Design of binary filters by sequential basis expansion Academic Article uri icon

abstract

  • 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 filters, where k < m. The error representation can be used for filter design from 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 (depending on the rate of deletion), and can result in improved filtering over a full search.

published proceedings

  • Proceedings of SPIE

author list (cited authors)

  • Jeanne, M., Marshall, S., & Dougherty, E. R.

citation count

  • 0

complete list of authors

  • Jeanne, Marion||Marshall, Stephen||Dougherty, Edward R

editor list (cited editors)

  • Kehtarnavaz, N.

publication date

  • April 2001