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Three-dimensional octonion wavelet transform

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Języki publikacji
EN
Abstrakty
EN
The necessities of processing of spatial data require developing new feature-sensitive tools such as extensions of the wavelet transform. Considering the advantages of the application of complex wavelets and their extension to quaternionic wavelets for twodimensional data structures, the new octonion discrete wavelet transform for the analysis of three-dimensional data structures was introduced in this paper. The construction of the wavelet pyramid as well as octonionic wavelets were presented.
Rocznik
Strony
33--38
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
  • Institute of Fundamentals of Machinery Design, Silesian University of Technology, Gliwice, Poland
Bibliografia
  • [1] Kingsbury N.G., Complex wavelets for shift invariant analysis and filtering of signals, App. Comput. Harmon. A. 2001, 10, 234-253.
  • [2] Liu Y., Jin J., Wang Q., Shen Y., Phases measure of image sharpness based on quaternion wavelet, Pattern Recogn. Lett. 2013, 34, 1063-1070.
  • [3] Lina J.-M., Complex Daubechies wavelets: filters design and applications, Proc. ISAAC Conference, University of Delaware, Newark 1997.
  • [4] Forster B., Blu T., Unser M., Complex B-splines and wavelets, Proc. 2nd International Conference on Computational Harmonic Analysis, Nashville 2004.
  • [5] Magarey J.F.A., Kingsbury N.G., Motion estimation using a complex-valued wavelet transform, IEEE Trans. Image Process. 1998, 6, 549-565.
  • [6] Forster B., Blu T., Unser M., A new family of complex rotation-covariant multiresolution bases in 2D, Proc. of SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing X, San Diego 2003, 5207, 475-479.
  • [7] Bayro-Corrochano E., de La Torre Gomora M.A., Image processing using the quaternion wavelet transform, Progress in Pattern Recognition, Image Analysis and Applications, Lect. Notes Comput. Sc. 2004, 3287, 613-620.
  • [8] Bayro-Corrochano E., The theory and use of the quaternion wavelet transform, J. Math. Imaging Vis. 2006, 24, 19-35.
  • [9] Bahri M., Ashino R., Vaillancourt R., Two-dimensional quaternion wavelet transform, Appl. Math. Comput. 2011, 218, 10-21.
  • [10] Soulard R., Carré P., Quaternionic wavelets for texture classification, Pattern Recogn. Lett. 2011, 32, 1669-1678.
  • [11] Gai S., Yang G., Zhang S., Multiscale texture classification using reduced quaternion wavelet transform, Int. J. Electron. Commun. 2013, 67, 233-241.
  • [12] Gai S., Yang G., Wan M., Employing quaternion wavelet transform for banknote classification, Neurocomputing 2013, 118, 171-178.
  • [13] Conway J.H., Smith D.A., On Quaternions and Octonions: Their Geometry, Arithmetic and Symmetry, Peters, 2003.
  • [14] Boya L.J., Composition algebras and the two faces of G2, arXiv:0911.3387v1, 2009.
  • [15] Hahn S.L., Snopek K.M., The unified theory of n-dimensional complex and hypercomplex analytic signals, Bull. Pol. Acad. Sci.-Te. 2011, 59, 167-181.
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Bibliografia
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bwmeta1.element.baztech-3ac2cdbc-a518-4d76-a48f-6c2d3ee2398a
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