fft_resize_test.m

介绍了傅立叶变换的基本原理

> script to test FFT for resized images... 

clear all 
close all 

global rho; 

INTERPOLATION_TYPE = 'Fourier'; 
>INTERPOLATION_TYPE = 'Provided'; 
WINDOW_TYPE = 'hann'; 
scaleVal = 4; 

input1 = imread('lena.bmp'); input1 = double(input1(:,:,1)); > cast inputs to doubles and only take first field 
input2 = imread('lena.bmp'); input2 = double(input2(:,:,1)); 

>input1 = zeros(256,256); 
>input1(82:174,82:174) = 1; 

>input2 = zeros(256,256); 
>input2(82:174,82:174) = 1; 
>input1 = imrotate(input1,45,'bicubic','crop'); 
input2 = imrotate(input2,45,'bicubic','crop'); 

figure,imagesc(input1),title('Input 1'),colormap('gray') 
figure,imagesc(input2),title('Input 2'),colormap('gray') 

>input1 = input1 - mean(mean(input1)); input2 = input2 - mean(mean(input2)); 

if (strcmp(INTERPOLATION_TYPE,'Fourier')) > For example, to transform a 256*256 image to a 128*128 image 
disp('Using FOURIER interpolation method') 

>input2_resized = interpft(interpft(input2,512,1),512,2); 
input2_fft = fftshift(fft2(input2)); > 1) make 2D-FFT of your image 

> input2_fft = fftshift(fft2(window2d(size(input2,1),size(input2,2),WINDOW_TYPE).*input2)); > take windowed FFT 
padded_input2_fft = zeros(1024,1024); padded_input2_fft(384:(384+255),384:(384+255)) = window2d(size(input2_fft,1),size(input2_fft,2),WINDOW_TYPE).*input2_fft; 
> padded_input2_fft = zeros(1088,1088); padded_input2_fft(416:(416+255),416:(416+255)) = window2d(size(input2_fft,1),size(input2_fft,2),WINDOW_TYPE).*input2_fft; 
>padded_input2_fft = zeros(1152,1152); padded_input2_fft(448:(448+255),448:(448+255)) = window2d(size(input2_fft,1),size(input2_fft,2),WINDOW_TYPE).*input2_fft; 
> padded_input2_fft = zeros(1280,1280); padded_input2_fft(512:(512+255),512:(512+255)) = window2d(size(input2_fft,1),size(input2_fft,2),WINDOW_TYPE).*input2_fft; 
> padded_input2_fft = zeros(1344,1344); padded_input2_fft(544:(544+255),544:(544+255)) = window2d(size(input2_fft,1),size(input2_fft,2),WINDOW_TYPE).*input2_fft; 
> padded_input2_fft = zeros(1408,1408); padded_input2_fft(576:(576+255),576:(576+255)) = window2d(size(input2_fft,1),size(input2_fft,2),WINDOW_TYPE).*input2_fft; 
>padded_input2_fft = zeros(1536,1536); padded_input2_fft(640:(640+255),640:(640+255)) = window2d(size(input2_fft,1),size(input2_fft,2),WINDOW_TYPE).*input2_fft; 

> padded_input2_fft(128:383,128:383) = input2_fft; 

figure(2),imagesc(log10(abs(padded_input2_fft))),title('padded magnitude spectrum of input 2') 

input2_resized = ifft2(ifftshift(padded_input2_fft)); 

> for i=4:4:size(input2_resized,1) > 4) take every second point 
> for j=4:4:size(input2_resized,2) 
> input2_downsampled(i/4,j/4) = input2_resized(i,j); 
> end 
> end 
> input2_resized = input2_downsampled; 

> crop a 256x256 section out of the resized image 
sht = (size(input2_resized,1)-size(input1,1))/2; swd = (size(input2_resized,2)-size(input1,2))/2; 
cropped_input2_resized = imcrop(input2_resized,[ceil(swd) ceil(sht) size(input1,2)-1 size(input1,1)-1]); 

figure(3),imagesc(abs(cropped_input2_resized)),title('Magnitude - Resized image 2 using Fourier Interpolation'),colormap('gray') 
> subplot(2,1,2),imagesc(angle(cropped_input2_resized)),title('Phase - Resized image 2 using Fourier Interpolation'),colormap('gray') 

