Fourier Analysis

Authored by: Pouli Tania , Reinhard Erik , Cunningham Douglas W.

Encyclopedia of Image Processing

Print publication date:  November  2018
Online publication date:  November  2018

Print ISBN: 9781482244908
eBook ISBN: 9781351032742
Adobe ISBN:

10.1201/9781351032742-140000480

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Abstract

In a given image, the probability that neighboring pixels have similar values tends to be high. This phenomenon is described by the autocorrelation function, which gives the correlation between pixels at different points in image space. But the autocorrelation function tends to be computationally inefficient in the image domain. Instead, it is customary to compute the power spectrum in the frequency domain, and the use the Fourier transform to bring the results back into the image domain. This approach tends to be more computationally efficient, and takes advantage of the mathematical properties in both domains.

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