A Canonical Form for Real Matrices under Orthogonal by Marnaghan F. D., Wintner A.

By Marnaghan F. D., Wintner A.

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We have chosen the threshold values w l , w2, w3 independently of the image, in order to apply the method to several different images. 29 Intensity difference20 15 10 5 0 60 40 20 0 30 20 Homogeneoussubdomains 10 0 5 10 15 20 25 j index Figure 2. Plots of the difference between the mean and the median values at increasing j - index in Cj” (top), C j (middle), C s (bottom) Figure 3. KNIGHT image in Kokaram CD: domain segmentation of the scratch vertical region. In the column on the right side the results of the recognition method are shown (1 = homogeneous, 2 = not-homogeneous domain) Hence we have defined a domain Dj to be non homogeneous if a t least one of the following tests is verified: 30 The thresholds have been calibrated on a large class of test images, with 256 Grey-levels representation, from old movie (Kokaram [6] CD) and also from MATLAB images data bank.

4) where any Rk = rk r; r i is given by three components. Vice versa, given the decomposition Eq. 4) it is possible to reconstruct the original function f with an inverse procedure. 35 6) When the bases are not orthogonal a new-pair - (Cp, of a refinable and a wavelet function, which generates a MRA { y, W j } ,is considered, in order to compute the generalized Fourier expansion of a given function [5]. The pairs (cp,$) and (Cp,q)are dual or biorthogonal, in the sense that - < cpj,n,-Cpj~,n~ >= 6j,jjdn3nj < v j , n ,$jl,nl >= 0 < $j,n, $j/,nl >= 6j,jt6n,nt, < $j,n, Cpjt,nf>= 0.

L. Lo Cascio, Proc. Wavelets & Splines, S. Petersburg 2003 (submitted). 3. A. D. Rayan, Wavelets and multiscale signal processing, ChapmanHall, London (1995). 4. C. de Boor, A practical guide to spline. Springer-Verlag, Berlin (1998). 5. I. Daubechies, Ten lectures. SIAM, Philadelphia (1992). 6. A. Kokaram, Motion Picture Restoration. Springer Berlin (1998). 7. H. Moeck and K. Herrmann, In Advanced Mathematical and Tools in Metrology V, Series on Advances in Mathematics for applied sciences, 57 Ciarlini, Cox, Filipe, Pavese, Richter Eds, Singapore, World Scientific, 270 (2001).

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