Digital Filters Based on Order Statistics

Abstract

The median filter and its modifications, described in chapter 4, are a special case of a large class of nonlinear filters that is based on order statistics. This class includes a variety of nonlinear filters, e.g., L-filters, α-trimmed mean filters, max/median filters and median hybrid filters. Most of them are based on the well-known L-estimators. Therefore, they have excellent robustness properties. Others are modifications or extensions of the median filter. Nonlinear filters based on order statistics have been designed to meet various criteria, e.g., robustness, adaptivity to noise probability distributions, preservation of edge information, preservation of image details. Thus, each of them has optimal performance for specific figures of merit and specific noise characteristics.