Filtering an image consists of applying a filter, which is a linear operator, to each pixel of an image to modify its intensity. The new intensity of the pixel depends on the original intensity and the intensity of neighboring pixels. Thus, the filter is expressed as a matrix or, similarly, as an image. To study the concept of filtering, it is essential to start by introducing two mathematical tools.
The first tool is Convolution, which is the mathematical operation to calculate the effect of a filter on an image. The second tool is the Fourier transform, which introduce the notion of “frequency” in an image to represents the image in the frequency domain. Then Filtering presents some filters, which only keep certain frequencies of the image, such as the low-pass and high-pass filters.