clear all ; close all ; clc ; N = 96 ; p = 8; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Kernel definition %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% K = zeros(N,N); t = linspace(-1.2,1.2,N); alpha = 0.05; sigma = alpha*(1+min(t+1,1-t)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% TVIR construction %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% F = zeros(N,N) ; for j = 1:N F(:,j) = exp(-(t).^2/(2*sigma(j)^2)); F(:,j) = F(:,j) ./ sum(F(:,j)); end K = zeros(2*N,N) ; for j = 1:N Ind = (j):(N+j-1) ; K(Ind,j) = F(:,j) ; end kappa = 6 ; K = K((N/2-kappa):(3*N/2+kappa),:) ; figure(1) ; imagesc(K) ; axis equal ; colormap(flip(gray)) ; axis tight ; axis ij ; set(gca,'visible','off') ; print('-dpdf', 'kernel.pdf') ; figure(2) ; imagesc(F) ; axis equal ; colormap(flip(gray)) ; axis tight ; axis ij ; set(gca,'visible','off') ; print('-dpdf', 'tvir.pdf') ; % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%% Wavelet definition % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % n = 6 ; J = 2 ; % D = n-J ; % N = 2^n ; % BseOnd.type = 'Symmlet' ; % BseOnd.par = 6 ; % % tmpB = listIndBlocks1D(D,N) ; % Nb = size(tmpB,2) ; % B = zeros(Nb,2) ; % for i = 1:Nb % B(i,1) = tmpB{i}(1) ; % B(i,2) = tmpB{i}(end) ; % end % % % wfilter = MakeONFilter(BseOnd.type, BseOnd.par) ; % % % FWT = @(arg) FWT_PO(arg, J, wfilter) ; % IWT = @(arg) IWT_PO(arg, J, wfilter) ; % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%% Left Wavelet transform % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % wK = zeros(N,N) ; % wF = zeros(N,N) ; % for i = 1:N % wK(:,i) = FWT(K(:,i)) ; % wF(:,i) = FWT(F(:,i)); % end % % figure(3) ; imagesc(wK) ; axis equal ; colormap gray ; hold on ; % for k = 1:Nb % % lo = B(k,1)-1/2 ; % hi = B(k,2)+1/2 ; % % plot(linspace(1/2,N+1/2, 2), [lo,lo], 'r') ; % plot(linspace(1/2,N+1/2, 2), [hi,hi], 'r') ; % % plot(linspace(hix,hix, 2), linspace(loy,hiy, 2), 'r') ; % % plot(linspace(lox,hix, 2), linspace(loy,loy, 2), 'r') ; % % plot(linspace(lox,hix, 2), linspace(hiy,hiy, 2), 'r') ; % end % axis image ; axis tight ; axis equal ; axis ij ; % set(gca,'xtick',[]) ; set(gca,'ytick',[]) % hold off ; % print('-dpdf', 'wavelet_kernel.pdf') ; % % hold off Defin % figure(4) ; imagesc(wF) ; colormap(flip(gray)) ; hold on ; % for k = 1:Nb % % lo = B(k,1)-1/2 ; % hi = B(k,2)+1/2 ; % % plot(linspace(1/2,N+1/2, 2), [lo,lo], 'r') ; % plot(linspace(1/2,N+1/2, 2), [hi,hi], 'r') ; % % plot(linspace(hix,hix, 2), linspace(loy,hiy, 2), 'r') ; % % plot(linspace(lox,hix, 2), linspace(loy,loy, 2), 'r') ; % % plot(linspace(lox,hix, 2), linspace(hiy,hiy, 2), 'r') ; % end % axis image ; axis tight ; axis equal ; axis ij ; % set(gca,'xtick',[]) ; set(gca,'ytick',[]) % hold off ; % % print('-dpdf', 'wavelet_tvir.pdf') ; % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%% Right Wavelet transform % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Kw = zeros(N,N) ; % Fw = zeros(N,N) ; % for i = 1:N % Kw(i,:) = FWT(K(i,:)) ; % Fw(i,:) = FWT(F(i,:)); % end % % figure(4) ; imagesc(Kw) ; axis equal ; colormap gray ; set(gca,'xtick',[]) ; set(gca,'ytick',[]) % hold off % figure(5) ; imagesc(Fw) ; colormap(flip(gray)) ; hold on ; % for k = 1:Nb % % lo = B(k,1)-1/2 ; % hi = B(k,2)+1/2 ; % % plot([lo,lo], linspace(1/2,N+1/2, 2), 'r') ; % plot([hi,hi], linspace(1/2,N+1/2, 2), 'r') ; % % plot(linspace(hix,hix, 2), linspace(loy,hiy, 2), 'r') ; % % plot(linspace(lox,hix, 2), linspace(loy,loy, 2), 'r') ; % % plot(linspace(lox,hix, 2), linspace(hiy,hiy, 2), 'r') ; % end % axis image ; axis tight ; axis equal ; axis ij ; % set(gca,'xtick',[]) ; set(gca,'ytick',[]) % hold off ; % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%% Left and right Wavelet transform % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % wKw = zeros(N,N) ; % wFw = zeros(N,N) ; % for i = 1:N % wKw(i,:) = FWT(wK(i,:)) ; % wFw(i,:) = FWT(wF(i,:)); % end % % figure(6) ; imagesc(wKw) ; axis equal ; colormap gray ; set(gca,'xtick',[]) ; set(gca,'ytick',[]) % hold off % figure(7) ; displayTheta(B, wFw, 'linear') ; set(gca,'xtick',[]) ; set(gca,'ytick',[])