Criteria of convergence of median filters and perturbation theorem

Repeated application of the median filter to any finite length sequence con verges to a root in a finite number of passes, This requires padding on eac h end of the sequence. In some applications, such padding may be inappropri ate because of the overemphasis on the endpoints, However, there are some o f infinite-length sequences whose median filters are not convergent, In thi s paper, necessary and/or sufficient conditions on infinite-length sequence s are derived in order that their median filters converge to roots of categ ory I. Moreover, we study convergence of median filters of perturbed sequen ces. The results obtained extend the previous theory on convergence of medi an filters.