A New Algorithm For Order Statistic

Abstract

A new algorithm for rank filtering and stack filtering is presented here. This algorithm is simple and results in fast and easy implementations. It is based on transforming the given sequence into equivalent rank preserving sequences by means of bit manipulation. The algorithm can also implement stack filters without requiring threshold decomposition. INTRODUCTION Rank order filters(RF) [l] are nonlinear discrete time translation invariant filters. Ease of implementation has seen widespread use of these filters in speech and image processing. Used to determine the i-th order statistic of a set of n elements; i.e., i-th smallest element in a set, the minimum of a set of n elements for example corresponds to the first order statistic ( i = l), the maximum to the n-th order statistic (i = n). A median, therefore, corresponds to the n/2th order statistic or the “halfway point” of the set. Such bounds are used to suppress impulse noise, as well as to preserve edges, though using these bounds can complicate edge detection. Because of the success o f these filters, a new class of filters called stack filters[l4] has been developed, shown to form a large class of easily implementable nonlinear filters. The RF, as well as all compositions of morphological filters[2], are special cases of stack filters. This paper presents a new algorithm for rank order and stack filtering. based on transforming the given sequence into rank-preserving sequences shown to be less complex while yielding improved performance. A VLSI implementation of this filter has been reported in [20]. Organized into the following sections, this paper briefly reviews rank order and stack filters in Section 2. In Section 3, a new algorithm for rank order filtering is proposed with a modification of this algorithm which realizes stack filtering. Then, in Section 4, various methods of implementation of the proposed algorithms are described, where, the H-tree design of these filters is shown to be most area efficient. Finally, in Section 5, the complexity of the proposed scheme is discussed. through bit manipulation. The proposed rank order and stack filters are