PROB3.rar_optical flow_prob3.rar_prob3.zip_图像识别

function [h,g] = daubechies(N) % [h,g] = duabechies(N) % Compute coefficients for Daubechies' family of wavelets. The % coefficients in the vector h determine the dilation equation % % \phi(x) = \sqrt{2}\sum_{k=0}^{2N-1} h_{k+1} \phi(2x-k) % % Coefficients in the vector g establish the wavelet \psi(x) in % terms of the scale function \phi(x) % % \psi(x) = \sqrt{2}\sum_{k=0}^{2N-1} g_{k+1} \phi(2x-k) % % where g_{k} = (-1)^{k-1}h_{2N-k+1}. h is a vector with of length % 2N satisfying the constraints: % % a) \sum h = sqrt(2) % b) \sum h_{k}h{k-2m} = \delta_{0m} % c) Regularity of \phi(x) prop. to N (see notes) % % The algorithm is based on Daubechies' 1988 paper in % Communications on Pure and Applied Mathematics. % JCK: September 9, 1991 % Copyright (c) 1991 Jeffrey C. Kantor if round(N)~=N | (N<1), error('Order must be an integer >=1'); end % Compute coefficients of polynomial P(y) of order N-1, store % in vector pN is ascending order p = 1; pN = [p]; for j=1:N-1, p = (N+j-1)*p/j; pN = [pN,p]; end % Now compute polynomial abs(Q(z))^2, z = exp(iw) f = [-1 2 -1]/4; fc = f; q2 = pN(1); for k=1:N-1, q2 = [0,q2,0] + pN(k+1)*fc; fc = conv(fc,f); end % q2 is a polynomial with coefficients in ascending order of % powers ranging from 1-N to N-1. The coefficients of z^-k and % z^k are the same. Roots are eigenvalues of a companion matrix. r = eig([-q2(2:length(q2))./q2(1);eye(2*N-3),zeros(2*N-3,1)]); % Construct q from the roots outside the unit disk q = poly(r(find(abs(r)>1))); % Normalize phase so that q(0) is real q0 = q(length(q)); q = q*(conj(q0)/abs(q0)); % Everything should be real, so drop the imag parts q = real(q); % Now compute h by multiplying with (0.5(1+z))^N for k = 1:N, q = conv(q,[1/2 1/2]); end % Normalize, since the normalization was lost in the factoring % and reconstruction of q h = sqrt(2)*q/sum(q); % Report result in ascending order h = h(length(h):-1:1); % Compute the quadrature mirror filter from h g = qmf(h);