Suppose that an image processing operator F acting on two input images
A and B produces output images C and D respectively.
If the operator F is *linear*, then

where *a* and *b* are constants.
In practice, this means that each pixel in the
output of a *linear* operator is the weighted sum of
a set of pixels in the input image.

By contrast, *non-linear* operators are all the other operators.
For example, the threshold operator is non-linear,
because individually, corresponding pixels in the two images A and B
may be below the threshold, whereas the pixel obtained by adding
A and B may be above threshold.
Similarly, an absolute value operation is non-linear:

as is the exponential operator:

.