> input2_resized_fft = fftshift(fft2(cropped_input2_resized)); 
input2_resized_fft = fftshift(fft2(window2d(size(cropped_input2_resized,1),size(cropped_input2_resized,2),WINDOW_TYPE).*cropped_input2_resized)); > take windowed FFT 

h = hipass_filter(size(input2_resized_fft,1),size(input2_resized_fft,2)); 
filt_input2_resized_fft = h.*input2_resized_fft; 
figure(4),imagesc(abs(filt_input2_resized_fft)),title('high-pass filtered magnitude spectrum of input 2 resized with WINDOWING...'),colorbar 

log_polar_input2_fft = imlogpolar(abs(filt_input2_resized_fft),256,256,'bicubic'); 

figure(5),imagesc(log_polar_input2_fft),title('Log-polar version of figure 4') 


input1_fft = fftshift(fft2(window2d(size(input1,1),size(input1,2),WINDOW_TYPE).*input1)); > take windowed FFT 
h = hipass_filter(size(input1_fft,1),size(input1_fft,2)); 
filt_input1_fft = h.*input1_fft; 
figure(6),imagesc(abs(filt_input1_fft)),title('high-pass filtered magnitude spectrum of input 1 with WINDOWING...'),colorbar 
log_polar_input1_fft = imlogpolar(abs(filt_input1_fft),256,256,'bicubic'); 
figure(7),imagesc(log_polar_input1_fft),title('Log-polar version of figure 5') 

cps_rs = crosspowerspectrum(log_polar_input1_fft,log_polar_input2_fft); 
figure(8),imagesc(cps_rs),title('Phase Correlation'),colormap('gray') 
[i,j] = find(cps_rs == max(max(cps_rs))); 
disp(['Rotation = ',num2str((j-1)*(360/256))]) 
disp(['Scale = ',num2str(rho(i))]) 


> 

>input2_ifft = ifft2(input2_fft,512,512); > 3) do 2D-IFFT after padding the necessary amount 
>for i=2:2:size(input2_ifft,1) > 4) take every second point 
> for j=2:2:size(input2_ifft,2) 
> input2_resized(i/2,j/2) = input2_ifft(i,j); 
> end 
>end 
> input2 = input2_resized; 
elseif(strcmp(INTERPOLATION_TYPE,'Provided')) 
fft_input1 = fftshift(fft2(input1)); 
fft_input2 = fftshift(fft2(input2)); 
h = hipass_filter(size(fft_input1,1),size(fft_input1,2)); 
filt_input1_fft = h.*fft_input1; 
h = hipass_filter(size(fft_input2,1),size(fft_input2,2)); 
filt_input2_fft = h.*fft_input2; 

figure, imagesc(abs(filt_input1_fft)),title('Filtered magnitude spectrum of image1'),colorbar 
figure, imagesc(abs(filt_input2_fft)),title('Filtered magnitude spectrum of image2'),colorbar 

input2 = imresize(input2,4,'bicubic'); 
fft_input2 = fftshift(fft2(input2)); 
h = hipass_filter(size(fft_input2,1),size(fft_input2,2)); 
filt_input2_fft = h.*fft_input2; 
figure,imagesc(input2),title('Resized image 2'),colormap('gray') 
figure, imagesc(abs(filt_input2_fft)),title('Filtered magnitude spectrum of image2 after resizing'),colorbar 

>disp('Using BILINEAR interpolation method') 
>if(scaleVal>1) 
> input2 = imresize(input2,scaleVal,'bilinear'); 
>end 
end 



> -------------------- thje Fourier interpolation technique as cut and pasted from fourier_mellin stuff 
> disp('Using Fourier Interpolation to generate resized image -> the pixel range for the scaled output is changed which is not good') 
> input2_fft = fftshift(fft2(rotsclIm)); > 1) make 2D-FFT of your image 
> newHt = scaleVal*size(rotsclIm,1) 
> newWd = scaleVal*size(rotsclIm,2) 
> padded_input2_fft = zeros(newHt,newWd); > zero-pad the FFT to the necessary size 
> startHt = ceil((newHt-size(rotsclIm,1))/2); 
> startWd = ceil((newHt-size(rotsclIm,2))/2); 
> padded_input2_fft(startHt:(startHt+size(rotsclIm,1)-1),startWd:(startWd+size(rotsclIm,2)-1)) = window2d(size(input2_fft,1),size(input2_fft,2),'hann').*input2_fft; > wndow the FFT 
> rotsclIm = (ifft2(ifftshift(padded_input2_fft))); > inverse FFT and get rid of and hopefully negligible imaginary parts