGoogle Scholar
  11. Nava FP, Martel AF: Planar shape representation based on multiwavelets. Proceedings of 10th European Signal Processing Conference (EUSIPCO '00), September 2000, Tampere, FinlandGoogle Scholar
  12. Goodman TNT, Lee SL:Wavelets of multiplicity . Transactions of the American Mathematical Society 1994,342(1):307-324. 10.2307/2154695MathSciNetMATHGoogle Scholar
  13. Strela V, Heller PN, Strang G, Topiwala P, Heil C: The application of multiwavelet filterbanks to image processing. IEEE Transactions on Image Processing 1999,8(4):548-563. 10.1109/83.753742View ArticleGoogle Scholar
  14. Burrus CS, Gopinath RA, Guo H: Introduction to Wavelets and Wavelet Transforms. Prentice-Hall, Upper Saddle River, NJ, USA; 1998.Google Scholar
  15. Strela V: Multiwavelets: theory and applications, Ph.D. thesis. Massachusetts Institute of Technology, Cambridge, Mass, USA; 1996.Google Scholar
  16. Mallat S: Zero-crossings of a wavelet transform. IEEE Transactions on Information Theory 1991,37(4):1019-1033. 10.1109/18.86995MathSciNetView ArticleGoogle Scholar
  17. El Rube I, Ahmed M, Kamel M: Wavelet approximation-based affine invariant shape representation functions. IEEE Transactions on Pattern Analysis and Machine Intelligence 2006,28(2):323-327.View ArticleGoogle Scholar
  18. Paulik MJ, Wang YD: Three-dimensional object recognition using vector wavelets. Proceedings of the IEEE International Conference on Image Processing, October 1998, Chicago, Ill, USA 3: 586-590.Google Scholar
  19. Daubechies I: Ten Lectures on Wavelets. SIAM, Philadelphia, Pa, USA; 1992.View ArticleMATHGoogle Scholar
  20. Geronimo GS, Hardin DP, Massopust PR: Fractal functions and wavelet expansions based on several functions. Journal of Approximation Theory 1994,78(3):373-401. 10.1006/jath.1994.1085MathSciNetView ArticleMATHGoogle Scholar
  21. Chui CK, Lian JA: A study of orthonormal multiwavelets. In CAT Report 351. Texas A&M University, Canyon, Tex, USA; 1995.Google Scholar
  22. Shen L-X, Tan HH, Tham JY: Symmetric-antisymmetric orthonormal multiwavelets and related scalar wavelets. Applied and Computational Harmonic Analysis 2000,8(3):258-279. 10.1006/acha.1999.0288MathSciNetView ArticleMATHGoogle Scholar
  23. Turcajova R, Strela V: Smooth hermite spline multiwavelets. in preparationGoogle Scholar
  24. Strela V: A note on construction of biorthogonal multi-scaling functions. In Contemporary Mathematics. Volume 216. Edited by: Aldroubi A, Lin EB. American Mathematical Society, Providence, RI, USA; 1998:149-157.Google Scholar
  25. Selesnick I: Cardinal multiwavelets and the sampling theorem. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '99), March 1999, Phoenix, Ariz, USA 3: 1209-1212.View ArticleGoogle Scholar
  26. Berkner K, Massopust PR: Translation invariant multiwavelet transforms. In Tech. Rep. CML TR 98-06. Computational Mathematics Laboratory, Rice University, Houston, Tex, USA; 1998.Google Scholar


© Güney and Ertüzün 2007