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I have some alloy microstructure images, showing elongated grains (darker colours) and the grain boundaries (lighter colours). If I take the Fourier transform of the image, there are directional bands in the Fourier image.

Is there a relationship between the angle of these bands in the Fourier image and the orientation of the grain boundaries in the real space image?

Another observation is that if high frequencies are removed, and the inverse Fourier transform is taken, a significant amount of noise is removed, and I am mostly left with the grain boundaries of the microstructure. Is there any other kind of useful information that can be extracted from the Fourier image?

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    $\begingroup$ The added tag might not only be useful overall, but will also help to get this unanswered question bumped up. Also, can the last paragraph not be a separate question? Asking 2 questions in one might make it seem more difficult for some people to answer. $\endgroup$
    – Nike Dattani - No Free Time
    Commented Jun 12, 2020 at 22:48
  • $\begingroup$ It is a really interesting question. But I have a problem, wanting to know whether an image was uploaded because I cannot see any image. $\endgroup$
    – user1099
    Commented Jul 28, 2020 at 13:07
  • $\begingroup$ @lee there was no image posted, but that may assist people if the OP can add these images. $\endgroup$
    – Tyberius ♦
    Commented Aug 3, 2020 at 19:43

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General Info

As far as I understand you're taking a Fourier Transform of an image. In your case, that image corresponds to that of a microstructure alloy. So basically in 2D-Fourier transforms we are trying to model the intensity levels of the image and represent it in terms of a frequency plot. This is analogous to the 1D Fourier transform.

Is there a relationship between the angle of these bands in the Fourier image and the orientation of the grain boundaries in the real space image?

This can only be answered if there was an image provided. But still one could say that there is a relationship between the bands and the orientation of the grain boundaries. In the image of simple patters given below you can see the relation between the Spatial and Fourier domains. For an image of an alloy microstructure we cannot explicitly see the realtionship due to the immense detail in the spatial domain.

2D Fourier Transform

Another observation is that if high frequencies are removed, and the inverse Fourier transform is taken, a significant amount of noise is removed, and I am mostly left with the grain boundaries of the microstructure. Is there any other kind of useful information that can be extracted from the Fourier image?

This disappearence of noise takes place because the noise being a sharply varying intensity value is modelled by high frequencies in the Frequency domain. Removing those will in face reveal the boundaries which are represented by smoothly varing intensity values.

Hope this helps. :)

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