Do image grayscales influence the spectrum (Fourier magnitude) image?

0
votes

Say I have an image with a black (grayscale = 0) background with a white (grayscale = 255) box in it, and I look at the Fourier transform of it, or rather the spectrum (log of the transform's magnitude). As we know, It will be a 2D Sinc function.

Now I'll turn the white box into a gray box, that is, I'll set the previously white color to grayscale 100.

Will the Fourier spectrum image change? Are there some cases in which it will change and others in which it doesn't ("invariant to grayscale changes")?

1
image-processing

1 Answers

0
votes

No the shape of signal will not change with amplitude change

  • what change is only the amplitude
  • it is the same as you would multiply the signal by constant
  • here an example:
  • FFT magnitude preservation
  • all FFT images are scaled by the same ratio so you can actually see the image (would be dark)
  • as you can see the pattern is the same for all gray shades
  • what changes is the magnitude (brightness)