The concept of frequency spectrum exists because it is possible to sum sines and cosines of various frequencies together to make any periodic signal. The frequencies of these individual sinusoids make up the spectrum of the final signal. Now when it comes to image processing we treat image as a signal similar to sound for example in that it has a bandwidth and it is possible to filter certain frequencies it to achieve various results.

What I am not clear about is, how did people get concept of frequency in 2D? Sinusiods are 1D signals, how can we extend this concept of frequency into 2D? Is it possible to do the same in 3D and do filtering in 3D? Does anyone do that in any application?

I fully understand low pass, high pass, band pass and band stop filters. Their frequency respons curves are quite straight forward. What I do not understand is, how is this extended into 2D?

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    $\begingroup$ If it helps, you can think of each row of pixels in your 2D image as a 1D signal. Ditto for the columns. $\endgroup$
    – Paul R
    Dec 10 '13 at 15:37
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    $\begingroup$ Have a look at this related stack exchange question. $\endgroup$
    – porten
    Dec 10 '13 at 16:10
  • $\begingroup$ Go to the beach and you'll see plenty of 2d waves $\endgroup$
    – Aaron
    Dec 10 '13 at 17:58
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    $\begingroup$ The frequencies that you're used to in sound waves are frequencies in time (and are thus measured in "Hz," a time-based unit). With spatial frequency, instead of counting oscillations per second, we count oscillations per centimeter/some other distance measure. So in a sense, the domain (time vs. space) is arbitrary - we're counting oscillations along the x-axis. To extend that to 2D can look like this. $\endgroup$
    – dpbont
    Mar 11 '14 at 8:07
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    $\begingroup$ Question already answered here: What does frequency domain denote in case of images?. You can also take a look in here. $\endgroup$
    – jojek
    Apr 9 '14 at 18:48

Frequency, by its definition, means how frequently something occurs. You can treat images as planes where you have data points, ie. the pixels of the data. In images a frequency can be thought of as how frequently the sinusoidal components of the structure repeat per unit distance (where your unit would be the distance of a pixel).


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