Replace phases of image FFT

Question

I have 2 images of the same scene, captured by different cameras. So they a bit displaced. As far as I can understood, phases of FFT contains info about image details. My goal is to take intensity from first image, details from second and produce enhanced highly detailed image with proper intensity.

I tried to solve problem as is - apply FFT for both images, take magnitudes from first image and phases from second and apply iFFT. But I didn't get what I want. Image looked corrupted, see below.

Then I tried to compute Phase correlation , align images and apply the algorithm described above again. Result was the same.

Is it possible to do what I want? May be I need to do some calculations in frequency domain, like phase shifting? Matlab code is highly appreciated!

Answer 1

What you want to do is impossible with your technique. The phase of an FFT does not provide the details of an image. Even if it did, why would it enhance an image, if you exchanged the "details" of both images without any calculation?

The phase of an FFT of an image mainly holds the structure information, i.e. how the frequencies contribute to the image (in terms of phase offsets). This is valid for fine and coarse structures in the image. The magnitude tells you, how much each frequency contributes to the image. This information is in most cases less important, as can be seen by the general shape of the 2D magnitude spectrum (many strong low frequency contributions and a rapid decay towards higher frequencies).

I assume, what you would like do do is more a quite complex problem to be solved in image space. You might want to look for publications and algorithms on super-resolution for your application.

Answer 2

My partner wrote this code in an image processing class and it worked. I hoped you will find here a hint of what you did wrong:

Brad_X = fft2(double(Brad_pic));
Brad_X_shifted = fftshift(Brad_X);

Baboon_X = fft2(double(Baboon_pic));
Baboon_X_shifted = fftshift(Baboon_X);

Brad_phase  = angle(Brad_X);
Brad_amp    = abs(Brad_X);

Baboon_phase  = angle(Baboon_X);
Baboon_amp    = abs(Baboon_X);

Brad_exp_baboon = Brad_amp.*(exp(1i*Baboon_phase));
Baboon_exp_brad = Baboon_amp.*(exp(1i*Brad_phase));

Brad_exp_baboon_pic = abs(ifft2(Brad_exp_baboon));
Baboon_exp_brad_pic = abs(ifft2(Baboon_exp_brad));

    figure;
subplot(1,2,1); imshow(Brad_exp_baboon_pic,[]); title('Brad Amp, Baboon Phase');
subplot(1,2,2); imshow(Baboon_exp_brad_pic,[]); title('Baboon Amp, Brad Phase');

In case you were wondering, we are indeed taking a picture of Brad Pitt and a picture of a baboon and changing their phase and amplitude. The result is not perfect, but I wouldn't expect it to be perfect either.

Answer 3

If @GaiusJulius's code doesn't help then neither will this. It doesn't appear to have the same issues yours does. Can you share your original two images?

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R Code Below

#30406

require("EBImage")

image_url <- "http://www.lhup.edu/~dsimanek/3d/stereo/sailboats.jpg"
image_file <- basename(image_url)

if (!file.exists(image_file))
{
  download.file(image_url,image_file)
}

library(jpeg)
image <- readJPEG(image_file)
dims <- dim(image)

i1 <- flip(t(image[,1:(dims[2]/2),1]))
i2 <- flip(t(image[,(dims[2]/2 + 1):dims[2],1]))

I1 <- fft(i1)
I2 <- fft(i2)

I3 <- abs(I1) * exp(1i*Arg(I2))
i3 <- abs(fft(I3, inverse = TRUE) / length(I3))

par(mfrow=c(2,2))
image(i1, col  = gray((0:32)/32), axes = FALSE)
title("Image 1")
image(i2, col  = gray((0:32)/32), axes = FALSE)
title("Image 2")
image(i3, col  = gray((0:32)/32), axes = FALSE)
title("1's amplitude, 2's phase")