I'm new to image processing and am learning about the Fourier transform. I've read that FT decomposes a function to its constituent frequencies. However, I'm not sure how to tell which is a low frequency or high frequency region in an FT image and why the transforms are shaped in the way they are.

The top two pictures are input images. The bottom two are the corresponding FTs

For instance, in the image above why is the FT of the line oriented in the opposite direction and why is there a bright dot at the center of the random noise image? What are the ways the FT can be helpful here? Also, is there a trick or a general method of analysis that would work for a better understanding of FTs across a variety of images?

  • \$\begingroup\$ youtube.com/watch?v=D9ziTuJ3OCw see the stripes on the left? They are the 2D sinusoidal components of the image on the right. By adding harmonic components of different frequency and different direction you create the image. All of this is in 'space' space. In the frequency space a single harmonic component is identified by its frequency, its direction and its amplitude. Think a single dirac delta in the fx,fy plane with an amplitude representing the strength for each 'striped component' on the left. Low spatial frequencies are near the origin, high freq are far from it. \$\endgroup\$ – Sredni Vashtar Apr 27 at 1:52
  • \$\begingroup\$ It completely depends what you're doing. As for the center dot, that's going to be your DC or average value, so it should match whatever the average pixel value is across the entire image. \$\endgroup\$ – MadHatter Apr 27 at 1:52
  • \$\begingroup\$ The center is DC and each concentric ring around the center as you proceed outward is at a "higher frequency" than a ring found within it. Look up "spatial filtering" in some optics book. They will provide ample examples for you to gain a "feel" for the concepts involved. (I believe Hecht's book on Optics is one of the "go to" books worth having.) \$\endgroup\$ – jonk Apr 27 at 2:33
  • \$\begingroup\$ In addition to the above comments (note the DC offset is average of the image), your diagonal lines are a lot more difficult to build intuition for than, say, horizontal or vertical lines. Try doing horizontal and vertical first and it'll help. The FFT of a horizontal line is a vertical line. A horizontal line actually is a very narrow (lots of high frequency components) pulse from top to bottom. imagine a standard 1D pulse wave stretched all the way across. So, to create that horizontal line, you need a lot of components in the Y direction. \$\endgroup\$ – jyoung999 Apr 27 at 2:55

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