Optimal morphological filters for discrete random sets under a union or intersection noise model

Nicholaos D. Sidiropoulos, John S. Baras, Carlos A. Berenstein

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

We consider the problem of optimal binary image restoration under a union or intersection noise model. Union noise is well suited to model random clutter (obscuration), whereas intersection noise is a good model for random sampling. Our approach is random set-theoretic, i.e. digital images are viewed as realizations of a uniformly bounded discrete random set. First we provide statistical proofs of some 'folk theorems' of Morphological filtering. In particular, we prove that, under some reasonable worst-case statistical scenarios, Morphological openings, closings, unions of openings, and intersections of closings, can be viewed as MAP estimation of the signal based on the noisy observation. Then we propose a 'generic' procedure for the design of optimal Morphological filters for independent union or intersection noise.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
PublisherPubl by Int Soc for Optical Engineering
Pages402-413
Number of pages12
Editionpt 1
ISBN (Print)0819410187
StatePublished - Jan 1 1993
EventVisual Communications and Image Processing '92 - Boston, MA, USA
Duration: Nov 18 1992Nov 20 1992

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Numberpt 1
Volume1818
ISSN (Print)0277-786X

Conference

ConferenceVisual Communications and Image Processing '92
CityBoston, MA, USA
Period11/18/9211/20/92

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