Cropping image in matlab

Question

I need to do the following for an image in the matlab:

1. Load the image.
2. compute FFT ( Fast Fourier Transform ) of the image.
3. shift frequency components to the center.
4. crop the image like follow ( if the image res. is 1000x1000 , the needed part of the image is like the following Coordinates: 100,100,800,800. which is a smaller image. (The idea of applying filter to remove high frequencies).
5. inverse shift.
6. inverse fourier transform.

. . .

My code look like this:

I = imread('2.jpg'); %loading

ID = im2double(I);
FID = fft2(ID); %FFT
F = fftshift(FID); %shifting

F = imcrop(F,[100, 100, 800, 800]);

FID = ifftshift(F); %inverse of shifting
IFID = ifft2(FID); %inverse of FFT

I8 = im2uint8(IFID);

The problem is when i want to Crop the image, imcrop function couldn't crop an image of type "complex double" , as i think ..

Error:

Error using imcrop>checkCData (line 410) Invalid input image.

Error in imcrop>parseInputs (line 256) checkCData(a);

Error in imcrop (line 93) [x,y,a,cm,spatial_rect,h_image,placement_cancelled] = parseInputs(varargin{:});

ِAny help ? .. also are there another function for cropping?

Answer 1

The problem is indeed the complex values in the tensor F. A proof is the fact that replacing imcrop(F,[100, 100, 800, 800]) by imcrop(abs(F),[100, 100, 800, 800]).

A suggestion I have is to decompose the signal F in a magnitude and phase part and to use imcrop on those two images, followed by a reconstruction. As far as understand 'imcrop' this should yield the same result.

The code would look then like:

I = imread('PersonalPhoto.JPG'); %loading

ID = im2double(I);
FID = fft2(ID); %FFT
F = fftshift(FID); %shifting

Fabs = imcrop(abs(F),[100, 100, 800, 800]);
Fang = imcrop(angle(F),[100, 100, 800, 800]);

F = Fabs.*exp(1j.*Fang);

FID = ifftshift(F); %inverse of shifting
IFID = ifft2(FID); %inverse of FFT

I8 = im2uint8(IFID);

Answer 2

Cropping a real-valued decomposition of the image (either the magnitude and phase, or the real and imaginary part) would avoid the reported error from imcrop.

However, since you indicated that your intention is to filter high frequency components, you should note that cropping will also have the side effect of reducing the resulting time-domain image.

To preserve the image size, you may consider zeroing out those frequency bins instead (short of a using a more elaborate filter design). You can achieve this by multiplying the frequency domain data with a matrix acting as a mask over the frequency component you want to keep.

The code to achieve this would look like:

% create a mask to zero-out high frequency components
H = zeros(size(I));
halfwidth = 400;
xmin = size(H,2)/2+1 - halfwidth;
xmax = size(H,2)/2+1 + halfwidth;
ymin = size(H,1)/2+1 - halfwidth;
ymax = size(H,1)/2+1 + halfwidth;
H(xmin:xmax, ymin:ymax, :) = 1;

% apply mask
F = F.*H;

Which would give you the following overall code:

I = imread('2.jpg'); %loading

ID = im2double(I);
FID = fft2(ID); %FFT
F = fftshift(FID); %shifting

% create a mask to zero-out high frequency components
H = zeros(size(I));
halfwidth = 400;
xmin = size(H,2)/2+1 - halfwidth;
xmax = size(H,2)/2+1 + halfwidth;
ymin = size(H,1)/2+1 - halfwidth;
ymax = size(H,1)/2+1 + halfwidth;
H(xmin:xmax, ymin:ymax, :) = 1;

% apply mask
F = F.*H;

FID = ifftshift(F); %inverse of shifting
IFID = real(ifft2(FID)); %inverse of FFT

I8 = im2uint8(IFID);