- Research Article
- Open Access
Recognition of Planar Objects Using Multiresolution Analysis
EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 070351 (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.
Weiss I: Geometric invariants and object recognition. International Journal of Computer Vision 1993,10(3):207–231. 10.1007/BF01539536
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. 10.1109/34.56206
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. 10.1109/34.771318
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. 10.1109/34.954605
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. 10.1109/34.608288
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.2004.39
Mallat S, Zhong S: Characterization of signals from multiscale edges. IEEE Transactions on Pattern Analysis and Machine Intelligence 1992,14(2):710–732.
Martin MB, Bell AE: New image compression techniques using multiwavelets and multiwavelet packets. IEEE Transactions on Image Processing 2001,10(4):500–510. 10.1109/83.913585
Bui TD, Chen G: Translation-invariant denoising using multiwavelets. IEEE Transactions on Signal Processing 1998,46(12):3414–3420. 10.1109/78.735315
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.2005.1205
Nava FP, Martel AF: Planar shape representation based on multiwavelets. Proceedings of 10th European Signal Processing Conference (EUSIPCO '00), September 2000, Tampere, Finland
Goodman TNT, Lee SL:Wavelets of multiplicity . Transactions of the American Mathematical Society 1994,342(1):307–324. 10.2307/2154695
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. 10.1109/83.753742
Burrus CS, Gopinath RA, Guo H: Introduction to Wavelets and Wavelet Transforms. Prentice-Hall, Upper Saddle River, NJ, USA; 1998.
Strela V: Multiwavelets: theory and applications, Ph.D. thesis. Massachusetts Institute of Technology, Cambridge, Mass, USA; 1996.
Mallat S: Zero-crossings of a wavelet transform. IEEE Transactions on Information Theory 1991,37(4):1019–1033. 10.1109/18.86995
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.
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.
Daubechies I: Ten Lectures on Wavelets. SIAM, Philadelphia, Pa, USA; 1992.
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.1994.1085
Chui CK, Lian JA: A study of orthonormal multiwavelets. In CAT Report 351. Texas A&M University, Canyon, Tex, USA; 1995.
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.1999.0288
Turcajova R, Strela V: Smooth hermite spline multiwavelets. in preparation
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.
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.
Berkner K, Massopust PR: Translation invariant multiwavelet transforms. In Tech. Rep. CML TR 98-06. Computational Mathematics Laboratory, Rice University, Houston, Tex, USA; 1998.
About this article
Cite this article
Güney, N., Ertüzün, A. Recognition of Planar Objects Using Multiresolution Analysis. EURASIP J. Adv. Signal Process. 2007, 070351 (2006). https://doi.org/10.1155/2007/70351
- Information Technology
- Signal Processing
- Quantum Information
- Superior Performance
- Wavelet Coefficient