Representing images in ways other than pixels allows for powerful processing. This subject, based on signal processing, requires a mathematical fluency to understand the concepts fully. Many software programs include tools such as fast-Fourier transform filters and wavelet-based filters. Luckily we don’t need to derive the math to understand how to use these utilities. However, some background information can make parameters a bit more understandable.
We can deconstruct images as the sum of periodic variations of brightness and represent the frequencies we get by sine and cosine functions. This process is a Fourier transform. In fact, you can represent images by transforming them from brightness at any pixel position to a frequency with a particular amplitude.
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