Design of binary filters by sequential basis expansion
Marion Jeanne, Stephen W. Marshall, Edward R. Dougherty · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2001
The mean-absolute error of an increasing binary window-based filter can be expressed in terms of the errors of the individual erosions that comprise its erosion representation. This can be done recursively, so that the error of an m-erosion filter can be represented via errors of k-erosion filter can be represented via errors of k- erosion filters, where k < m. The error representation can be used for filter design form sample realizations by estimating the errors of individual erosions and then recursively computing the errors of multiple-erosion filters. Even for modestly large windows, the method is limited to obtaining filters composed of a relatively small number of erosions because the optimal (m + 1)-erosion filter need not be a superset of the optimal m-erosion filter. This paper considers two suboptimal search strategies to achieve faster design, and thereby permit filters comprised of larger numbers of erosions. A strict sequential search strategy proceeds under the assumption that the optimal (m + 1)-erosion filter is a superset of the optimal m-erosion filter. A look-ahead search strategy, in which erosion structuring elements are occasionally deleted from the growing basis, is close to a strict sequential search in computational efficiency, and can result in improved filtering over a full search.