Root properties of median filters under three appending strategies

The root structure of median roots is analyzed by applying three different appending strategies, the first and last value carry on strategy, the constant value appending strategy, and the circular appending strategy, to the finite input signals. It is also shown that these three appending strategies have a significant effect on the root structure and the cardinality of the root set. It was demonstrated that the appended root signals of the median filter under the circular strategy either consist of constant neighborhoods only or consist of nonconstant neighborhoods only. It is impossible to have a median root under the circular strategy consisting of some constant neighborhoods and some nonconstant neighborhoods