What is linear filtering and non-linear filtering?

Linear filtering of digital image processing:
Output image fo (x, y) = T [fi (x, y)], T is a linear operator, that is: the value of each pixel in the output image is the result of the weighted sum of the values of each pixel in the input image.
Non-linear filtering operators include non-linear operations such as absolute value acquisition and zero placement.

The raw data and the filtering result of a linear filter are arithmetic operations, that is, they are implemented using addition, subtraction, multiplication, division, and other operations, such as the mean filter (the average value of the pixel gray value in the template) and Gaussian filter (Gaussian weighted average. Since linear filters are arithmetic operations and have fixed templates, the transfer function of the filter can be identified and unique (the transfer function is the Fourier transformation of the template ).
The raw data of a non-linear filter has a logical relationship with the filter result, that is, it is implemented by logical operations, such as the maximum filter, minimum filter, and median filter, it is achieved by comparing the gray scale values in a certain neighborhood. There is no fixed template, so there is no specific transfer function (because there is no template for Fourier transformation). In addition, expansion and corrosion are also achieved through the maximum and minimum filters.