Question

Which one of the following is NOT a linear operation?

• A. Convolution
• B. Moving average
• C. Filtering with a median filter
• D. Similarity transformation

Hint:

Any filter that computes a weighted sum is linear. Order-statistic filters (median, min, max) are nonlinear.

Answer 1

The Correct Option is C

Convolution is a linear operator (it satisfies additivity and homogeneity).
The moving–average filter is a special case of linear convolution with a box kernel.
A similarity transformation (uniform scale $+$ rotation $+$ optional translation) is linear in the intensity domain and affine in geometry; it preserves linearity of combinations of signals.
The median filter selects the median of samples in a window, which does not satisfy additivity or homogeneity (e.g., $\text{median}(x+y)\neq\text{median}(x)+\text{median}(y)$). Hence it is nonlinear.