%% localization demo
%% transform image, threshold DFT, and reconstruct

% get image
load chess
% get 2D FFT of image
X= X-mean(mean(X)); % get rid of the DC component
X = zeros(126); X(21:35,21:60)=1;
FX = fft2(X); 
sFX = fftshift(FX);

% display results 
figure(1)
imshow(X,[])
title('original image');

figure(2)
imshow(log(0.1+abs(sFX)),[]);
title('shifted log(1+|dft|)');

%threshhold
tlev = 0.05*max(max(abs(FX)));
tFX = FX;
J = find(abs(FX)< tlev);
tFX(J) = zeros(size(J));
rX = real(ifft2(tFX));
stFX = fftshift(tFX);

% display results 
figure(3)
imshow(log(0.1+abs(stFX)),[]);
title('thresholded, shifted log(1+|dft|)');

figure(4)
imshow(rX,[])
title('reconstructed image');

figure(5)
mesh(rX)
rotate3d

compression_ratio = 100-100*length(J)/length(X(:))
percent_retained_energy = 100*sum(sum(rX.*rX))/sum(sum(X.*X))