ORDER STATISTIC DISTRIBUTIONS WITH MULTIPLE WINDOWS

Algorithms for computing the distributions of order statistic related estimators with moving or multiple windows are presented. These algorithms can be used to compute joint distributions of moving window estimators, such as moving median filters, or of estimators made from ranking operations on multiple windows, such as many "stacked" or "morphological" filters. The algorithms presented here make no distributional assumptions on the underlying random variables, but do make assumptions on the dependency between them. For instance, the random variables may be independent, Markov, or Markov corrupted by an independent noise source. Unlike other approaches, these algorithms have polynomial complexity in the number of random variables. It is shown how these algorithms are easily implemented. Finally, two computational examples of the behavior of median filters are given.