Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30184
Analytical Analysis of Image Representation by Their Discrete Wavelet Transform

Authors: R. M. Farouk

Abstract:

In this paper, we present an analytical analysis of the representation of images as the magnitudes of their transform with the discrete wavelets. Such a representation plays as a model for complex cells in the early stage of visual processing and of high technical usefulness for image understanding, because it makes the representation insensitive to small local shifts. We found that if the signals are band limited and of zero mean, then reconstruction from the magnitudes is unique up to the sign for almost all signals. We also present an iterative reconstruction algorithm which yields very good reconstruction up to the sign minor numerical errors in the very low frequencies.

Keywords: Wavelets, Image processing signal processing, Image reconstruction

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330451

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1052

References:


[1] J. Jones and L. Palmer , An evaluation of two-dimensional Gabor filter model of simple receptive fields in cat striate cortex, J. Neurophysiology 1987, pp.1233-1258.
[2] M. Lades, C. Vorbr├╝ggen, J. Buhmann J. Lange C. von. der MalsburgR .P. W├╝rtz, Distortion Invariant Object Recognition in the Dynamic Link Architecture, IEEE Transaction on computer, vol.42, number 3, 1993, pp.300-310.
[3] G. Kaiser, Friendly Guide to Wavelets, Birkhäuser, 1994.
[4] R. M. Farouk , A system for Finding and segmenting a hand in Partially cluttered scene, may 2007, Proceeding ICAS 29-31.
[5] J. G. Daugman Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters, Journal of the Optical Society of America vol. 2 number 7, 1985, pp. 1362-1373.
[6] D. A. Pollen, S. F. Ronner, Phase relationships between adjacent simple cells in the visual cortex, Science vol.212 , 1981, pp.1409-1411.
[7] C A. Daniel Steven F. Ronner, Visual cortical neurons as localized spatial frequency filter, IEEE Trans. on systems vol.38, number 2, 1992, pp. 587-607.
[8] R. M. Farouk, Reconstruction of objects from images with partial occlusion, PhD thesis 2006.
[9] I. Fogel D. Sagi, Gabor filters as texture discriminator, Biological Cybernetics, vol 16, 1989, pp.103-113.
[10] W. Xing B. Bhanu, Gabor Wavelet Representation for 3-D Object Recognition, IEEE Transactions on Image Processing vol. 6 number 1, 1997, pp.47-64.
[11] L. Shen L. Bai M. Fairhurst, Gabor wavelets and General Discriminant Analysis for face identification and verifications, J. Image vision computing vol. 25, 2007, pp. 553-563.
[12] G. Xijin S. Iwata, Learning the parts of objects by Auto-association, vol.15, 2002, pp.285-295.
[13] P.H. Gardenier , B.C. McClellan R. H. T. Bates, Fourier transform magnitudes are unique pattern recognition templates, Biological Cybernetics vol. 54 pp.385-391 1986.
[14] M. Nabti A. Bouridane, An effective and fast iris recognition system based on a combined multiscale feature extraction technique, Pattern Recognition vol. 41 2008.
[15] 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 vol. 30 number 2 , pp.140-154 1982.
[16] M. H. Hayes H. J. McClellan, Reducible polynomials in more than one variable, Proceeding of IEEE vol.70 number 2 pp. 197-198 1982.
[17] J. R. Fienup, Reconstruction of complex-valued object from the modulus of its Fourier transform using a support constraint, J. of Optical Society of America vol.4 number 1 pp. 118-123 1987.