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Discrete Fourier transform based pattern classifiers

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Języki publikacji
EN
Abstrakty
EN
A technique for pattern classification using the Fourier transform combined with the nearest neighbor classifier is proposed. The multidimensional fast Fourier transform (FFT) is applied to the patterns in the data base. Then the magnitudes of the Fourier coefficients are sorted in descending order and the first P coefficients with largest magnitudes are selected, where P is a design parameter. These coefficients are then used in further processing rather than the original patterns. When a noisy pattern is presented for classification, the pattern’s P Fourier coefficients with largest magnitude are extracted. The coefficients are arranged in a vector in the descending order of their magnitudes. The obtained vector is referred to as the signature vector of the corresponding pattern. Then the distance between the signature vector of the pattern to be classified and the signature vectors of the patterns in the data base are computed and the pattern to be classified is matched with a pattern in the data base whose signature vector is closest to the signature vector of the pattern being classified.
Rocznik
Strony
15--22
Opis fizyczny
Bibliogr. 19 poz., rys., wykr.
Twórcy
autor
  • Department of Mathematical Sciences, San Diego State University, San Diego, CA 92182, USA
autor
  • School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA
Bibliografia
  • [1] J. Altmann and H.J.P. Reitb¨ock, “A fast correlation method for scale- and translation-invariant pattern recognition”, IEEE Trans. on Pattern Analysis and Machine Intelligence PAMI-6 (1), 46-57 (1984).
  • [2] H.J. Reitboeck and J. Altmann, “A model for size- and rotationinvariant pattern processing in the visual system”, Biological Cybernetics 51 (2), 113-121 (1984).
  • [3] P.H. Gardenier, B.C. McCallum, and R.T. Bates, “Fourier transform magnitudes are unique pattern recognition templates”, Biological Cybernetics 54 (6), 385-391 (1986).
  • [4] G.Y. Chen, T.D. Bui, and A. Krzyżak, “Invariant pattern recognition using radon, dual-tree complex wavelet and Fourier transforms”, Pattern Recognition 42 (9), 2013-2019 (2009).
  • [5] R. Barakat and G. Newsam, “Necessary conditions for a unique solution to two-dimensional phase recovery”, J. Mathematical Physics 25 (11), 3190-3193 (1984).
  • [6] P.L. Van Hove, J.S. Lam, and A.V. Oppenheim, “Signal reconstruction from Fourier transform amplitude”, in Applications of Digital Image Processing IV, ed. A.G. Tescher, pp. 214-225, SPIE - The International Society for Optical Engineering, Washington, 1982.
  • [7] L.S. Taylor, “The phase retrieval problem”, IEEE Trans. on Antennas and Propagation AP-29 (2), 386-391 (1981).
  • [8] E.J. Akutowicz, “On the determination of the phase of a Fourier integral, I”, Trans. American Mathematical Society 83, 179-192 (1956).
  • [9] E.J. Akutowicz, “On the determination of the phase of a Fourier integral, II”, Proc. American Mathematical Society 8, 234-238 (1957).
  • [10] M.H. Hayes, J.S. Lim, and A.V. Oppenheim, “Signal reconstruction from phase or magnitude”, IEEE Trans. on Acoustics, Speech, and Signal Processing ASSP-28 (6), 672-680 (1980).
  • [11] M.H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform”, IEEE Trans. on Acoustics, Speech, and Signal Processing ASSP-30 (2), 140-154 (1982).
  • [12] R.H.T. Bates and M.J. McDonnell, Image Restoration and Reconstruction, Oxford University Press, New York, 1986.
  • [13] H. Dym and H.P. McKean, Fourier Series and Integrals, Academic Press, New York, 1972.
  • [14] J.S. Walker, Fourier Analysis, Oxford University Press, New York, 1988.
  • [15] R.C. Gonzalez and P. Wintz, Digital Image Processing, Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1977.
  • [16] C. Oh and S.H. Żak, “Image recall using a large scale generalized Brain-State-in-a-Box neural network”, Int. J. Applied Mathematics and Computer Science 15 (1), 99-114 (2005).
  • [17] C.T. Zahn and R.Z. Roskies, “Fourier descriptors for plane closed curves”, IEEE Trans. on Computers C-21, 269-281 (1972).
  • [18] E. Persoon and K.S. Fu, “Shape discrimination using Fourier descriptors”, IEEE Trans. On Systems, Man and Cybernetics 7 (3), 170-179 (1977).
  • [19] A. Krzyżak, S.Y. Leung, and C.Y. Suen, “Reconstruction of two-dimensional patterns from Fourier descriptors”, Machine Vision and Applications 2 (3), 123-140 (1989).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-3ff15a38-9ac8-4784-a669-4efc969834b4
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