www.pudn.com > 666bandelets_toolbox.zip > test_single_square.m

% test for lagrangian optimisation over a single square 
% 
%   Copyright (c) 2005 Gabriel Peyré 
 
n = 32; 
 
global wavelet_vm; 
wavelet_vm = 0; 
 
options.n = 512;    % size of the undelying big image 
p = 16; 
name = 'barb'; 
name = 'line'; 
disp('Loading image.'); 
options.use_wavelets = 1; 
M = load_image_small_square(name, p, options); 
y = l2error(M(:)); 
 
T = 10; 
 
% factor 2 over-sampling 
s = 6; 
wavelet_vm = 0; 
disp('Computing optimal direction.'); 
[MW1,theta] = compute_best_direction(M,T,s); 
y1 = l2error(MW1(:)); 
 
% exhaustive search haar 
s = Inf; 
wavelet_vm = 0; 
disp('Computing optimal direction.'); 
[MW2,theta] = compute_best_direction(M,T,s); 
y2 = l2error(MW2(:)); 
 
% exhaustive search 7-9 
s = Inf; 
wavelet_vm = 4; 
disp('Computing optimal direction.'); 
[MW3,theta] = compute_best_direction(M,T,s); 
y3 = l2error(MW3(:)); 
 
q = 0.5*p^2; 
sel = 1:q; 
plot(   log2(sel), log2(y(sel)), ... 
        log2(sel), log2(y1(sel)), ... 
        log2(sel), log2(y2(sel)), ... 
        log2(sel), log2(y3(sel)) ); 
legend('original', 'haarx2', 'haarxInf', '7/9xInf'); 
axis([0, log2(q), -2, max(log2(y))]); 
 
% plot_geometry(theta, M); 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% display of the Lagrangian 
% compute tested directions 
[Y,X] = meshgrid(0:n-1, 0:n-1); X = X(:); Y = Y(:); 
X(1) = []; Y(1) = []; 
Theta = atan2(Y(:),X(:)); 
Theta = unique(Theta); 
Theta = [-Theta(end-1:-1:2); Theta]'; 
Theta = ( Theta + [Theta(2:end),Theta(1)+pi] )/2; 
% compute Lagrangian 
lambda = 3/(4*7); 
% compute the lagrangian 
L = []; % to store the  
for theta = Theta 
    MW = perform_warped_wavelet(M,theta,1); 
    % compute the quantized vector and number of bits 
    [MWt,tmp,R] = perform_quantization(MW(:),T); 
    % compute the approximation error 
    E = sum( (MWt(:)-MW(:)).^2); 
    % compute the lagrangian 
    L = [L, E + lambda*R*t^2]; 
end 
 
% the more the Lagrian as a frank minimum, the cleaner the geometry 
% on the square is. 
plot(Theta, L); 
axis tight: 
title('Lagrangian in function of geometry angle.'); 
ylabel('L(theta)'); 
xlabel('Theta')