Frequency filters alter pixel values with respect to the periodicity and spatial distribution of the variations in light intensity in the image. Unlike spatial filters, frequency filters do not apply directly to a spatial image, but to its frequency representation. The frequency representation of an image is obtained through the Fast Fourier Transform (FFT) function, which reveals information about the periodicity and dispersion of the patterns found in the source image.

You can filter the spatial frequencies seen in an FFT image. The inverse FFT function then restores a spatial representation of the filtered FFT image.

Frequency processing is another technique for extracting information from an image. Instead of using the location and direction of light-intensity variations, you can use frequency processing to manipulate the frequency of the occurrence of these variations in the spatial domain. This new component is called the spatial frequency, which is the frequency with which the light intensity in an image varies as a function of spatial coordinates.

Spatial frequencies of an image are computed with the FFT. The FFT is calculated in two steps—a 1D Fast Fourier transform of the rows, followed by a 1D Fast Fourier transform of the columns of the previous results. The complex numbers that compose the FFT plane are encoded in a 64-bit floating-point image called a complex image. The complex image is formed by a 32-bit floating point number representing the real part and a 32-bit floating point number representing the imaginary part.

In an image, details and sharp edges are associated with moderate to high spatial frequencies because they introduce significant gray-level variations over short distances. Gradually varying patterns are associated with low spatial frequencies. By filtering spatial frequencies, you can remove, attenuate, or highlight the spatial components to which they relate.

Use a lowpass frequency filter to attenuate or remove, or truncate, high frequencies present in the image. This filter suppresses information related to rapid variations of light intensities in the spatial image. An inverse FFT, used after a lowpass frequency filter, produces an image in which noise, details, texture, and sharp edges are smoothed.

A highpass frequency filter attenuates or removes, or truncates, low frequencies present in the complex image. This filter suppresses information related to slow variations of light intensities in the spatial image. In this case, an inverse FFT used after a highpass frequency filter produces an image in which overall patterns are sharpened and details are emphasized.

A mask frequency filter removes frequencies contained in a mask specified by the user. Using a mask to alter the Fourier transform of an image offers more possibilities than applying a lowpass or highpass filter. The image mask is composed by the user and can describe very specific frequencies and directions in the image. You can apply this technique, for example, to filter dominant frequencies as well as their harmonics in the frequency domain.