FFT Combination of Two Images

I am trying to take two simple images (a horizontal slit and a vertical slit), take the fft2 of each individual image, combine the fft2 version of the two images using some sort of operation to make a single fft2 image, then take the ifft2 of that combined image to get a new original image of the horizontal and vertical slits combined. I am stuck on the combining operation. I've tried 'or' and 'bitor' but it's not quite working. The ifft2 does not result in the correct image. Someone please help!

Here is my attempt at the code:

horz = zeros(16, 16);
horz(:, 8-2:8+2) = 255.;

vert = zeros(16, 16);
vert(8-2:8+2, :) = 255.;

f_horz = fft2(horz);

f_horzshift = fftshift(f_horz);

f_vert = fft2(vert);

f_vertshift = fftshift(f_vert);

bitorop = bitor(f_horzshift, f_vertshift); 

inverse = ifft2(bitorop);

surf (abs(inverse))

[Geoff Hayes]

John - when I run your above code, I observe the following error

 Error using bitor
 Inputs must be real.

which makes sense since your f_horzshift and f_vertshift involve complex numbers.

Since the Fourier transform is linear, then why not just add the two

 inverse = ifft2(f_horzshift + f_vertshift);

Why choose bit operations over the above? And what is the correct image?

[John Smith]

I tried a simple addition of the two fourier versions, but where the two intersect in the middle, there is twice the intensity, since they are adding. I need everything to be at one level, if that makes sense. Is there a way to change a specific coordinate in MatLab? The only reason I was trying 'or' or 'bitor' was to avoid this intensity spike at the point of intersection.

I know it would be easier to just start off with an image of the two already combined, but I need to know how to do it in this 'roundabout fourier' fashion for a fourier filtering project that I am working on.

Answer 1

[Image Analyst]

No, you don't do that at all. That would not make any physical sense. What are you trying to do anyway? Do you want the FT of the product of the vertical slit and a horizontal slit? If so, you know that multiplication in one domain is convolution in the other domain, not anything with bit processing.

[John Smith]

I do not need the product. I simply need to combine the FT of two images, then take the inverse of that combination. It cannot be a multiplication/convolution/addition operation since that would result in a different image. It needs to be some sort of logic operation such as 'or', but I am new to MatLab and just cannot figure out the syntax to correct my code that I posted above.

Again, I know this seems like a roundabout way of doing it, but I need to figure out this process for a fourier filtering/masking project I am working on.

[Image Analyst]

ORing, ANDing or any other bit level operation on the bitplanes of the two spectra would produce nonsense.

If you want to do Fourier filtering, see my attached demo.

[John Smith]

If I add the two FT images, it works, except in the middle where the two intersect, the value is twice as high as the rest since the two points are adding. Is there a way to change a specific coordinate on a surface plot to a custom value?

I really appreciate your help btw.

[Image Analyst]

You can set a matrix value with indexing and assignment

yourMatrix(row, column) = newValue;

But I don't know why you're adding two spectra. And then why you're changing some of the values like that. It doesn't seem to be what you should be doing in Fourier filtering. Maybe you can explain the theoretical basis for this kind of filtering.

[John Smith]

I guess I wouldn't call what I'm doing right now particularly filtering, I just need to get familiar with the fft/ifft process on MatLab. I added the two spectra and tried to change that value, but it is still showing a spike in the middle where the two added at that point of intersection. Here's the code so you can see what's happening. As you can see, when I take the inverse, I get the image I want, except the spike that's in the middle. Any tips on how to get rid of that middle value (255,255) that's spiking? Thanks so much.

horz= zeros(512, 512);

horz(:, 256-4:256+4) = 255.;

vert = zeros(512, 512);

vert(256-8:256+8, :) = 255.;

f_horz = fft2(horz);

f_horzshift = fftshift(f_horz);

f_vert = fft2(vert);

f_vertshift = fftshift(f_vert);

addop = f_horzshift + f_vertshift;

addop(255,255) = 0;

surf (abs(addop))

inv = ifft2(addop);

surf (abs(inv))