Fast computation of a class of running filters

This paper focuses on the computation of a class of running filters defined as the n-ary extension of an associative, commutative, and idempotent binary operation T on an ordered sequence of operands. The well-known max/min filters are the prominent representatives of the class. For any arbitrary window filter of size n, the existence of a fast algorithm of complexity O(log₂ n) T operations is proven. A remarkable feature of the proof is its ability to generate a particular solution for every n. In addition to the theoretical results, practical implementation aspects regarding the flexibility of pipeline processors for fast computation of the one-dimensional (1-D) and two-dimensional (2-D) running filters are investigated