Criteria of convergence of median filters and perturbation theorem

Repeated application of the median filter to any finite length sequence converges to a root in a finite number of passes. This requires padding on each end of the sequence. In some applications, such padding may be inappropriate because of the overemphasis on the endpoints. However, there are some of infinite-length sequences whose median filters are not convergent. In this paper, necessary and/or sufficient conditions on infinite-length sequences are derived in order that their median filters converge to roots of category I. Moreover, we study convergence of median filters of perturbed sequences. The results obtained extend the previous theory on convergence of median filters.