Abstract
In this paper, we extend the recently introduced concept of fractional wavelet transform to obtain directional subbands of an image. Fractional wavelet decomposition is based on two-channel unbalanced lifting structures whereby it is possible to decompose a given discrete-time signal x[n] sampled with period T into two sub-signals x 1[n] and x 2[n] whose average sampling periods are pT and qT, respectively. Fractions p and q are rational numbers satisfying the condition: 1/p + 1/q = 1. Filters used in the lifting structure are designed using the Lagrange interpolation formula. 2-d separable and non-separable extensions of the proposed fractional wavelet transform are developed. Using a non-separable unbalanced lifting structure, directional subimages for five different directions are obtained.
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© 2012 Springer-Verlag Berlin Heidelberg
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Keskin, F., Çetin, A.E. (2012). Directionally Selective Fractional Wavelet Transform Using a 2-D Non-separable Unbalanced Lifting Structure. In: Salerno, E., Çetin, A.E., Salvetti, O. (eds) Computational Intelligence for Multimedia Understanding. MUSCLE 2011. Lecture Notes in Computer Science, vol 7252. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32436-9_9
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DOI: https://doi.org/10.1007/978-3-642-32436-9_9
Publisher Name: Springer, Berlin, Heidelberg
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