# How we define frequency in an image? [duplicate]

How we define frequency in an image?

1. Does the repetition of a single gray level defines the frequency?(Example: can a black(single color/constant region) background image be called high frequency image?) I think it is not so.

Or

1. Does the frequency depends on number of changes in the gray levels in an image? If so Why? I couldn't able to relate the image frequency with the signal frequency where we say high frequency signal when the same cycle is repeated many times in a unit time.

If an image has large values at high frequency components then the data is changing rapidly on a short distance scale. e.g. a page of text

If the image has large low frequency components then the large scale features of the picture are more important. e.g. a single fairly simple object which occupies most of the image.

Thus low frequency correspond to slow varying information ( continuous surface) high frequency correspond to quickly varying information ( eg. edges)

The frequency of some image signal was traditionally given by a number of cycles-per-millimeter (or per other spatial unit). This is a historical unit of measurement that is related to the invention of photography and comparing lenses.

A cycle is also called a pair of lines. It is created by the alternance of a dark-then-white pattern. If the black and white lines have the same width, then you have a pure frequency. If the lines get thinner and thinner (as in most resolution test charts), then you have some chirp.

A constant region, whatever the color, is some continuous signal. High frequencies correspond to spatially fast changes in intensity: a pattern of dots or of thin zebras is high frequencies.

Since an image is a 2D signal, frequencies are defined with respect to their horizontal and vertical components (obviously, some diagonal pattern can be created by having non-continuous horizontal and vertical components). You can find an example of resolution chart here.

If you want to experiment by yourself, you can try to generate various frequencies by creating fake 2D Fourier transforms with only 1 non-zero frequency and invert them.

Another definition is from the basic mathematical theory provided by Mr. Fourier, where any (non-pathological) waveform or image can be represented by the composition of a bunch of sinusoids or sinusoidal patterns of different frequencies, even if there is no readily apparent repeating pattern or frequency of changes in the waveform or image.
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