Optimal Filtering of Digital Binary Images Corrupted by Union/Intersection Noise

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

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


We model digital binary image data as realizations of a uniformly bounded discrete random set (or discrete random set, for short), which is a mathematical object that can be directly defined on a finite lattice. We consider the problem of estimating realizations of discrete random sets distorted by a degradation process that can be described by a union/intersection noise model. Two distinct optimal filtering approaches are pursued. The first involves a class of “mask” filters, which arises quite naturally from the set-theoretic analysis of optimal filters. The second approach involves a class of morphological filters. We prove that under i.i.d noise morphological openings, closings, unions of openings, and intersections of closings can be viewed as MAP estimators of morphologically smooth signals. Then, we show that by using an appropriate (under a given degradtion model) expansion of the optimal filter, we can obtain universal characterizations of optimality that do not rely on strong assumptions regarding the spatial interaction of geometrical primitives of the signal and the noise. The results generalize to gray-level images in a fairly straightforward manner.

Original languageEnglish (US)
Pages (from-to)382-403
Number of pages22
JournalIEEE Transactions on Image Processing
Issue number4
StatePublished - Jul 1994
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received July 2, 1992; revised April 19, 1993. This work was supported by NSF grant NSFD CDR 8803012, through the Engineering Research Center’s Program. The authors are with the Institute of Systems Research, University of Maryland, College Park, MD 20742. IEEE Log Number 9400312.


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