www.pudn.com > 666bandelets_toolbox.zip > test_plot_bandelet.m, change:2005-09-02,size:2519b

% plot a bandelet 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
n = 16; 
Jw = log2(64);     % wavelet scale  (2^Jw = size of the wavelet image) 
Jb = 3;             % bandelet scale (1=finest) 
k = 2;              % alpert function type 
q = 3;              % wavelet direction 
alpert_vm = [2,2]; 
theta = 1/sqrt(2);  % geometry orientation 
 
str = ['bandelet_' 'Jb' num2str(Jb) '_Jw' num2str(Jw) '_k' num2str(k) '_q' num2str(q) '_n' num2str(n)]; 
 
options.use_mex = 0; 
 
 
 
% scale localisation 
 
% build a dirac function 
[Y,X] = meshgrid(1:n,1:n); 
t = -sin(theta)*X(:) + cos(theta)*Y(:); 
pos = [t,X(:)]'; 
 
% test fwd just to get the info 
[w,info] = perform_alpert_transform_2d(t,pos,alpert_vm, 1, options); 
% select coefficient 
I = find( info.k==k & info.l == max(info.l-Jb+1) ); 
u = I(round(end/2)); 
 
y = zeros(n^2,1); 
y(u) = 1; 
 
[w,info] = perform_alpert_transform_2d(y,pos,alpert_vm, -1, options); 
 
 
M = reshape(w,n,n); 
M = M+1e-5*(rand(n)-0.5); 
 
I = find(M>=0); 
M(I) = rescale(M(I)); 
I = find(M<0); 
M(I) = -rescale(-M(I)); 
 
 
% interpolation 
m = 1024; 
 
[selx,sely] = compute_quadrant_selection(Jw,q); 
selx = selx(end/2-n/2+1:end/2+n/2); 
sely = sely(end/2-n/2+1:end/2+n/2); 
MW = zeros(m,m); 
MW(selx,sely) = M; 
 
% backward transform 
options.wavelet_vm = 3; 
M1 = perform_wavelet_transform(MW,1,-1, options); 
 
% extract approximatrly the support 
w = 0.1; 
a = 2^Jw/(2*m)+w; 
A2 = M1( round(end/2-a*m+1):round(end/2+a*m), round(end/2-a*m+1):round(end/2+a*m) ); 
 
n1 = round( (1+w)*n/2 )*2; 
n1 = n; 
A1 = zeros(n1,n1); 
A1( end/2-n/2+1:end/2+n/2, end/2-n/2+1:end/2+n/2 ) = M; 
 
clf; 
subplot(1,2,1); 
imagesc(A1); 
axis square; axis off; 
colormap gray(256); 
 
subplot(1,2,2); 
imagesc(A2); 
axis square; axis off; 
 
% save 
rep = 'images/'; 
warning off; 
imwrite(rescale(A1), [rep str '_discrete.png'], 'png'); 
imwrite(rescale(A2), [rep str '_continuous.png'], 'png'); 
warning on; 
 
return; 
 
 
 
%%% 
% plot a bandelet 
 
global wavelet_vm; 
wavelet_vm = 1; 
theta = 1/sqrt(2); 
n = 32; 
 
 
% scale localisation 
Jb = 1; 
 
% build a dirac function 
[Y,X] = meshgrid(1:n,1:n); 
t = -sin(theta)*X(:) + cos(theta)*Y(:); 
[tmp,I] = sort(t); 
 
 
k = 3/2 * n/2^Jb; 
y = zeros(n^2,1); 
y(k) = 1; 
 
if wavelet_vm==1 
     y = reorder_coefs(y,1,-1); 
end 
 
Mb = zeros(n,n); 
Mb(I) = y; 
 
M = perform_warped_wavelet(Mb,theta,-1); 
M = M+1e-5*(rand(n)-0.5); 
 
I = find(M>=0); 
M(I) = rescale(M(I)); 
I = find(M<0); 
M(I) = -rescale(-M(I)); 
 
imagesc(M); 
colormap gray(256);