Rank order filters and priority queues

Rank-Sensitive Priority Queues

We introduce the rank-sensitive priority queue — a data structure that always knows the minimum element it contains, for which insertion and deletion take O(log(n/r)) time, with n being the number of elements in the structure, and r being the rank of the element being inserted or deleted (r = 1 for the minimum, r = n for the maximum). We show how several elegant implementations of rank-sensitiv...

Priority queues and the Bruhat order

Valid input-output pairs for priority queue sorting—the “Insert /DeleteMaximum” paradigm—are characterized in terms of paths in the Hasse diagram for the weak Bruhat order on permutations. The priority queue process on a permutation works as follows. Start with a permutation (the initial input) on the left, a container in the middle and an output permutation, initially empty, on the right. A st...

Scalable Parallel Rank Order Filters

Rank-order Filters and Bayes Posterior Decision

This paper gives the optimal stack filtering theory under the mean absolute error (MAE) criterion a completely new meaning in terms of the a posteriori Bayes minimum-cost decision. It is shown that under certain conditions this always leads to a rank-order filter (ROF) as the best filter in the minimum MAE sense. It is further shown that for a mostly practical case, the solution becomes the med...

Image Algebra and Rank-order Filters

The unifying role that is one of the attractions of image algebra is distinctly less obvious when we come to include median filters and their many close relatives (weighted median filters, rank-order filters, weighted rankorder filters). The convolutional filters, which are linear, and the morphological filters, which are not, fit in naturally and indeed have a pleasingly similar appearance in ...