4 ms·

Does anything interesting happen if you take the frequency domain representation of an image, represent the frequency domain as an image itself, and compress th

Does anything interesting happen if you take the frequency domain representation of an image, represent the frequency domain as an image itself, and compress that with some sort of image compression? For example, encode the frequency domain representation as a low quality JPEG, and then undo the steps to turn it back into the "original". How do the JPEG artifacts on the frequency domain manifest in the resulting image?

yngvizzle 5y ago
the frequency domain of the frequency domain is just a flipped version of the original image, so that would not work. the idea of frequency-domain based compression is that natural images have little high-frequency information.
thrdbndndn 5y ago
With only a slight compression, the image would go shit or totally unrecognizable. A quick album (there are captions): https://imgur.com/a/7yHPzRH https://imgur.com/a/7yHPzRH
- jstanley 5y ago
  Thanks, this is exactly what I wanted to see.
- verall 5y ago
  > 4:2:0 chroma subsample the fft This is hilarious but I don't think it makes any sense.
  - thrdbndndn 5y ago
    yeah, just wanted to try a 'typical' one. I also tried 70% 444, still unrecognizable.
- randyrand 5y ago
  impressive how quickly you coded that up.
mjlm 5y ago
This wouldn't work well because in the frequency domain representation, different "pixels" have very different importance for the overall appearance of the image: The pixels at the center of the frequency domain representation represent low frequencies, so compressing them will drastically alter the appearance of the image. On the other hand, the corners/edges of the frequency domain representation represent high frequencies, i.e. image details that can be removed without causing the image to change much. That's the crucial benefit of the Fourier transform for compression: it decomposes the image into important bits (low frequencies) and relatively less portant bits (high frequencies). Applying compression that doesn't take that structure into account won't work well.
- Lorin 5y ago
  I'm into the glitch art scene and this makes me wonder what happens if you crop/erase patterns of the frequency domain representation and put it back together...
- diedyesterday 5y ago
  Minor note. If the original data is a time-signal like in electrical engineering (amplitude vs. time function), then the "frequency domain pixels" (its transform) are different frequencies (points in frequency domain: how many repetitions in a second, etc.) and the time-signal's transform function becomes an amplitude vs. frequency graph. But if the original data is an image (matrix or grid of pixels in space), then the "frequency domain pixels" are different wave-numbers (aka spatial frequencies: how many repetitions in a meter, etc.) and the Fourier transform (of the pixel grid) is a amplitude vs. wave-number function.
matja 5y ago
You can try with Imagemagick (https://legacy.imagemagick.org/Usage/fourier/#im_fft https://legacy.imagemagick.org/Usage/fourier/#im_fft) : for quality in 50 75 90 95 99 ; do # FFT convert source.png -fft +depth +adjoin source_fft_%d.png # compress FFT magnitude and phase convert source_fft_0.png -quality $quality source_fft_magnitude.jpg convert source_fft_1.png -quality $quality source_fft_phase.jpg # IFFT convert source_fft_magnitude.jpg source_fft_phase.jpg -ift out.$quality.png done
- jstanley 5y ago
  Thanks, this is great. I found it works a lot better if you leave the magnitude alone and only mess with the phase. The image is still recognisable even at quite harsh compression of the phase file, but almost totally unrecognisable at even minor compression of the magnitude file.
sxg 5y ago
Your idea is analogous to what’s done in MRI image reconstruction. “Images” are actually obtained in the frequency domain, but there are various undersampling strategies to accelerate the frequency domain data acquisition. These are then reconstructed into actual images with the inverse FFT.

yngvizzle 5y ago

the frequency domain of the frequency domain is just a flipped version of the original image, so that would not work. the idea of frequency-domain based compression is that natural images have little high-frequency information.

thrdbndndn 5y ago

With only a slight compression, the image would go shit or totally unrecognizable. A quick album (there are captions): https://imgur.com/a/7yHPzRH https://imgur.com/a/7yHPzRH

jstanley 5y ago
Thanks, this is exactly what I wanted to see.
verall 5y ago
> 4:2:0 chroma subsample the fft This is hilarious but I don't think it makes any sense.
- thrdbndndn 5y ago
  yeah, just wanted to try a 'typical' one. I also tried 70% 444, still unrecognizable.
randyrand 5y ago
impressive how quickly you coded that up.

mjlm 5y ago

This wouldn't work well because in the frequency domain representation, different "pixels" have very different importance for the overall appearance of the image: The pixels at the center of the frequency domain representation represent low frequencies, so compressing them will drastically alter the appearance of the image. On the other hand, the corners/edges of the frequency domain representation represent high frequencies, i.e. image details that can be removed without causing the image to change much. That's the crucial benefit of the Fourier transform for compression: it decomposes the image into important bits (low frequencies) and relatively less portant bits (high frequencies). Applying compression that doesn't take that structure into account won't work well.

Lorin 5y ago
I'm into the glitch art scene and this makes me wonder what happens if you crop/erase patterns of the frequency domain representation and put it back together...
diedyesterday 5y ago
Minor note. If the original data is a time-signal like in electrical engineering (amplitude vs. time function), then the "frequency domain pixels" (its transform) are different frequencies (points in frequency domain: how many repetitions in a second, etc.) and the time-signal's transform function becomes an amplitude vs. frequency graph. But if the original data is an image (matrix or grid of pixels in space), then the "frequency domain pixels" are different wave-numbers (aka spatial frequencies: how many repetitions in a meter, etc.) and the Fourier transform (of the pixel grid) is a amplitude vs. wave-number function.

matja 5y ago

You can try with Imagemagick (https://legacy.imagemagick.org/Usage/fourier/#im_fft https://legacy.imagemagick.org/Usage/fourier/#im_fft) : for quality in 50 75 90 95 99 ; do # FFT convert source.png -fft +depth +adjoin source_fft_%d.png # compress FFT magnitude and phase convert source_fft_0.png -quality $quality source_fft_magnitude.jpg convert source_fft_1.png -quality $quality source_fft_phase.jpg # IFFT convert source_fft_magnitude.jpg source_fft_phase.jpg -ift out.$quality.png done

jstanley 5y ago
Thanks, this is great. I found it works a lot better if you leave the magnitude alone and only mess with the phase. The image is still recognisable even at quite harsh compression of the phase file, but almost totally unrecognisable at even minor compression of the magnitude file.

sxg 5y ago

Your idea is analogous to what’s done in MRI image reconstruction. “Images” are actually obtained in the frequency domain, but there are various undersampling strategies to accelerate the frequency domain data acquisition. These are then reconstructed into actual images with the inverse FFT.