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

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

doi:10.1117/12.131458

1 November 1992 Optimal morphological filters for discrete random sets under a union or intersection noise model

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

Proceedings Volume 1818, Visual Communications and Image Processing '92; (1992) https://doi.org/10.1117/12.131458
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States

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.

Citation Download Citation

Nicholaos D. Sidiropoulos, John S. Baras, and Carlos A. Berenstein "Optimal morphological filters for discrete random sets under a union or intersection noise model", Proc. SPIE 1818, Visual Communications and Image Processing '92, (1 November 1992); https://doi.org/10.1117/12.131458

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