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Non-linear Filtering

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:


©2003 R. Fisher, S. Perkins, A. Walker and E. Wolfart.

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