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The theory of geometrical wavelets is new and has found already many applications in different fields of digital image processing, though finding many others is still possible and justified. Although images are two dimensional objects they include areas which have different intrinsic (local) dimensionality. Ones of them are more important in the visual perception while the others are less important. The main problem lies in constructing good extractors, which can efficiently extract intrinsic two dimensional areas hidden in images (that is the more important ones). There are some well known nonlinear techniques which can do it relatively effectively. For example the one based on spectral methods, or especially on Volterra series or the one basing on tensors. In this paper there is presented the very novel approach of extracting of intrinsic two dimensional areas based on the theory of geometrical wavelets, especially beamlets. Basing on them the new intrinsic dimensional selective operator has been defined. As performed experiments have shown, giving quite satisfactory results, this approach may constitute serious competition for the well known methods used so far in the theory of intrinsic dimensional operators.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
99--112
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland, alisow@ux2.math.us.edu.pl
Bibliografia
- [1] Canděs E.: Ridgelets: Theory and Applications, Ph.D. Thesis, Departament of Statistics, Stanford University, 1998.
- [2] Canděs E.: What is a Curvelet?, Notices of the American Mathematical Society, Vol. 50, No. 11, 2003, pp. 1402-1403.
- [3] Canděs E., Donoho D.: Curvelets - A Surprisingly Effective Nonadaptive Representation For Objects with Edges, Curves and Surfaces Fitting, A. Cohen, C. Rabut, and L.L. Schumaker, Eds. Saint-Malo: Vanderbilt University Press, 1999.
- [4] Do M.N.: Directional Multiresolution Image Representations, Ph.D. Thesis, Department of Communication Systems, Swiss Federal Institute of Technology Lausanne, November, 2001.
- [5] Donoho D.L.: Wedgelets: Nearly-minimax estimation of edges, Annals of Statistics, Vol. 27, 1999, pp. 859-897.
- [6] Donoho D.L., Huo X.: Beamlets and Multiscale Image Analysis, Lecture Notes in Computational Science and Engineering, Multiscale and Multiresolution Methods, Springer, 2001.
- [7] Fisher R.B.: CVonline: The Evolving, Distributed, Non-Proprietary, On-Line Compendium of Computer Vision, http://www.dai.ed.ac.uk/CVonline/.
- [8] Kaiser P.K.: The Joy of Visual Perception, http://www.yorku.ca/eve/theioy.htm.
- [9] Mitra S.K., Sicuranza G.L.: Nonlinear Image Processing, Academic Press, San Diego, 2001.
- [10] Prieto M.S., Allen A.R.: A Similarity Metric for Edge Images, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 25, No. 10, 2003, pp. 1265-1273.
- [11] Resnikoff H., Wells R.O.Jr: Wavelet Analysis, Springer-Verlag, New York, 2002.
- [12] Romberg J., Wakin M., Baraniuk R.: Multiscale Geometric Image Processing, SPIE Visual Communications and Image Processing, Lugano, Switzerland, July, 2003.
- [13] Romberg J., Wakin M., Baraniuk R.: Approximation and Compression of Piecewise Smooth Images Using a Wavelet/Wedgelet Geometric Model, IEEE International Conference on Image Processing, September, 2003.
- [14] Verveer P.J., Duin R.P.W.: En Evaluation of Intrinsic Dimensionality Estimators, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 17, No. 1, 1995.
- [15] Waterloo BragZone: http://links.uwaterloo.ca/bragzone.base.html.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD2-0001-0021