TY - GEN

T1 - Optimal morphological filters for discrete random sets under a union or intersection noise model

AU - Sidiropoulos, Nicholaos D.

AU - Baras, John S.

AU - Berenstein, Carlos A.

PY - 1993/1/1

Y1 - 1993/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0027270683&partnerID=8YFLogxK

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M3 - Conference contribution

AN - SCOPUS:0027270683

SN - 0819410187

T3 - Proceedings of SPIE - The International Society for Optical Engineering

SP - 402

EP - 413

BT - Proceedings of SPIE - The International Society for Optical Engineering

PB - Publ by Int Soc for Optical Engineering

T2 - Visual Communications and Image Processing '92

Y2 - 18 November 1992 through 20 November 1992

ER -