Optimal stack filtering and the estimation and structural approaches to image processing

Summary form only given. Two approaches have been used in the past to design rank-order-based nonlinear filters to enhance or restore images: the structural approach and the estimation approach. The first approach requires structural descriptions of the image and the process which has altered it, whereas the second required statistical descriptions. The many different classes of rank-order-based filters that have been developed over the last few decades have been reviewed in the context of these two approaches. One of these filter classes, stack filters, has been investigated. These filters, which are defined by a weak superposition property and an ordering property, contain all compositions of 2D rank-order operations. The recently developed theory of minimum-mean-absolute-error (MMAE) stack filtering has been extended to two dimensions. A theory of optimal stack filtering under structural constraints and goals has been developed for the structural approach to image processing. These two optimal stack filtering theories have been combined into a single design theory for rank-order-based filters